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7
fc5d6c28aca127b81d57
7b7140f05508d5e226b1
7b7140f05508d5e226b1
train
pareto_5efforts
inventory_word_problem
1
concise
-1
false
50,000
Zeynep starts with 131 test tubes. Then, in order, Zeynep doubles the stock; then hands 120 to a customer; then receives a delivery of 28; then doubles the stock. How many test tubes does Zeynep have at the end? Final line: `ANSWER: <answer>`.
Zeynep starts with 131 test tubes. Then, in order, Zeynep doubles the stock; then hands 120 to a customer; then receives a delivery of 28; then doubles the stock. How many test tubes does Zeynep have at the end?
340
integer
state_simulation
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
low
0.7
0.99
We need solve simple arithmetic. Need be careful. Start 131. doubles: 262. hands 120: 142. receives 28: 170. doubles: 340. Answer 340. Need final with exact format.
Zeynep starts with 131 test tubes. After doubling: \(131 \times 2 = 262\). After handing 120 to a customer: \(262 - 120 = 142\). After receiving 28: \(142 + 28 = 170\). After doubling again: \(170 \times 2 = 340\). ANSWER: 340
340
true
true
stop
119
177
1.27
v3
16,000
1
5
fc5d6c28aca127b81d57
7b7140f05508d5e226b1
7b7140f05508d5e226b1
train
pareto_5efforts
inventory_word_problem
1
concise
-1
false
50,000
Zeynep starts with 131 test tubes. Then, in order, Zeynep doubles the stock; then hands 120 to a customer; then receives a delivery of 28; then doubles the stock. How many test tubes does Zeynep have at the end? Final line: `ANSWER: <answer>`.
Zeynep starts with 131 test tubes. Then, in order, Zeynep doubles the stock; then hands 120 to a customer; then receives a delivery of 28; then doubles the stock. How many test tubes does Zeynep have at the end?
340
integer
state_simulation
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
medium
0.7
0.99
We need answer simple arithmetic. Need be careful order. Starts 131. doubles stock: 262. hands 120 to customer: 142. receives delivery 28: 170. doubles stock: 340. Final 340. Need final line exactly. Could include reasoning. Ensure no issue "stock" test tubes. Answer 340.
Zeynep starts with 131 test tubes. - Double: \(131 \times 2 = 262\) - Hand 120 to customer: \(262 - 120 = 142\) - Receive 28: \(142 + 28 = 170\) - Double: \(170 \times 2 = 340\) ANSWER: 340
340
true
true
stop
120
199
1.46
v3
16,000
1
5
fc5d6c28aca127b81d57
7b7140f05508d5e226b1
7b7140f05508d5e226b1
train
pareto_5efforts
inventory_word_problem
1
concise
-1
false
50,000
Zeynep starts with 131 test tubes. Then, in order, Zeynep doubles the stock; then hands 120 to a customer; then receives a delivery of 28; then doubles the stock. How many test tubes does Zeynep have at the end? Final line: `ANSWER: <answer>`.
Zeynep starts with 131 test tubes. Then, in order, Zeynep doubles the stock; then hands 120 to a customer; then receives a delivery of 28; then doubles the stock. How many test tubes does Zeynep have at the end?
340
integer
state_simulation
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
high
0.7
0.99
We need solve simple arithmetic. Need be careful order. Starts 131. Then in order: doubles stock; hands 120 to customer; receives delivery 28; doubles stock. Compute: 131*2=262; -120=142; +28=170; *2=340. Final answer 340. Need final line.
Start with 131. 1. Double: \(131 \times 2 = 262\) 2. Hand 120 to customer: \(262 - 120 = 142\) 3. Receive 28: \(142 + 28 = 170\) 4. Double: \(170 \times 2 = 340\) ANSWER: 340
340
true
true
stop
121
199
1
v3
16,000
1
5
fc5d6c28aca127b81d57
7b7140f05508d5e226b1
7b7140f05508d5e226b1
train
pareto_5efforts
inventory_word_problem
1
concise
-1
false
50,000
Zeynep starts with 131 test tubes. Then, in order, Zeynep doubles the stock; then hands 120 to a customer; then receives a delivery of 28; then doubles the stock. How many test tubes does Zeynep have at the end? Final line: `ANSWER: <answer>`.
Zeynep starts with 131 test tubes. Then, in order, Zeynep doubles the stock; then hands 120 to a customer; then receives a delivery of 28; then doubles the stock. How many test tubes does Zeynep have at the end?
340
integer
state_simulation
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
xhigh
0.7
0.99
We need solve simple arithmetic. Need final answer. Let's compute carefully. Start 131. Doubles stock: 262. Hands 120 to customer: 142. Receives delivery 28: 170. Doubles stock: 340. Answer 340. Need final with ANSWER: 340.
ANSWER: 340
340
true
true
stop
121
99
0.61
v3
16,000
1
5
fc5d6c28aca127b81d57
7b7140f05508d5e226b1
7b7140f05508d5e226b1
train
pareto_5efforts
inventory_word_problem
1
concise
-1
false
50,000
Zeynep starts with 131 test tubes. Then, in order, Zeynep doubles the stock; then hands 120 to a customer; then receives a delivery of 28; then doubles the stock. How many test tubes does Zeynep have at the end? Final line: `ANSWER: <answer>`.
Zeynep starts with 131 test tubes. Then, in order, Zeynep doubles the stock; then hands 120 to a customer; then receives a delivery of 28; then doubles the stock. How many test tubes does Zeynep have at the end?
340
integer
state_simulation
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
max
0.7
0.99
We need solve simple arithmetic. Need final answer. Let's compute: start 131. doubles: 262. hands 120: 142. receives 28: 170. doubles: 340. Answer 340. Need final line exactly. Could include reasoning. Ensure no trick? "doubles the stock" maybe doubles stock then hands? In order yes. final.
Zeynep starts with 131 test tubes. - Double: \(131 \times 2 = 262\) - Hand off 120: \(262 - 120 = 142\) - Receive 28: \(142 + 28 = 170\) - Double: \(170 \times 2 = 340\) ANSWER: 340
340
true
true
stop
121
203
1.19
v3
16,000
1
5
3c7a5c4cc967455ddebf
905d6d14a09c3edf9b23
905d6d14a09c3edf9b23
train
pareto_5efforts
code_tracing
1
concise
-1
false
50,000
What does this Python program print? ```python x, y = 8, 3 for i in range(12): if i % 2 == 0: x += y * 8 else: y += x - 3 x %= 11; y %= 11 print(x + y) ``` Final line: `ANSWER: <answer>`.
What does this Python program print? ```python x, y = 8, 3 for i in range(12): if i % 2 == 0: x += y * 8 else: y += x - 3 x %= 11; y %= 11 print(x + y) ```
11
integer
code_execution
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
low
0.7
0.99
Simulate carefully. x=8,y=3. i=0 even: x += y*8 = 8+24=32; mod11: 32%11=10. y unchanged 3. then x%=11 (done), y%=11 (3). i=1 odd: y += x-3 = 3 + (10-3)=10; mod? after branch x%=11? code: else y += x-3; then x %=11; y%=11. x=10%11=10; y=10%11=10. i=2 even: x += y*8 =10+80=90; %11=2 (88). y=10. then x%=11 =>2, y%=11=>10...
ANSWER: 11
11
true
true
stop
132
546
1.77
v3
16,000
1
5
3c7a5c4cc967455ddebf
905d6d14a09c3edf9b23
905d6d14a09c3edf9b23
train
pareto_5efforts
code_tracing
1
concise
-1
false
50,000
What does this Python program print? ```python x, y = 8, 3 for i in range(12): if i % 2 == 0: x += y * 8 else: y += x - 3 x %= 11; y %= 11 print(x + y) ``` Final line: `ANSWER: <answer>`.
What does this Python program print? ```python x, y = 8, 3 for i in range(12): if i % 2 == 0: x += y * 8 else: y += x - 3 x %= 11; y %= 11 print(x + y) ```
11
integer
code_execution
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
medium
0.7
0.99
We need answer question. Need compute. Let's carefully simulate. Initial x=8,y=3. Loop i 0..11. At each: if i even: x += y*8 else y += x-3. Then x %=11; y %=11. Need final x+y. Let's simulate manually or mentally. Use modular arithmetic maybe. Let's table. i=0 even: x = 8 + 3*8 = 8+24=32. mod11 = 32%11=10 (since 22...
The program alternates between updating `x` and `y`, reducing both modulo 11 each iteration. Tracing through the 12 iterations gives a final state of `x = 8`, `y = 3`, so `x + y = 11`. ANSWER: 11
11
true
true
stop
133
790
3.08
v3
16,000
1
5
3c7a5c4cc967455ddebf
905d6d14a09c3edf9b23
905d6d14a09c3edf9b23
train
pareto_5efforts
code_tracing
1
concise
-1
false
50,000
What does this Python program print? ```python x, y = 8, 3 for i in range(12): if i % 2 == 0: x += y * 8 else: y += x - 3 x %= 11; y %= 11 print(x + y) ``` Final line: `ANSWER: <answer>`.
What does this Python program print? ```python x, y = 8, 3 for i in range(12): if i % 2 == 0: x += y * 8 else: y += x - 3 x %= 11; y %= 11 print(x + y) ```
11
integer
code_execution
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
high
0.7
0.99
We need answer problem. Need compute program output. Need final line ANSWER: <answer>. Let's simulate carefully. Python: x, y = 8, 3 for i in range(12): if i % 2 == 0: x += y * 8 else: y += x - 3 x %= 11; y %= 11 print(x + y) Need compute. Let's simulate step by step. Need be careful order...
The program prints `11`. ANSWER: 11
11
true
true
stop
134
740
1.71
v3
16,000
1
5
3c7a5c4cc967455ddebf
905d6d14a09c3edf9b23
905d6d14a09c3edf9b23
train
pareto_5efforts
code_tracing
1
concise
-1
false
50,000
What does this Python program print? ```python x, y = 8, 3 for i in range(12): if i % 2 == 0: x += y * 8 else: y += x - 3 x %= 11; y %= 11 print(x + y) ``` Final line: `ANSWER: <answer>`.
What does this Python program print? ```python x, y = 8, 3 for i in range(12): if i % 2 == 0: x += y * 8 else: y += x - 3 x %= 11; y %= 11 print(x + y) ```
11
integer
code_execution
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
xhigh
0.7
0.99
We need answer Python program print. Need compute. Let's analyze carefully. Need final with answer. Let's simulate. x=8,y=3. Loop i 0..11. If i even: x += y*8. else: y += x - 3. Then x %=11; y %=11. Print x+y. Let's compute step by step. Need careful modulo after update. Initial x=8,y=3. i=0 even: x += y*8 = 8+24=3...
ANSWER: 11
11
true
true
stop
134
718
2.23
v3
16,000
1
5
3c7a5c4cc967455ddebf
905d6d14a09c3edf9b23
905d6d14a09c3edf9b23
train
pareto_5efforts
code_tracing
1
concise
-1
false
50,000
What does this Python program print? ```python x, y = 8, 3 for i in range(12): if i % 2 == 0: x += y * 8 else: y += x - 3 x %= 11; y %= 11 print(x + y) ``` Final line: `ANSWER: <answer>`.
What does this Python program print? ```python x, y = 8, 3 for i in range(12): if i % 2 == 0: x += y * 8 else: y += x - 3 x %= 11; y %= 11 print(x + y) ```
11
integer
code_execution
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
max
0.7
0.99
We need answer Python program output. Need compute. Let's simulate carefully. x,y=8,3. loop i 0..11. if i even: x += y*8; else y += x-3; then x%=11; y%=11. Need final x+y. Let's compute. Let's do manually or reason. I'll simulate table. Initial x=8,y=3. i=0 even: x = 8 + 3*8 = 8+24=32; x%11=10 (32 mod11=10). y uncha...
The program ends with `x = 8` and `y = 3`, so `x + y = 11`. ANSWER: 11
11
true
true
stop
134
643
2.53
v3
16,000
1
5
049255fc68ea76a4cc16
a3dcb71554b5c3f6cb28
a3dcb71554b5c3f6cb28
train
pareto_5efforts
combinatorics_count
1
concise
-1
false
50,000
How many ordered sequences of 5 integers, each between 1 and 3 inclusive, have a sum of exactly 14? Final line: `ANSWER: <answer>`.
How many ordered sequences of 5 integers, each between 1 and 3 inclusive, have a sum of exactly 14?
5
integer
dynamic_programming
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
low
0.7
0.99
We need number of ordered 5-tuples (x1..x5) with each in {1,2,3} sum=14. Let yi=xi-1 in {0,1,2}, sum yi = 14-5=9. Count solutions yi∈{0,1,2} sum 9, max possible 10. Equivalent count of 5 variables each 0-2 summing 9. Total without upper bound: C(9+4,4)=C(13,4)=715? Actually nonnegative sum 9: C(13,4)=715. Subtract tho...
ANSWER: 5
5
true
true
stop
82
360
1.52
v3
16,000
1
5
049255fc68ea76a4cc16
a3dcb71554b5c3f6cb28
a3dcb71554b5c3f6cb28
train
pareto_5efforts
combinatorics_count
1
concise
-1
false
50,000
How many ordered sequences of 5 integers, each between 1 and 3 inclusive, have a sum of exactly 14? Final line: `ANSWER: <answer>`.
How many ordered sequences of 5 integers, each between 1 and 3 inclusive, have a sum of exactly 14?
5
integer
dynamic_programming
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
medium
0.7
0.99
We need solve combinatorics. Need count ordered sequences (x1..x5) with each xi in {1,2,3}, sum 14. Need final answer. Compute. Let yi = xi -1 in {0,1,2}, sum yi = 14 -5 =9. Need number of 5-tuples yi in [0,2] summing 9. Max sum 10. Count. Could use inclusion-exclusion. Total nonnegative solutions to sum yi=9 without ...
We need count 5-tuples \((x_1,\dots,x_5)\) with \(x_i\in\{1,2,3\}\) and sum 14. Let \(y_i=x_i-1\), so \(y_i\in\{0,1,2\}\) and \[ \sum y_i = 14-5=9. \] The maximum possible sum of the \(y_i\)'s is \(5\cdot 2=10\). Thus a sum of 9 means the total "deficit" from 2 is \(10-9=1\). Equivalently, if \(d_i=2-y_i\), then \(d...
5
true
true
stop
83
863
2.8
v3
16,000
1
5
049255fc68ea76a4cc16
a3dcb71554b5c3f6cb28
a3dcb71554b5c3f6cb28
train
pareto_5efforts
combinatorics_count
1
concise
-1
false
50,000
How many ordered sequences of 5 integers, each between 1 and 3 inclusive, have a sum of exactly 14? Final line: `ANSWER: <answer>`.
How many ordered sequences of 5 integers, each between 1 and 3 inclusive, have a sum of exactly 14?
5
integer
dynamic_programming
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
high
0.7
0.99
We need solve combinatorics. Need count ordered 5-tuples (a1..a5) each in {1,2,3} sum 14. Need final answer with line. Let's compute carefully. We can transform xi in {1,2,3}, sum 14. Let yi=xi-1 in {0,1,2}, sum = 14-5=9, with each yi <=2. Count nonnegative solutions y1..y5 <=2 sum 9. Max sum if all 2 =10. Count total...
We need ordered 5-tuples \((a_1,\dots,a_5)\) with each \(a_i\in\{1,2,3\}\) and sum \(14\). The maximum possible sum is \(5\cdot 3=15\). Let \(d_i=3-a_i\), so each \(d_i\in\{0,1,2\}\) and \[ \sum d_i = 15-14 = 1. \] Thus exactly one of the \(d_i\) equals \(1\) and the rest are \(0\). There are \(5\) choices for which...
5
true
true
stop
84
712
3.96
v3
16,000
1
5
049255fc68ea76a4cc16
a3dcb71554b5c3f6cb28
a3dcb71554b5c3f6cb28
train
pareto_5efforts
combinatorics_count
1
concise
-1
false
50,000
How many ordered sequences of 5 integers, each between 1 and 3 inclusive, have a sum of exactly 14? Final line: `ANSWER: <answer>`.
How many ordered sequences of 5 integers, each between 1 and 3 inclusive, have a sum of exactly 14?
5
integer
dynamic_programming
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
xhigh
0.7
0.99
We need answer combinatorics. Need final line ANSWER. Need solve. Count ordered 5-tuples (x_i in {1,2,3}) sum 14. Let's compute. Max sum 15, min 5. Need count. Let y_i = x_i-1 in {0,1,2}, sum y = 14-5=9. Count nonnegative y_i <=2 sum 9 over 5. Max sum if all 2 =10, so deficit from 10: z_i = 2-y_i in {0,1,2}, sum z = 10...
We need count ordered 5-tuples of values in {1,2,3} summing to 14. Shift by 1: let \(y_i=x_i-1\in\{0,1,2\}\). Then sum \(y_i=14-5=9\). Since max sum of five \(y_i\) is 10, let \(z_i=2-y_i\in\{0,1,2\}\). Then sum \(z_i=10-9=1\). There are 5 choices for which one \(z_i\) equals 1, so 5 sequences. ANSWER: 5
5
true
true
stop
84
329
1.55
v3
16,000
1
5
049255fc68ea76a4cc16
a3dcb71554b5c3f6cb28
a3dcb71554b5c3f6cb28
train
pareto_5efforts
combinatorics_count
1
concise
-1
false
50,000
How many ordered sequences of 5 integers, each between 1 and 3 inclusive, have a sum of exactly 14? Final line: `ANSWER: <answer>`.
How many ordered sequences of 5 integers, each between 1 and 3 inclusive, have a sum of exactly 14?
5
integer
dynamic_programming
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
max
0.7
0.99
We need solve combinatorics. Need count ordered 5-tuples (a1..a5) with each in {1,2,3}, sum 14. Need final answer. Need be careful. Let's compute. Let xi in {1,2,3}. Sum 14. Max sum 15 (all 3). Min 5. Deficit from all 3: let di = 3 - ai ∈ {0,1,2}. Sum di = 15-14=1. Count ordered 5-tuples di in {0,1,2} summing 1. Each ...
We need count ordered 5-tuples with entries in {1,2,3} summing to 14. Write each entry as \(3-d_i\), where \(d_i\in\{0,1,2\}\). Then \[ \sum (3-d_i)=15-\sum d_i=14 \] so \[ \sum d_i=1. \] Thus exactly one \(d_i=1\) and the rest are 0. There are 5 choices for which position has the 2 (since \(3-1=2\)). ANSWER: 5
5
true
true
stop
84
418
2.45
v3
16,000
1
5
e1d8586fe5c89c402b2e
c0c27e17b77943062a88
c0c27e17b77943062a88
train
pareto_5efforts
modular_arithmetic
1
concise
-1
false
50,000
What is the remainder when 18^470 is divided by 100? Final line: `ANSWER: <answer>`.
What is the remainder when 18^470 is divided by 100?
24
integer
python_pow_mod
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
low
0.7
0.99
We need remainder 18^470 mod 100. Compute. Need final. Let's solve carefully. We need mod 100. φ(100)=40. gcd(18,100)=2 not coprime, can't directly Euler. Use CRT: mod 4 and mod 25. 18^470 mod 4: 18≡2 mod4. 2^2=0 mod4 for exponent>=2, so 0 mod4. mod 25: 18≡ -7. gcd(18,25)=1. φ(25)=20. 470 mod20 = 10? 20*23=460, rema...
ANSWER: 24
24
true
true
stop
75
364
1.17
v3
16,000
1
5
e1d8586fe5c89c402b2e
c0c27e17b77943062a88
c0c27e17b77943062a88
train
pareto_5efforts
modular_arithmetic
1
concise
-1
false
50,000
What is the remainder when 18^470 is divided by 100? Final line: `ANSWER: <answer>`.
What is the remainder when 18^470 is divided by 100?
24
integer
python_pow_mod
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
medium
0.7
0.99
We need answer compute 18^470 mod 100. Need final with reasoning. Let's solve. Compute 18^470 mod 100. Since gcd(18,100)=2 not coprime. Need careful. We can use CRT or pattern. Mod 4 and mod 25 then combine. 18^470 mod 4: 18≡2 mod4, 2^? For exponent>=2, 2^n ≡0 mod4. 470>=2 so 0 mod4. Mod 25: gcd(18,25)=1. φ(25)=20....
We need \(18^{470} \bmod 100\). Use CRT: - Mod \(4\): \(18\equiv 2\), and \(2^{470}\equiv 0 \pmod 4\) since \(470\ge 2\). - Mod \(25\): \(\phi(25)=20\), so \(470\equiv 10 \pmod{20}\). Thus \[ 18^{470}\equiv 18^{10}\equiv (-7)^{10}=7^{10} \pmod{25}. \] Since \(7^2=49\equiv -1 \pmod{25}\), we get \(7^{10}=(7^2)...
24
true
true
stop
76
823
2.7
v3
16,000
1
5
e1d8586fe5c89c402b2e
c0c27e17b77943062a88
c0c27e17b77943062a88
train
pareto_5efforts
modular_arithmetic
1
concise
-1
false
50,000
What is the remainder when 18^470 is divided by 100? Final line: `ANSWER: <answer>`.
What is the remainder when 18^470 is divided by 100?
24
integer
python_pow_mod
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
high
0.7
0.99
We need solve 18^470 mod 100. Need final answer with boxed? User says final line ANSWER: <answer>. Need compute. Let's solve carefully. We need remainder of 18^470 mod 100. Compute using modular arithmetic. gcd(18,100)=2 not coprime. Need handle powers. 18^1=18 mod100 18^2=324 mod100=24 18^3=24*18=432 mod100=32 18^4...
The remainder is found by noting the repeating cycle of powers of 18 modulo 100: \[ 18^2\equiv 24,\ 18^3\equiv 32,\ 18^4\equiv 76,\ 18^5\equiv 68,\ 18^6\equiv 24,\dots \] For \(n\ge 2\), the values repeat every 4 powers. Since \[ 470 \equiv 2 \pmod 4, \] we have \[ 18^{470}\equiv 18^2\equiv 24 \pmod{100}. \] ANSW...
24
true
true
stop
77
1,018
2.81
v3
16,000
1
5
e1d8586fe5c89c402b2e
c0c27e17b77943062a88
c0c27e17b77943062a88
train
pareto_5efforts
modular_arithmetic
1
concise
-1
false
50,000
What is the remainder when 18^470 is divided by 100? Final line: `ANSWER: <answer>`.
What is the remainder when 18^470 is divided by 100?
24
integer
python_pow_mod
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
xhigh
0.7
0.99
We need answer problem: remainder 18^470 mod 100. Need final with ANSWER: 76? Let's compute carefully. Need compute 18^470 mod 100. Let's solve. phi(100)=40, gcd(18,100)=2 not coprime so Euler not directly. Use CRT mod4 and mod25. Mod4: 18 ≡2. 18^470 mod4 = 2^470 mod4 =0 for exponent>=2. So remainder ≡0 mod4. Mod25...
ANSWER: 24
24
true
true
stop
77
718
2.54
v3
16,000
1
5
e1d8586fe5c89c402b2e
c0c27e17b77943062a88
c0c27e17b77943062a88
train
pareto_5efforts
modular_arithmetic
1
concise
-1
false
50,000
What is the remainder when 18^470 is divided by 100? Final line: `ANSWER: <answer>`.
What is the remainder when 18^470 is divided by 100?
24
integer
python_pow_mod
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
max
0.7
0.99
We need solve 18^470 mod 100. Need final with reasoning and answer. Need be careful. Compute. We can use Carmichael/euler. Let's solve. 18^470 mod 100. Since gcd(18,100)=2 not coprime. Need handle. Compute powers mod 100. Let's do carefully. 18^1=18 18^2=324 mod100=24 18^3=24*18=432 mod100=32 18^4=32*18=576 mod100=7...
We need compute \(18^{470} \pmod{100}\). Using the Chinese Remainder Theorem: - Modulo \(4\): \(18\equiv 2\), and \(2^{470}\equiv 0 \pmod{4}\) since \(470\ge 2\). - Modulo \(25\): \(\phi(25)=20\), and \(470\equiv 10 \pmod{20}\). Thus \[ 18^{470}\equiv 18^{10}\pmod{25}. \] Since \(18\equiv -7\pmod{25}\), \[ ...
24
true
true
stop
77
1,015
3.16
v3
16,000
1
5
478d32589368cb667381
8163f17fa95543df56ec
8163f17fa95543df56ec
train
pareto_5efforts
shortest_path
1
concise
-1
false
50,000
An undirected road network has these roads (with lengths): - B–C: 3 - A–E: 6 - A–B: 11 - D–C: 1 - A–D: 3 - C–F: 8 - B–D: 4 What is the length of the shortest route from A to F? Final line: `ANSWER: <answer>`.
An undirected road network has these roads (with lengths): - B–C: 3 - A–E: 6 - A–B: 11 - D–C: 1 - A–D: 3 - C–F: 8 - B–D: 4 What is the length of the shortest route from A to F?
12
integer
dijkstra
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
low
0.7
0.99
We need shortest path A to F in undirected weighted graph. Nodes: A,B,C,D,E,F. Edges: B-C 3, A-E 6, A-B 11, D-C 1, A-D 3, C-F 8, B-D 4. Need shortest A to F. Let's compute. Edges from A: E 6, B 11, D 3. Need reach F via C likely. Paths: A-D (3) - C (1) - F (8) =12. A-D-B? etc. A-D-B 3+4=7, B-C 3 =>10, +8=18. A-B 11 +.....
ANSWER: 12
12
true
true
stop
137
191
1.03
v3
16,000
1
5
478d32589368cb667381
8163f17fa95543df56ec
8163f17fa95543df56ec
train
pareto_5efforts
shortest_path
1
concise
-1
false
50,000
An undirected road network has these roads (with lengths): - B–C: 3 - A–E: 6 - A–B: 11 - D–C: 1 - A–D: 3 - C–F: 8 - B–D: 4 What is the length of the shortest route from A to F? Final line: `ANSWER: <answer>`.
An undirected road network has these roads (with lengths): - B–C: 3 - A–E: 6 - A–B: 11 - D–C: 1 - A–D: 3 - C–F: 8 - B–D: 4 What is the length of the shortest route from A to F?
12
integer
dijkstra
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
medium
0.7
0.99
We need solve shortest path. Need final answer. Let's compute. Graph undirected weighted. Edges: B-C 3 A-E 6 A-B 11 D-C 1 A-D 3 C-F 8 B-D 4 Need shortest A to F. Let's list adjacency: A: E(6), B(11), D(3) B: C(3), A(11), D(4) C: B(3), D(1), F(8) D: C(1), A(3), B(4) E: A(6) F: C(8) Dijkstra from A: dist A=0. Neighbo...
The shortest path from A to F is A–D–C–F, with length \(3 + 1 + 8 = 12\). ANSWER: 12
12
true
true
stop
138
365
1.68
v3
16,000
1
5
478d32589368cb667381
8163f17fa95543df56ec
8163f17fa95543df56ec
train
pareto_5efforts
shortest_path
1
concise
-1
false
50,000
An undirected road network has these roads (with lengths): - B–C: 3 - A–E: 6 - A–B: 11 - D–C: 1 - A–D: 3 - C–F: 8 - B–D: 4 What is the length of the shortest route from A to F? Final line: `ANSWER: <answer>`.
An undirected road network has these roads (with lengths): - B–C: 3 - A–E: 6 - A–B: 11 - D–C: 1 - A–D: 3 - C–F: 8 - B–D: 4 What is the length of the shortest route from A to F?
12
integer
dijkstra
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
high
0.7
0.99
We need solve shortest path. Need final answer. Need maybe include reasoning. Let's compute. Graph undirected weighted: Nodes A,B,C,D,E,F. Edges: B-C 3 A-E 6 A-B 11 D-C 1 A-D 3 C-F 8 B-D 4 Need shortest A to F. Paths: A-D-C-F: 3+1+8=12. A-B? A-B 11, B-D 4, D-C1, C-F8 =24; B-C3 C-F8 + A-B11=22. A-E no connection to F?...
The shortest route is A → D → C → F, with total length 3 + 1 + 8 = 12. ANSWER: 12
12
true
true
stop
139
235
1.4
v3
16,000
1
5
478d32589368cb667381
8163f17fa95543df56ec
8163f17fa95543df56ec
train
pareto_5efforts
shortest_path
1
concise
-1
false
50,000
An undirected road network has these roads (with lengths): - B–C: 3 - A–E: 6 - A–B: 11 - D–C: 1 - A–D: 3 - C–F: 8 - B–D: 4 What is the length of the shortest route from A to F? Final line: `ANSWER: <answer>`.
An undirected road network has these roads (with lengths): - B–C: 3 - A–E: 6 - A–B: 11 - D–C: 1 - A–D: 3 - C–F: 8 - B–D: 4 What is the length of the shortest route from A to F?
12
integer
dijkstra
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
xhigh
0.7
0.99
We need solve shortest path. Need output final answer line. Let's compute. Graph undirected edges: B-C 3 A-E 6 A-B 11 D-C 1 A-D 3 C-F 8 B-D 4 Nodes A,B,C,D,E,F. Need shortest A to F. Edges: A-D 3, D-C 1 => A-C 4. C-F 8 => 12. A-D 3, D-B 4 => A-B 7? Actually A-D-B =7, vs A-B 11. Then B-C 3 => A-C via D-B-C =10? D-B-C...
The shortest route from A to F is A → D → C → F, with length 3 + 1 + 8 = 12. ANSWER: 12
12
true
true
stop
139
293
1.35
v3
16,000
1
5
478d32589368cb667381
8163f17fa95543df56ec
8163f17fa95543df56ec
train
pareto_5efforts
shortest_path
1
concise
-1
false
50,000
An undirected road network has these roads (with lengths): - B–C: 3 - A–E: 6 - A–B: 11 - D–C: 1 - A–D: 3 - C–F: 8 - B–D: 4 What is the length of the shortest route from A to F? Final line: `ANSWER: <answer>`.
An undirected road network has these roads (with lengths): - B–C: 3 - A–E: 6 - A–B: 11 - D–C: 1 - A–D: 3 - C–F: 8 - B–D: 4 What is the length of the shortest route from A to F?
12
integer
dijkstra
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
max
0.7
0.99
We need solve shortest path. Need provide reasoning. Graph undirected weighted. Vertices A,B,C,D,E,F. Edges: B-C 3, A-E 6, A-B 11, D-C 1, A-D 3, C-F 8, B-D 4. Need shortest A to F. Compute. A to D =3, D-C=1 => A-D-C =4, C-F=8 =>12. A-B? A-D-B=3+4=7 (vs 11), then B-C=3 =>10, +8=18. A-E dead end? E only A. So 12. Need f...
The shortest route is A → D → C → F, with length 3 + 1 + 8 = 12. ANSWER: 12
12
true
true
stop
139
206
1.84
v3
16,000
1
5
b02e316dddd1d3381085
f51ef3075ca483061623
f51ef3075ca483061623
train
pareto_5efforts
probability
1
concise
-1
false
50,000
A bag has 7 red, 5 blue marbles. You draw 4 marbles without replacement. What is the probability that at least 4 of them are red? Give the answer as a reduced fraction p/q. Final line: `ANSWER: <answer>`.
A bag has 7 red, 5 blue marbles. You draw 4 marbles without replacement. What is the probability that at least 4 of them are red? Give the answer as a reduced fraction p/q.
7/99
reduced_fraction
exact_fractions_hypergeometric
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
low
0.7
0.99
We draw 4 marbles from 12 total (7 red, 5 blue). Need probability at least 4 red among the 4 drawn, i.e., all 4 red. Number of ways: C(7,4)/C(12,4). C(7,4)=35. C(12,4)=495. Reduced: 35/495 = 7/99.
We draw 4 marbles from 12 total. "At least 4 red" means all 4 drawn are red. \[ P = \frac{\binom{7}{4}}{\binom{12}{4}} = \frac{35}{495} = \frac{7}{99} \] ANSWER: 7/99
7/99
true
true
stop
101
183
7.29
v3
16,000
1
5
b02e316dddd1d3381085
f51ef3075ca483061623
f51ef3075ca483061623
train
pareto_5efforts
probability
1
concise
-1
false
50,000
A bag has 7 red, 5 blue marbles. You draw 4 marbles without replacement. What is the probability that at least 4 of them are red? Give the answer as a reduced fraction p/q. Final line: `ANSWER: <answer>`.
A bag has 7 red, 5 blue marbles. You draw 4 marbles without replacement. What is the probability that at least 4 of them are red? Give the answer as a reduced fraction p/q.
7/99
reduced_fraction
exact_fractions_hypergeometric
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
medium
0.7
0.99
We need solve probability. Need parse: bag 7 red, 5 blue total 12. Draw 4 marbles without replacement. Probability that at least 4 of them are red? Since draw 4, "at least 4 of them are red" means all 4 red. Need compute C(7,4)/C(12,4). Let's compute. C(7,4)=35. C(12,4)=495? 12*11*10*9/24 = 11880/24=495. Probability=35...
We draw 4 marbles total, so “at least 4 red” means all 4 are red. Total ways to choose 4 from 12: \[ \binom{12}{4}=495 \] Ways to choose 4 red from 7: \[ \binom{7}{4}=35 \] Probability: \[ \frac{35}{495}=\frac{7}{99} \] ANSWER: 7/99
7/99
true
true
stop
102
296
1.34
v3
16,000
1
5
b02e316dddd1d3381085
f51ef3075ca483061623
f51ef3075ca483061623
train
pareto_5efforts
probability
1
concise
-1
false
50,000
A bag has 7 red, 5 blue marbles. You draw 4 marbles without replacement. What is the probability that at least 4 of them are red? Give the answer as a reduced fraction p/q. Final line: `ANSWER: <answer>`.
A bag has 7 red, 5 blue marbles. You draw 4 marbles without replacement. What is the probability that at least 4 of them are red? Give the answer as a reduced fraction p/q.
7/99
reduced_fraction
exact_fractions_hypergeometric
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
high
0.7
0.99
We need answer probability. Need parse: Bag 7 red, 5 blue. Draw 4 without replacement. Probability that at least 4 of them are red. Since draw 4, at least 4 red means all 4 red. Compute C(7,4)/C(12,4). Need reduced fraction. C(7,4)=35. C(12,4)=495? 12*11*10*9/24 = 11880/24=495. 35/495 = 7/99. Answer 7/99. Need final w...
We draw 4 marbles from 12 total. “At least 4 red” means all 4 drawn are red. Number of favorable draws: \(\binom{7}{4}=35\). Total draws: \(\binom{12}{4}=495\). Probability: \[ \frac{35}{495}=\frac{7}{99}. \] ANSWER: 7/99
7/99
true
true
stop
103
251
1.05
v3
16,000
1
5
b02e316dddd1d3381085
f51ef3075ca483061623
f51ef3075ca483061623
train
pareto_5efforts
probability
1
concise
-1
false
50,000
A bag has 7 red, 5 blue marbles. You draw 4 marbles without replacement. What is the probability that at least 4 of them are red? Give the answer as a reduced fraction p/q. Final line: `ANSWER: <answer>`.
A bag has 7 red, 5 blue marbles. You draw 4 marbles without replacement. What is the probability that at least 4 of them are red? Give the answer as a reduced fraction p/q.
7/99
reduced_fraction
exact_fractions_hypergeometric
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
xhigh
0.7
0.99
We need answer probability. Need parse: bag 7 red, 5 blue. Draw 4 without replacement. Probability that at least 4 of them are red. Since draw 4, "at least 4 red" means all 4 red. Compute hypergeometric. Total ways C(12,4). Red ways C(7,4). Probability = C(7,4)/C(12,4). C7,4=35. C12,4=495? 12*11*10*9/24 = 11880/24=495....
ANSWER: 7/99
7/99
true
true
stop
103
182
0.93
v3
16,000
1
5
b02e316dddd1d3381085
f51ef3075ca483061623
f51ef3075ca483061623
train
pareto_5efforts
probability
1
concise
-1
false
50,000
A bag has 7 red, 5 blue marbles. You draw 4 marbles without replacement. What is the probability that at least 4 of them are red? Give the answer as a reduced fraction p/q. Final line: `ANSWER: <answer>`.
A bag has 7 red, 5 blue marbles. You draw 4 marbles without replacement. What is the probability that at least 4 of them are red? Give the answer as a reduced fraction p/q.
7/99
reduced_fraction
exact_fractions_hypergeometric
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
max
0.7
0.99
We need solve probability. Need final answer reduced fraction. Problem: bag 7 red, 5 blue total 12. Draw 4 without replacement. Probability at least 4 of them are red. Since draw 4, at least 4 red means all 4 red. Probability choose 4 red from 7 / choose 4 from 12. Compute C(7,4)/C(12,4). C7,4=35. C12,4=495? 12*11*10*9...
ANSWER: 7/99
7/99
true
true
stop
103
174
0.82
v3
16,000
1
5
bdd50a70b925b8614ce2
f1d1fae752eb48a22fc4
f1d1fae752eb48a22fc4
train
pareto_5efforts
knights_knaves
1
concise
-1
false
50,000
Each person below is either a knight (always tells the truth) or a knave (always lies). - Dalia says: "At least one of Oskar and Jonas is a knave." - Oskar says: "Dalia is a knight." - Jonas says: "Oskar and I are the same type." - Nia says: "Jonas is a knight or Dalia is a knight." Determine who is a knight. List the ...
Each person below is either a knight (always tells the truth) or a knave (always lies). - Dalia says: "At least one of Oskar and Jonas is a knave." - Oskar says: "Dalia is a knight." - Jonas says: "Oskar and I are the same type." - Nia says: "Jonas is a knight or Dalia is a knight." Determine who is a knight. List the ...
Dalia, Nia, Oskar
comma_list_alphabetical_or_none
truth_table_enumeration
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
low
0.7
0.99
We need solve knights/knaves. Need determine all. Let's reason. Let D,O,J,N boolean knight (true). Statements: D says: "At least one of Oskar and Jonas is a knave." i.e. (O false or J false) = not (O and J). So D truthful iff (not O or not J). O says: "Dalia is a knight." O truthful iff D. J says: "Oskar and I are s...
ANSWER: Dalia, Nia, Oskar
Dalia, Nia, Oskar
true
true
stop
170
400
1.77
v3
16,000
1
5
bdd50a70b925b8614ce2
f1d1fae752eb48a22fc4
f1d1fae752eb48a22fc4
train
pareto_5efforts
knights_knaves
1
concise
-1
false
50,000
Each person below is either a knight (always tells the truth) or a knave (always lies). - Dalia says: "At least one of Oskar and Jonas is a knave." - Oskar says: "Dalia is a knight." - Jonas says: "Oskar and I are the same type." - Nia says: "Jonas is a knight or Dalia is a knight." Determine who is a knight. List the ...
Each person below is either a knight (always tells the truth) or a knave (always lies). - Dalia says: "At least one of Oskar and Jonas is a knave." - Oskar says: "Dalia is a knight." - Jonas says: "Oskar and I are the same type." - Nia says: "Jonas is a knight or Dalia is a knight." Determine who is a knight. List the ...
Dalia, Nia, Oskar
comma_list_alphabetical_or_none
truth_table_enumeration
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
medium
0.7
0.99
We need solve knights knaves. Need final answer. Let's analyze. Variables D,O,J,N each K (knight truth) or V (knave lie). Statements: D: "At least one of Oskar and Jonas is a knave." Equivalent (O is knave OR J is knave) i.e. not both knights. Truth value T iff (¬O_knight ∨ ¬J_knight) i.e. O or J false. O: "Dalia is ...
The consistent assignment is: - Dalia: knight - Oskar: knight - Jonas: knave - Nia: knight ANSWER: Dalia, Nia, Oskar
Dalia, Nia, Oskar
true
true
stop
171
673
2.66
v3
16,000
1
5
bdd50a70b925b8614ce2
f1d1fae752eb48a22fc4
f1d1fae752eb48a22fc4
train
pareto_5efforts
knights_knaves
1
concise
-1
false
50,000
Each person below is either a knight (always tells the truth) or a knave (always lies). - Dalia says: "At least one of Oskar and Jonas is a knave." - Oskar says: "Dalia is a knight." - Jonas says: "Oskar and I are the same type." - Nia says: "Jonas is a knight or Dalia is a knight." Determine who is a knight. List the ...
Each person below is either a knight (always tells the truth) or a knave (always lies). - Dalia says: "At least one of Oskar and Jonas is a knave." - Oskar says: "Dalia is a knight." - Jonas says: "Oskar and I are the same type." - Nia says: "Jonas is a knight or Dalia is a knight." Determine who is a knight. List the ...
Dalia, Nia, Oskar
comma_list_alphabetical_or_none
truth_table_enumeration
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
high
0.7
0.99
We need solve knights knaves. Need parse statements. Need determine all consistent assignments. Need list knights alphabetical. Need final line ANSWER: ... Let's solve carefully. People: Dalia, Oskar, Jonas, Nia. Each K (knight) or V (knave). Statements: Dalia: "At least one of Oskar and Jonas is a knave." Equivalen...
Dalia says at least one of Oskar and Jonas is a knave. If Dalia were a knave, her statement would be false, forcing both Oskar and Jonas to be knights; but then Oskar’s claim “Dalia is a knight” would be false, contradicting Oskar being a knight. So Dalia is a knight. Thus Oskar is a knight, Jonas is a knave, and Nia’s...
Dalia, Nia, Oskar
true
true
stop
172
832
3.18
v3
16,000
1
5
bdd50a70b925b8614ce2
f1d1fae752eb48a22fc4
f1d1fae752eb48a22fc4
train
pareto_5efforts
knights_knaves
1
concise
-1
false
50,000
Each person below is either a knight (always tells the truth) or a knave (always lies). - Dalia says: "At least one of Oskar and Jonas is a knave." - Oskar says: "Dalia is a knight." - Jonas says: "Oskar and I are the same type." - Nia says: "Jonas is a knight or Dalia is a knight." Determine who is a knight. List the ...
Each person below is either a knight (always tells the truth) or a knave (always lies). - Dalia says: "At least one of Oskar and Jonas is a knave." - Oskar says: "Dalia is a knight." - Jonas says: "Oskar and I are the same type." - Nia says: "Jonas is a knight or Dalia is a knight." Determine who is a knight. List the ...
Dalia, Nia, Oskar
comma_list_alphabetical_or_none
truth_table_enumeration
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
xhigh
0.7
0.99
We need solve knights/knaves. Need final answer format. Need reason carefully. Let's parse. People: Dalia, Oskar, Jonas, Nia. Each knight truth, knave lie. Statements: Dalia says: "At least one of Oskar and Jonas is a knave." i.e. ¬(O knight and J knight)? At least one knave among O,J means not both knights. Oskar sa...
Dalia, Nia, and Oskar are knights; Jonas is a knave. ANSWER: Dalia, Nia, Oskar
Dalia, Nia, Oskar
true
true
stop
172
1,291
4.33
v3
16,000
1
5
bdd50a70b925b8614ce2
f1d1fae752eb48a22fc4
f1d1fae752eb48a22fc4
train
pareto_5efforts
knights_knaves
1
concise
-1
false
50,000
Each person below is either a knight (always tells the truth) or a knave (always lies). - Dalia says: "At least one of Oskar and Jonas is a knave." - Oskar says: "Dalia is a knight." - Jonas says: "Oskar and I are the same type." - Nia says: "Jonas is a knight or Dalia is a knight." Determine who is a knight. List the ...
Each person below is either a knight (always tells the truth) or a knave (always lies). - Dalia says: "At least one of Oskar and Jonas is a knave." - Oskar says: "Dalia is a knight." - Jonas says: "Oskar and I are the same type." - Nia says: "Jonas is a knight or Dalia is a knight." Determine who is a knight. List the ...
Dalia, Nia, Oskar
comma_list_alphabetical_or_none
truth_table_enumeration
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
max
0.7
0.99
We need solve knights knaves. Need produce final answer line. Let's analyze carefully. Persons: Dalia, Oskar, Jonas, Nia. Each knight/truth or knave/lie. Statements: D: "At least one of Oskar and Jonas is a knave." = (Oskar knave OR Jonas knave). Equiv not both knights. O: "Dalia is a knight." J: "Oskar and I are the...
ANSWER: Dalia, Nia, Oskar
Dalia, Nia, Oskar
true
true
stop
172
621
2.65
v3
16,000
1
5
4fba9525949d44176f44
cf09b691011a7312bcb4
cf09b691011a7312bcb4
train
pareto_5efforts
meeting_slot
1
concise
-1
false
50,000
Working hours are 09:00–17:00. A 90-minute meeting must start on a quarter hour (:00, :15, :30, :45) and fit entirely inside everyone's free time. - Zeynep: busy 10:00–10:45, 15:15–16:00 - Keiko: busy 15:30–17:00 - Leila: busy 14:15–15:15 What is the earliest possible start time? Answer in HH:MM (24-hour) format. Fina...
Working hours are 09:00–17:00. A 90-minute meeting must start on a quarter hour (:00, :15, :30, :45) and fit entirely inside everyone's free time. - Zeynep: busy 10:00–10:45, 15:15–16:00 - Keiko: busy 15:30–17:00 - Leila: busy 14:15–15:15 What is the earliest possible start time? Answer in HH:MM (24-hour) format.
10:45
hh:mm_24h
interval_scan
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
low
0.7
0.99
We need solve scheduling. Need earliest start time for 90-min meeting, start on quarter hour, fit entirely inside everyone's free time within working hours 09:00-17:00. Need consider intersection of free times. People busy: Zeynep: 10:00-10:45, 15:15-16:00. Free: 09:00-10:00, 10:45-15:15, 16:00-17:00. Keiko: busy 15:3...
ANSWER: 10:45
10:45
true
true
stop
197
666
2.49
v3
16,000
1
5
4fba9525949d44176f44
cf09b691011a7312bcb4
cf09b691011a7312bcb4
train
pareto_5efforts
meeting_slot
1
concise
-1
false
50,000
Working hours are 09:00–17:00. A 90-minute meeting must start on a quarter hour (:00, :15, :30, :45) and fit entirely inside everyone's free time. - Zeynep: busy 10:00–10:45, 15:15–16:00 - Keiko: busy 15:30–17:00 - Leila: busy 14:15–15:15 What is the earliest possible start time? Answer in HH:MM (24-hour) format. Fina...
Working hours are 09:00–17:00. A 90-minute meeting must start on a quarter hour (:00, :15, :30, :45) and fit entirely inside everyone's free time. - Zeynep: busy 10:00–10:45, 15:15–16:00 - Keiko: busy 15:30–17:00 - Leila: busy 14:15–15:15 What is the earliest possible start time? Answer in HH:MM (24-hour) format.
10:45
hh:mm_24h
interval_scan
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
medium
0.7
0.99
We need solve scheduling. Need earliest start time 90 min meeting quarter hour, within working hours 09:00-17:00, fit entirely inside everyone's free time. Need account free time = working hours minus busy intervals. Meeting start on quarter hour, duration 90 min. Need start S such that S >= 09:00, S+90 <=17:00, S and ...
The earliest valid start is 10:45. ANSWER: 10:45
10:45
true
true
stop
198
1,018
3.24
v3
16,000
1
5
4fba9525949d44176f44
cf09b691011a7312bcb4
cf09b691011a7312bcb4
train
pareto_5efforts
meeting_slot
1
concise
-1
false
50,000
Working hours are 09:00–17:00. A 90-minute meeting must start on a quarter hour (:00, :15, :30, :45) and fit entirely inside everyone's free time. - Zeynep: busy 10:00–10:45, 15:15–16:00 - Keiko: busy 15:30–17:00 - Leila: busy 14:15–15:15 What is the earliest possible start time? Answer in HH:MM (24-hour) format. Fina...
Working hours are 09:00–17:00. A 90-minute meeting must start on a quarter hour (:00, :15, :30, :45) and fit entirely inside everyone's free time. - Zeynep: busy 10:00–10:45, 15:15–16:00 - Keiko: busy 15:30–17:00 - Leila: busy 14:15–15:15 What is the earliest possible start time? Answer in HH:MM (24-hour) format.
10:45
hh:mm_24h
interval_scan
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
high
0.7
0.99
We need solve scheduling. Need produce final with answer. Let's parse. Working hours 09:00-17:00. Meeting 90 minutes must start on quarter hour and fit entirely inside everyone's free time. Need earliest possible start time. Busy: Zeynep: 10:00-10:45, 15:15-16:00 Keiko: 15:30-17:00 Leila: 14:15-15:15 Free time inter...
The common free intervals long enough for a 90-minute meeting start at 10:45. ANSWER: 10:45
10:45
true
true
stop
199
788
2.48
v3
16,000
1
5
4fba9525949d44176f44
cf09b691011a7312bcb4
cf09b691011a7312bcb4
train
pareto_5efforts
meeting_slot
1
concise
-1
false
50,000
Working hours are 09:00–17:00. A 90-minute meeting must start on a quarter hour (:00, :15, :30, :45) and fit entirely inside everyone's free time. - Zeynep: busy 10:00–10:45, 15:15–16:00 - Keiko: busy 15:30–17:00 - Leila: busy 14:15–15:15 What is the earliest possible start time? Answer in HH:MM (24-hour) format. Fina...
Working hours are 09:00–17:00. A 90-minute meeting must start on a quarter hour (:00, :15, :30, :45) and fit entirely inside everyone's free time. - Zeynep: busy 10:00–10:45, 15:15–16:00 - Keiko: busy 15:30–17:00 - Leila: busy 14:15–15:15 What is the earliest possible start time? Answer in HH:MM (24-hour) format.
10:45
hh:mm_24h
interval_scan
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
xhigh
0.7
0.99
We need solve scheduling. Need parse. Working hours 09:00-17:00. Meeting 90 min must start quarter hour and fit entirely inside everyone's free time. Given busy intervals. Need earliest possible start time. Need consider all participants free. Free time within working hours excluding busy. Meeting 90 min continuous, st...
The common free intervals long enough for a 90-minute meeting start on a quarter hour are checked. The earliest valid start is 10:45, giving an end at 12:15, within all participants’ free time. ANSWER: 10:45
10:45
true
true
stop
199
934
3.19
v3
16,000
1
5
4fba9525949d44176f44
cf09b691011a7312bcb4
cf09b691011a7312bcb4
train
pareto_5efforts
meeting_slot
1
concise
-1
false
50,000
Working hours are 09:00–17:00. A 90-minute meeting must start on a quarter hour (:00, :15, :30, :45) and fit entirely inside everyone's free time. - Zeynep: busy 10:00–10:45, 15:15–16:00 - Keiko: busy 15:30–17:00 - Leila: busy 14:15–15:15 What is the earliest possible start time? Answer in HH:MM (24-hour) format. Fina...
Working hours are 09:00–17:00. A 90-minute meeting must start on a quarter hour (:00, :15, :30, :45) and fit entirely inside everyone's free time. - Zeynep: busy 10:00–10:45, 15:15–16:00 - Keiko: busy 15:30–17:00 - Leila: busy 14:15–15:15 What is the earliest possible start time? Answer in HH:MM (24-hour) format.
10:45
hh:mm_24h
interval_scan
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
max
0.7
0.99
We need solve scheduling. Need parse problem. Working hours 09:00-17:00. Meeting 90 min must start on quarter hour and fit entirely inside everyone's free time. Need earliest possible start time. Free time = working hours minus busy intervals for each person. Meeting must fit in intersection of all free times? "fit ent...
The intersection of everyone's free time inside working hours is [09:00–10:00] and [10:45–14:15]. A 90-minute meeting cannot fit in the first interval, but can start at 10:45 in the second. ANSWER: 10:45
10:45
true
true
stop
199
1,061
3.12
v3
16,000
1
5
fff7be317a4e3f2dbaae
33c141d2d8a4263ddacc
33c141d2d8a4263ddacc
train
pareto_5efforts
venn_counting
1
concise
-1
false
50,000
104 students were surveyed. 40 joined chess. 43 joined drama. 51 joined robotics. 13 joined both chess and drama. 17 joined both chess and robotics. 17 joined both drama and robotics. 3 joined all three clubs. How many students joined exactly one of these clubs? Final line: `ANSWER: <answer>`.
104 students were surveyed. 40 joined chess. 43 joined drama. 51 joined robotics. 13 joined both chess and drama. 17 joined both chess and robotics. 17 joined both drama and robotics. 3 joined all three clubs. How many students joined exactly one of these clubs?
49
integer
set_enumeration
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
low
0.7
0.99
We need solve inclusion. Need final answer. Let's compute. Total 104 surveyed. Sets C,D,R sizes 40,43,51. Pair intersections: C∩D=13, C∩R=17, D∩R=17. Triple=3. Need exactly one club count. Formula: exactly one = sum singles - 2*sum pair-only? Let's compute. Number in at least one? Inclusion-exclusion: |C∪D∪R| = 40+...
ANSWER: 49
49
true
true
stop
124
482
2.16
v3
16,000
0.8
5
fff7be317a4e3f2dbaae
33c141d2d8a4263ddacc
33c141d2d8a4263ddacc
train
pareto_5efforts
venn_counting
1
concise
-1
false
50,000
104 students were surveyed. 40 joined chess. 43 joined drama. 51 joined robotics. 13 joined both chess and drama. 17 joined both chess and robotics. 17 joined both drama and robotics. 3 joined all three clubs. How many students joined exactly one of these clubs? Final line: `ANSWER: <answer>`.
104 students were surveyed. 40 joined chess. 43 joined drama. 51 joined robotics. 13 joined both chess and drama. 17 joined both chess and robotics. 17 joined both drama and robotics. 3 joined all three clubs. How many students joined exactly one of these clubs?
49
integer
set_enumeration
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
medium
0.7
0.99
We need solve inclusion-exclusion. Need count exactly one. Total surveyed 104 maybe includes none? Let's compute. Sets C,D,R. |C|=40, |D|=43, |R|=51. Pairwise intersections: C∩D=13, C∩R=17, D∩R=17. Triple=3. Need number joined exactly one club. Could compute using Venn regions. Let x = only C, etc. Pairwise only reg...
We can break the Venn diagram into regions. - Only chess and drama: \(13-3=10\) - Only chess and robotics: \(17-3=14\) - Only drama and robotics: \(17-3=14\) - All three: \(3\) Then: - Only chess: \(40-(10+14+3)=13\) - Only drama: \(43-(10+14+3)=16\) - Only robotics: \(51-(14+14+3)=19\) Exactly one club: \[ 13+16+19...
48
false
false
stop
125
447
2.1
v3
16,000
0.8
5
fff7be317a4e3f2dbaae
33c141d2d8a4263ddacc
33c141d2d8a4263ddacc
train
pareto_5efforts
venn_counting
1
concise
-1
false
50,000
104 students were surveyed. 40 joined chess. 43 joined drama. 51 joined robotics. 13 joined both chess and drama. 17 joined both chess and robotics. 17 joined both drama and robotics. 3 joined all three clubs. How many students joined exactly one of these clubs? Final line: `ANSWER: <answer>`.
104 students were surveyed. 40 joined chess. 43 joined drama. 51 joined robotics. 13 joined both chess and drama. 17 joined both chess and robotics. 17 joined both drama and robotics. 3 joined all three clubs. How many students joined exactly one of these clubs?
49
integer
set_enumeration
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
high
0.7
0.99
We need solve inclusion-exclusion. Need count exactly one of clubs. Let's compute. Total 104 surveyed. Sets C,D,R sizes 40,43,51. Pair intersections given. Triple 3. We need exactly one. Let's compute regions. Let a = exactly C only, b = exactly D only, c = exactly R only. Let cd = exactly C&D not R = 13-3=10. cr =...
ANSWER: 49
49
true
true
stop
126
308
1.29
v3
16,000
0.8
5
fff7be317a4e3f2dbaae
33c141d2d8a4263ddacc
33c141d2d8a4263ddacc
train
pareto_5efforts
venn_counting
1
concise
-1
false
50,000
104 students were surveyed. 40 joined chess. 43 joined drama. 51 joined robotics. 13 joined both chess and drama. 17 joined both chess and robotics. 17 joined both drama and robotics. 3 joined all three clubs. How many students joined exactly one of these clubs? Final line: `ANSWER: <answer>`.
104 students were surveyed. 40 joined chess. 43 joined drama. 51 joined robotics. 13 joined both chess and drama. 17 joined both chess and robotics. 17 joined both drama and robotics. 3 joined all three clubs. How many students joined exactly one of these clubs?
49
integer
set_enumeration
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
xhigh
0.7
0.99
We need solve inclusion-exclusion. Need final answer. Let's compute carefully. Total surveyed 104. Sets C,D,R sizes 40,43,51. Pair intersections: C∩D=13, C∩R=17, D∩R=17. Triple=3. Need number joined exactly one club. We can compute union size = 40+43+51 - (13+17+17) + 3 = 134 - 47 +3? Wait sum singles=134. pair sum=...
We can break the students into disjoint groups. - All three clubs: 3 - Chess & drama only: \(13-3=10\) - Chess & robotics only: \(17-3=14\) - Drama & robotics only: \(17-3=14\) Then only chess: \(40-(10+14+3)=13\) Only drama: \(43-(10+14+3)=16\) Only robotics: \(51-(14+14+3)=20\) So exactly one club: \(13+16+20=49...
49
true
true
stop
126
594
1.92
v3
16,000
0.8
5
fff7be317a4e3f2dbaae
33c141d2d8a4263ddacc
33c141d2d8a4263ddacc
train
pareto_5efforts
venn_counting
1
concise
-1
false
50,000
104 students were surveyed. 40 joined chess. 43 joined drama. 51 joined robotics. 13 joined both chess and drama. 17 joined both chess and robotics. 17 joined both drama and robotics. 3 joined all three clubs. How many students joined exactly one of these clubs? Final line: `ANSWER: <answer>`.
104 students were surveyed. 40 joined chess. 43 joined drama. 51 joined robotics. 13 joined both chess and drama. 17 joined both chess and robotics. 17 joined both drama and robotics. 3 joined all three clubs. How many students joined exactly one of these clubs?
49
integer
set_enumeration
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
max
0.7
0.99
We need solve inclusion-exclusion. Need final answer. Let's compute. Total 104 surveyed. Sets C,D,R sizes 40,43,51. Pairwise intersections: CD=13, CR=17, DR=17. Triple=3. Need exactly one club. Formula: |exactly one| = sum singles - 2*sum pairwise? Let's derive. For each person, count in exactly one. Let n1 = number...
Using inclusion–exclusion region counts: - Triple intersection: 3 - Chess & Drama only: 13 − 3 = 10 - Chess & Robotics only: 17 − 3 = 14 - Drama & Robotics only: 17 − 3 = 14 - Chess only: 40 − 10 − 14 − 3 = 13 - Drama only: 43 − 10 − 14 − 3 = 16 - Robotics only: 51 − 14 − 14 − 3 = 20 Exactly one club: 13 + 16 + 20 = ...
49
true
true
stop
126
535
6.07
v3
16,000
0.8
5
5c24fe643eba86351987
80d429755f28e99d7d66
80d429755f28e99d7d66
train
pareto_5efforts
inventory_word_problem
2
concise
-1
false
50,000
Olga starts with 149 bottles. Then, in order, Olga loses 61 to damage; then splits the stock into 5 equal groups (whole items only), keeps one group plus any leftover items, and gives the other groups away; then matches the current count with an equal new shipment; then buys 56 more; then receives a delivery of 38; the...
Olga starts with 149 bottles. Then, in order, Olga loses 61 to damage; then splits the stock into 5 equal groups (whole items only), keeps one group plus any leftover items, and gives the other groups away; then matches the current count with an equal new shipment; then buys 56 more; then receives a delivery of 38; the...
162
integer
state_simulation
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
low
0.7
0.99
Let's compute step by step. Start: 149. Loses 61 to damage: 149-61 = 88. Splits stock into 5 equal groups (whole items only), keeps one group plus leftover, gives other groups away. So 88 // 5 = 17 per group, leftover 88 % 5 = 3. Keeps one group (17) + leftover (3) = 20. Matches current count with equal new shipment: ...
ANSWER: 162
162
true
true
stop
153
194
0.97
v3
16,000
1
5
5c24fe643eba86351987
80d429755f28e99d7d66
80d429755f28e99d7d66
train
pareto_5efforts
inventory_word_problem
2
concise
-1
false
50,000
Olga starts with 149 bottles. Then, in order, Olga loses 61 to damage; then splits the stock into 5 equal groups (whole items only), keeps one group plus any leftover items, and gives the other groups away; then matches the current count with an equal new shipment; then buys 56 more; then receives a delivery of 38; the...
Olga starts with 149 bottles. Then, in order, Olga loses 61 to damage; then splits the stock into 5 equal groups (whole items only), keeps one group plus any leftover items, and gives the other groups away; then matches the current count with an equal new shipment; then buys 56 more; then receives a delivery of 38; the...
162
integer
state_simulation
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
medium
0.7
0.99
We need solve word problem carefully. Need parse sequence. Need final answer line. Let's restate: Olga starts with 149 bottles. Then in order: 1. loses 61 to damage. 2. splits the stock into 5 equal groups (whole items only), keeps one group plus any leftover items, and gives the other groups away. 3. matches the curr...
Start: 149 After damage: 149 − 61 = 88 Split into 5 groups: 88 = 5×17 + 3, keeps 17 + 3 = 20 Equal shipment doubles: 20 × 2 = 40 Buy 56: 40 + 56 = 96 Delivery 38: 96 + 38 = 134 Purchase 28: 134 + 28 = 162 ANSWER: 162
162
true
true
stop
154
595
1.82
v3
16,000
1
5
5c24fe643eba86351987
80d429755f28e99d7d66
80d429755f28e99d7d66
train
pareto_5efforts
inventory_word_problem
2
concise
-1
false
50,000
Olga starts with 149 bottles. Then, in order, Olga loses 61 to damage; then splits the stock into 5 equal groups (whole items only), keeps one group plus any leftover items, and gives the other groups away; then matches the current count with an equal new shipment; then buys 56 more; then receives a delivery of 38; the...
Olga starts with 149 bottles. Then, in order, Olga loses 61 to damage; then splits the stock into 5 equal groups (whole items only), keeps one group plus any leftover items, and gives the other groups away; then matches the current count with an equal new shipment; then buys 56 more; then receives a delivery of 38; the...
162
integer
state_simulation
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
high
0.7
0.99
We need solve word problem. Need parse carefully. Olga starts with 149 bottles. Then in order: 1 loses 61 to damage. 2 splits the stock into 5 equal groups (whole items only), keeps one group plus any leftover items, and gives the other groups away. 3 matches the current count with an equal new shipment. 4 buys 56 more...
ANSWER: 162
162
true
true
stop
155
357
2.03
v3
16,000
1
5
5c24fe643eba86351987
80d429755f28e99d7d66
80d429755f28e99d7d66
train
pareto_5efforts
inventory_word_problem
2
concise
-1
false
50,000
Olga starts with 149 bottles. Then, in order, Olga loses 61 to damage; then splits the stock into 5 equal groups (whole items only), keeps one group plus any leftover items, and gives the other groups away; then matches the current count with an equal new shipment; then buys 56 more; then receives a delivery of 38; the...
Olga starts with 149 bottles. Then, in order, Olga loses 61 to damage; then splits the stock into 5 equal groups (whole items only), keeps one group plus any leftover items, and gives the other groups away; then matches the current count with an equal new shipment; then buys 56 more; then receives a delivery of 38; the...
162
integer
state_simulation
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
xhigh
0.7
0.99
We need solve word problem. Need parse carefully. Let's restate. Olga starts with 149 bottles. Then, in order: 1. loses 61 to damage 2. splits the stock into 5 equal groups (whole items only), keeps one group plus any leftover items, and gives the other groups away 3. matches the current count with an equal new shipme...
Start: 149 After damage: 149 − 61 = 88 Split into 5 groups: 88 = 5×17 + 3, keep 17 + 3 = 20 Match with equal shipment: 20 + 20 = 40 Buy 56: 40 + 56 = 96 Delivery 38: 96 + 38 = 134 Purchase 28: 134 + 28 = 162 ANSWER: 162
162
true
true
stop
155
492
1.56
v3
16,000
1
5
5c24fe643eba86351987
80d429755f28e99d7d66
80d429755f28e99d7d66
train
pareto_5efforts
inventory_word_problem
2
concise
-1
false
50,000
Olga starts with 149 bottles. Then, in order, Olga loses 61 to damage; then splits the stock into 5 equal groups (whole items only), keeps one group plus any leftover items, and gives the other groups away; then matches the current count with an equal new shipment; then buys 56 more; then receives a delivery of 38; the...
Olga starts with 149 bottles. Then, in order, Olga loses 61 to damage; then splits the stock into 5 equal groups (whole items only), keeps one group plus any leftover items, and gives the other groups away; then matches the current count with an equal new shipment; then buys 56 more; then receives a delivery of 38; the...
162
integer
state_simulation
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
max
0.7
0.99
We need solve word problem carefully. Need parse operations. Olga starts 149 bottles. Then in order: 1. loses 61 to damage. 2. splits the stock into 5 equal groups (whole items only), keeps one group plus any leftover items, and gives the other groups away. 3. matches the current count with an equal new shipment. 4. bu...
Start: 149 bottles. After losing 61: 149 − 61 = 88. Split into 5 equal whole groups: 88 ÷ 5 = 17 per group with 3 leftover. Keeps one group plus leftover: 17 + 3 = 20. Matches with equal shipment: 20 + 20 = 40. Buys 56: 40 + 56 = 96. Delivery of 38: 96 + 38 = 134. Purchases 28: 134 + 28 = 162. ANSWER: 162
162
true
true
stop
155
591
2.47
v3
16,000
1
5
34656a873e5ccea2441e
41164a594b91576b0685
41164a594b91576b0685
train
pareto_5efforts
date_arithmetic
2
concise
-1
false
50,000
Start from Sunday, August 23, 2015. Subtract 203 days, then add 117 days, then subtract 156 days. What is the resulting date and weekday? Answer in the form YYYY-MM-DD Weekday. Final line: `ANSWER: <answer>`.
Start from Sunday, August 23, 2015. Subtract 203 days, then add 117 days, then subtract 156 days. What is the resulting date and weekday? Answer in the form YYYY-MM-DD Weekday.
2014-12-24 Wednesday
yyyy-mm-dd_weekday
python_datetime
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
low
0.7
0.99
Let me compute carefully. Start: Sunday, August 23, 2015. Subtract 203 days: Aug 23, 2015 minus 203 days. Let's compute. Aug 23 day-of-year 2015: Jan31 Feb28 Mar31 Apr30 May31 Jun30 Jul31 Aug23 = 31+28+31+30+31+30+31+23 = 235. So Aug 23 is day 235. Minus 203 days => day 32 of year? 235-203=32. Day 32 of 2015 = Feb 1...
ANSWER: 2014-12-24 Wednesday
2014-12-24 Wednesday
true
true
stop
111
2,335
9.35
v3
16,000
0.8
5
34656a873e5ccea2441e
41164a594b91576b0685
41164a594b91576b0685
train
pareto_5efforts
date_arithmetic
2
concise
-1
false
50,000
Start from Sunday, August 23, 2015. Subtract 203 days, then add 117 days, then subtract 156 days. What is the resulting date and weekday? Answer in the form YYYY-MM-DD Weekday. Final line: `ANSWER: <answer>`.
Start from Sunday, August 23, 2015. Subtract 203 days, then add 117 days, then subtract 156 days. What is the resulting date and weekday? Answer in the form YYYY-MM-DD Weekday.
2014-12-24 Wednesday
yyyy-mm-dd_weekday
python_datetime
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
medium
0.7
0.99
We need answer date calculation. Need produce final with ANSWER. Let's compute carefully. Start Sunday, August 23, 2015. Subtract 203 days, then add 117 days, then subtract 156 days. Net change = -203+117-156 = -242 days. So start date minus 242 days. Need resulting date and weekday. August 23, 2015 Sunday. Subtract ...
2014-12-25 Wednesday ANSWER: 2014-12-25 Wednesday
2014-12-25 Wednesday
false
false
stop
112
1,033
4.25
v3
16,000
0.8
5
34656a873e5ccea2441e
41164a594b91576b0685
41164a594b91576b0685
train
pareto_5efforts
date_arithmetic
2
concise
-1
false
50,000
Start from Sunday, August 23, 2015. Subtract 203 days, then add 117 days, then subtract 156 days. What is the resulting date and weekday? Answer in the form YYYY-MM-DD Weekday. Final line: `ANSWER: <answer>`.
Start from Sunday, August 23, 2015. Subtract 203 days, then add 117 days, then subtract 156 days. What is the resulting date and weekday? Answer in the form YYYY-MM-DD Weekday.
2014-12-24 Wednesday
yyyy-mm-dd_weekday
python_datetime
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
high
0.7
0.99
We need answer date. Need compute carefully. Start Sunday, August 23, 2015. Subtract 203 days, then add 117 days, then subtract 156 days. Need resulting date and weekday. Output form YYYY-MM-DD Weekday. Final ANSWER. Let's compute. Could do stepwise. Need be careful with leap years? 2015 non-leap. Let's compute. Star...
2014-12-24 Wednesday ANSWER: 2014-12-24 Wednesday
2014-12-24 Wednesday
true
true
stop
113
824
2.63
v3
16,000
0.8
5
34656a873e5ccea2441e
41164a594b91576b0685
41164a594b91576b0685
train
pareto_5efforts
date_arithmetic
2
concise
-1
false
50,000
Start from Sunday, August 23, 2015. Subtract 203 days, then add 117 days, then subtract 156 days. What is the resulting date and weekday? Answer in the form YYYY-MM-DD Weekday. Final line: `ANSWER: <answer>`.
Start from Sunday, August 23, 2015. Subtract 203 days, then add 117 days, then subtract 156 days. What is the resulting date and weekday? Answer in the form YYYY-MM-DD Weekday.
2014-12-24 Wednesday
yyyy-mm-dd_weekday
python_datetime
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
xhigh
0.7
0.99
We need compute date arithmetic. Need final date and weekday. Need be careful. Start Sunday, August 23, 2015. Subtract 203 days, add 117, subtract 156. Net change = -203 +117 -156 = -242 days. So start Aug 23, 2015 minus 242 days. Need resulting date and weekday. Let's compute accurately. Start date: 2015-08-23 Sunday...
2014-12-24 Wednesday ANSWER: 2014-12-24 Wednesday
2014-12-24 Wednesday
true
true
stop
113
2,018
7.09
v3
16,000
0.8
5
34656a873e5ccea2441e
41164a594b91576b0685
41164a594b91576b0685
train
pareto_5efforts
date_arithmetic
2
concise
-1
false
50,000
Start from Sunday, August 23, 2015. Subtract 203 days, then add 117 days, then subtract 156 days. What is the resulting date and weekday? Answer in the form YYYY-MM-DD Weekday. Final line: `ANSWER: <answer>`.
Start from Sunday, August 23, 2015. Subtract 203 days, then add 117 days, then subtract 156 days. What is the resulting date and weekday? Answer in the form YYYY-MM-DD Weekday.
2014-12-24 Wednesday
yyyy-mm-dd_weekday
python_datetime
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
max
0.7
0.99
We need solve date arithmetic. Need be careful. Starting Sunday, August 23, 2015. Subtract 203 days, add 117, subtract 156. Net change = -203+117-156 = -242 days. Need date 242 days before Aug 23 2015. Then weekday. Let's compute carefully. Start 2015-08-23 Sunday. Subtract 242 days. Compute. Need exact date. Let's d...
2014-12-24 Wednesday ANSWER: 2014-12-24 Wednesday
2014-12-24 Wednesday
true
true
stop
113
2,101
8.81
v3
16,000
0.8
5
eec98fb184bcb8723472
fd15031ba48b54676943
fd15031ba48b54676943
train
pareto_5efforts
code_tracing
2
concise
-1
false
50,000
What does this Python program print? ```python x, y = 6, 4 for i in range(13): if i % 2 == 0: x += y * 6 else: y += x - 4 x %= 1000; y %= 1000 print(x + y) ``` Final line: `ANSWER: <answer>`.
What does this Python program print? ```python x, y = 6, 4 for i in range(13): if i % 2 == 0: x += y * 6 else: y += x - 4 x %= 1000; y %= 1000 print(x + y) ```
1438
integer
code_execution
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
low
0.7
0.99
Let me trace through the program. x=6, y=4 i=0 (even): x += y*6 = 6 + 4*6 = 30; y unchanged; x%=1000 ->30, y%=1000 ->4. x=30,y=4 i=1 (odd): y += x-4 = 4 + 30-4 = 30; x unchanged; x%=1000,y%=1000. x=30,y=30 i=2 (even): x += y*6 = 30 + 30*6 = 210; y=30. x=210,y=30 i=3 (odd): y += x-4 = 30 + 210-4 = 236; x=210. x=210,y=2...
ANSWER: 1438
1438
true
true
stop
136
771
2.15
v3
16,000
1
5
eec98fb184bcb8723472
fd15031ba48b54676943
fd15031ba48b54676943
train
pareto_5efforts
code_tracing
2
concise
-1
false
50,000
What does this Python program print? ```python x, y = 6, 4 for i in range(13): if i % 2 == 0: x += y * 6 else: y += x - 4 x %= 1000; y %= 1000 print(x + y) ``` Final line: `ANSWER: <answer>`.
What does this Python program print? ```python x, y = 6, 4 for i in range(13): if i % 2 == 0: x += y * 6 else: y += x - 4 x %= 1000; y %= 1000 print(x + y) ```
1438
integer
code_execution
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
medium
0.7
0.99
We need answer. Need compute. Let's simulate carefully. Python code: x,y = 6,4 for i in range(13): if i%2==0: x += y*6 else: y += x-4 x %=1000; y%=1000 print(x+y) Need final with ANSWER. Let's compute step by step. Initialize x=6,y=4. i=0 even: x += y*6 =6+4*6=30. then mod: x=30,y=4. i=1 odd: y += x-4 =4+3...
ANSWER: 1438
1438
true
true
stop
137
1,292
3.01
v3
16,000
1
5
eec98fb184bcb8723472
fd15031ba48b54676943
fd15031ba48b54676943
train
pareto_5efforts
code_tracing
2
concise
-1
false
50,000
What does this Python program print? ```python x, y = 6, 4 for i in range(13): if i % 2 == 0: x += y * 6 else: y += x - 4 x %= 1000; y %= 1000 print(x + y) ``` Final line: `ANSWER: <answer>`.
What does this Python program print? ```python x, y = 6, 4 for i in range(13): if i % 2 == 0: x += y * 6 else: y += x - 4 x %= 1000; y %= 1000 print(x + y) ```
1438
integer
code_execution
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
high
0.7
0.99
We need answer. Need compute program. Need final with answer. Let's simulate carefully. Python: x,y=6,4 for i in range(13): i=0..12 if i even: x += y*6 else: y += x-4 x %=1000; y%=1000 print(x+y) Need compute. Let's do step by step accurately. Could use mental or derive. Let's simulate. Initial x=6,y=4. i=0 even: x...
ANSWER: 1438
1438
true
true
stop
138
735
2.36
v3
16,000
1
5
eec98fb184bcb8723472
fd15031ba48b54676943
fd15031ba48b54676943
train
pareto_5efforts
code_tracing
2
concise
-1
false
50,000
What does this Python program print? ```python x, y = 6, 4 for i in range(13): if i % 2 == 0: x += y * 6 else: y += x - 4 x %= 1000; y %= 1000 print(x + y) ``` Final line: `ANSWER: <answer>`.
What does this Python program print? ```python x, y = 6, 4 for i in range(13): if i % 2 == 0: x += y * 6 else: y += x - 4 x %= 1000; y %= 1000 print(x + y) ```
1438
integer
code_execution
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
xhigh
0.7
0.99
We need answer. Need compute. Let's simulate carefully. Python program. x,y=6,4 for i in range(13): if i%2==0: x += y*6 else: y += x-4 x %=1000; y%=1000 print(x+y) Need compute. Let's do manually or reason. Could simulate table. i=0 even: x=6+4*6=30; y=4. mod: x=30,y=4. i=1 odd: y=4 + (x-4)=4+26=30? Wait x curren...
ANSWER: 1438
1438
true
true
stop
138
1,127
2.62
v3
16,000
1
5
eec98fb184bcb8723472
fd15031ba48b54676943
fd15031ba48b54676943
train
pareto_5efforts
code_tracing
2
concise
-1
false
50,000
What does this Python program print? ```python x, y = 6, 4 for i in range(13): if i % 2 == 0: x += y * 6 else: y += x - 4 x %= 1000; y %= 1000 print(x + y) ``` Final line: `ANSWER: <answer>`.
What does this Python program print? ```python x, y = 6, 4 for i in range(13): if i % 2 == 0: x += y * 6 else: y += x - 4 x %= 1000; y %= 1000 print(x + y) ```
1438
integer
code_execution
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
max
0.7
0.99
We need answer simple Python program output. Need compute. Let's simulate carefully. x,y=6,4. loop i=0..12. i%2==0: x += y*6; else y += x-4; then mod 1000 each. Let's compute. Initial x=6,y=4. i=0 even: x = 6 + 4*6 = 30. y=4. mod: x=30,y=4. i=1 odd: y = 4 + (30-4)=30. x=30. mod. x=30,y=30. i=2 even: x=30 + 30*6=2...
ANSWER: 1438
1438
true
true
stop
138
652
2.28
v3
16,000
1
5
387d160186268d50acb3
5e72a4015965592664b8
5e72a4015965592664b8
train
pareto_5efforts
combinatorics_count
2
concise
-1
false
50,000
How many ordered sequences of 6 integers, each between 2 and 5 inclusive, have a sum of exactly 22? Final line: `ANSWER: <answer>`.
How many ordered sequences of 6 integers, each between 2 and 5 inclusive, have a sum of exactly 22?
546
integer
dynamic_programming
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
low
0.7
0.99
We need count ordered 6-tuples (a1,...,a6) with each in {2,3,4,5} sum 22. Let xi = ai-2 in {0,1,2,3}. Sum xi = 22 - 12 = 10. Count nonnegative solutions xi<=3 summing to 10. Total without upper bound C(10+6-1,6-1)=C(15,5)=3003. Subtract xi>=4. For one variable xi'=xi-4>=0 sum 6: C(6+5,5)=C(11,5)=462. Times 6 = 2772. ...
We let \(x_i = a_i - 2\), so each \(x_i \in \{0,1,2,3\}\) and \[ x_1+\cdots+x_6 = 22-12 = 10. \] Count solutions with \(0\le x_i\le 3\). By inclusion-exclusion: - Total nonnegative solutions: \(\binom{15}{5}=3003\). - Subtract one variable \(\ge 4\): \(6\binom{11}{5}=6\cdot 462=2772\). - Add back two variables \(\ge...
546
true
true
stop
82
476
2.35
v3
16,000
1
5
387d160186268d50acb3
5e72a4015965592664b8
5e72a4015965592664b8
train
pareto_5efforts
combinatorics_count
2
concise
-1
false
50,000
How many ordered sequences of 6 integers, each between 2 and 5 inclusive, have a sum of exactly 22? Final line: `ANSWER: <answer>`.
How many ordered sequences of 6 integers, each between 2 and 5 inclusive, have a sum of exactly 22?
546
integer
dynamic_programming
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
medium
0.7
0.99
We need solve combinatorics. Need count ordered sequences length 6, entries in {2,3,4,5}, sum 22. Need final answer. Let's compute carefully. Let x_i ∈ {2,3,4,5}. Sum 22. Let y_i = x_i - 2 ∈ {0,1,2,3}. Sum y_i = 22 - 12 = 10. Count nonnegative integer sequences length 6 with each ≤3 summing to 10. Total unrestricted ...
We need count ordered 6-tuples with entries in {2,3,4,5} summing to 22. Subtract 2 from each entry: let \(y_i\in\{0,1,2,3\}\), with \[ y_1+\cdots+y_6 = 22-12=10. \] Count solutions using inclusion-exclusion. Unrestricted nonnegative solutions: \[ \binom{10+6-1}{6-1}=\binom{15}{5}=3003. \] Subtract cases where some...
546
true
true
stop
83
875
2.85
v3
16,000
1
5
387d160186268d50acb3
5e72a4015965592664b8
5e72a4015965592664b8
train
pareto_5efforts
combinatorics_count
2
concise
-1
false
50,000
How many ordered sequences of 6 integers, each between 2 and 5 inclusive, have a sum of exactly 22? Final line: `ANSWER: <answer>`.
How many ordered sequences of 6 integers, each between 2 and 5 inclusive, have a sum of exactly 22?
546
integer
dynamic_programming
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
high
0.7
0.99
We need solve combinatorics. Need count ordered 6-tuples of integers in {2,3,4,5} summing to 22. Need final answer. Let's compute carefully. Let x_i in {2,...,5}, i=1..6, sum 22. Let y_i = x_i - 2 in {0,1,2,3}. Sum y_i = 22 - 12 = 10. Need number of ordered 6-tuples y_i in [0,3] summing 10. Total nonnegative without ...
We need the number of ordered 6-tuples \((x_1,\dots,x_6)\) with each \(x_i\in\{2,3,4,5\}\) and sum \(22\). Set \(y_i=x_i-2\), so each \(y_i\in\{0,1,2,3\}\) and \[ y_1+\cdots+y_6 = 22-12=10. \] Count solutions with \(0\le y_i\le 3\). By inclusion-exclusion: \[ \binom{10+6-1}{6-1} - \binom{6}{1}\binom{10-4+6-1}{6-1} ...
546
true
true
stop
84
753
2.58
v3
16,000
1
5
387d160186268d50acb3
5e72a4015965592664b8
5e72a4015965592664b8
train
pareto_5efforts
combinatorics_count
2
concise
-1
false
50,000
How many ordered sequences of 6 integers, each between 2 and 5 inclusive, have a sum of exactly 22? Final line: `ANSWER: <answer>`.
How many ordered sequences of 6 integers, each between 2 and 5 inclusive, have a sum of exactly 22?
546
integer
dynamic_programming
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
xhigh
0.7
0.99
We need answer count sequences length 6 entries in {2,3,4,5} sum 22. Need final answer. Let's compute carefully. Let x_i in {2..5}, sum=22. Let y_i = x_i-2 in {0..3}, sum y_i = 22 - 12 =10. Count 6-tuples y_i in [0,3] sum 10. Total nonnegative without upper bound C(10+5,5)=C(15,5)=3003? 15 choose5=3003 yes. Subtract ...
The number of ordered 6-tuples \((x_1,\dots,x_6)\) with each \(x_i\in\{2,3,4,5\}\) and sum 22 is found by setting \(y_i=x_i-2\in\{0,1,2,3\}\), so \(\sum y_i=10\). Counting such tuples gives \[ [x^{10}](1+x+x^2+x^3)^6=546. \] ANSWER: 546
546
true
true
stop
84
716
2.27
v3
16,000
1
5
387d160186268d50acb3
5e72a4015965592664b8
5e72a4015965592664b8
train
pareto_5efforts
combinatorics_count
2
concise
-1
false
50,000
How many ordered sequences of 6 integers, each between 2 and 5 inclusive, have a sum of exactly 22? Final line: `ANSWER: <answer>`.
How many ordered sequences of 6 integers, each between 2 and 5 inclusive, have a sum of exactly 22?
546
integer
dynamic_programming
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
max
0.7
0.99
We need answer count ordered sequences of length 6, entries in {2,3,4,5}, sum 22. Need compute. Let's solve. Variables xi in [2,5], sum 22. Let yi=xi-2 in [0,3], sum yi = 22 - 12 =10. Count nonnegative y_i <=3 summing 10. Total without upper: C(10+5,5)=C(15,5)=3003. Subtract those with yi>=4. Inclusion-exclusion. Let z...
ANSWER: 546
546
true
true
stop
84
673
2.54
v3
16,000
1
5
927fb54a942d0c1b7106
8929b582aff31ebea0f4
8929b582aff31ebea0f4
train
pareto_5efforts
modular_arithmetic
2
concise
-1
false
50,000
What is the remainder when 13^1574 is divided by 13? Final line: `ANSWER: <answer>`.
What is the remainder when 13^1574 is divided by 13?
0
integer
python_pow_mod
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
low
0.7
0.99
We need answer: remainder when 13^1574 divided by 13. Since base 13, any positive exponent divisible by 13? 13^1574 = 13 * 13^1573, so remainder 0. Need final with answer. Ensure format.
13^1574 is a multiple of 13, so its remainder upon division by 13 is 0. ANSWER: 0
0
true
true
stop
75
113
0.81
v3
16,000
1
5
927fb54a942d0c1b7106
8929b582aff31ebea0f4
8929b582aff31ebea0f4
train
pareto_5efforts
modular_arithmetic
2
concise
-1
false
50,000
What is the remainder when 13^1574 is divided by 13? Final line: `ANSWER: <answer>`.
What is the remainder when 13^1574 is divided by 13?
0
integer
python_pow_mod
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
medium
0.7
0.99
We need answer math question. Need remainder when 13^1574 divided by 13. Since base divisible by 13, any positive exponent yields divisible by 13, remainder 0. Need final line ANSWER: 0. Ensure no extra? Could include reasoning. Final answer exact format.
The number \(13^{1574}\) is a power of 13, so it is divisible by 13. Therefore, the remainder upon division by 13 is 0. ANSWER: 0
0
true
true
stop
76
125
0.95
v3
16,000
1
5
927fb54a942d0c1b7106
8929b582aff31ebea0f4
8929b582aff31ebea0f4
train
pareto_5efforts
modular_arithmetic
2
concise
-1
false
50,000
What is the remainder when 13^1574 is divided by 13? Final line: `ANSWER: <answer>`.
What is the remainder when 13^1574 is divided by 13?
0
integer
python_pow_mod
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
high
0.7
0.99
We need answer problem: remainder when 13^1574 divided by 13. Trivial: 13^1574 divisible by 13, remainder 0. Need final with reasoning and answer line. Ensure no hidden trick? 13^1574 mod 13 = 0. Yes.
The number \(13^{1574}\) is a power of 13, so it is divisible by 13. Therefore the remainder upon division by 13 is 0. ANSWER: 0
0
true
true
stop
77
130
0.77
v3
16,000
1
5
927fb54a942d0c1b7106
8929b582aff31ebea0f4
8929b582aff31ebea0f4
train
pareto_5efforts
modular_arithmetic
2
concise
-1
false
50,000
What is the remainder when 13^1574 is divided by 13? Final line: `ANSWER: <answer>`.
What is the remainder when 13^1574 is divided by 13?
0
integer
python_pow_mod
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
xhigh
0.7
0.99
We need answer remainder 13^1574 divided by 13. Trivial: 13^anything positive divisible by 13, remainder 0. Need final line. Ensure no weird.
13^1574 is a power of 13, so it is divisible by 13. Therefore the remainder is 0. ANSWER: 0
0
true
true
stop
77
91
1.08
v3
16,000
1
5
927fb54a942d0c1b7106
8929b582aff31ebea0f4
8929b582aff31ebea0f4
train
pareto_5efforts
modular_arithmetic
2
concise
-1
false
50,000
What is the remainder when 13^1574 is divided by 13? Final line: `ANSWER: <answer>`.
What is the remainder when 13^1574 is divided by 13?
0
integer
python_pow_mod
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
max
0.7
0.99
We need answer remainder 13^1574 divided by 13. That's 0. Need final line ANSWER: 0. Simple. But maybe trick? 13^1574 divisible by 13 yes remainder 0. Ensure final.
Since \(13^{1574}\) is a power of 13, it is divisible by 13. Therefore the remainder is 0. ANSWER: 0
0
true
true
stop
77
108
0.81
v3
16,000
1
5
43253dcd0b9988e37f23
a557fdf919d0c5291c46
a557fdf919d0c5291c46
train
pareto_5efforts
shortest_path
2
concise
-1
false
50,000
An undirected road network has these roads (with lengths): - A–B: 3 - B–D: 9 - F–G: 5 - B–F: 11 - D–E: 9 - A–F: 12 - G–C: 10 - E–B: 2 - A–G: 3 - A–D: 8 - C–E: 3 - B–C: 1 What is the length of the shortest route from A to G? Final line: `ANSWER: <answer>`.
An undirected road network has these roads (with lengths): - A–B: 3 - B–D: 9 - F–G: 5 - B–F: 11 - D–E: 9 - A–F: 12 - G–C: 10 - E–B: 2 - A–G: 3 - A–D: 8 - C–E: 3 - B–C: 1 What is the length of the shortest route from A to G?
3
integer
dijkstra
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
low
0.7
0.99
We need solve shortest path undirected weighted. Need final answer. Let's compute. Nodes A,B,C,D,E,F,G. Edges: AB3 BD9 FG5 BF11 DE9 AF12 GC10 EB2 AG3 AD8 CE3 BC1 Need shortest A to G. Direct AG=3. Since undirected, route length 3. Is there shorter? no negative. So answer 3. Need final with answer. Ensure no trick? sh...
The direct road A–G has length 3, and all edge lengths are positive, so no alternate route can be shorter. ANSWER: 3
3
true
true
stop
179
167
8.12
v3
16,000
1
5
43253dcd0b9988e37f23
a557fdf919d0c5291c46
a557fdf919d0c5291c46
train
pareto_5efforts
shortest_path
2
concise
-1
false
50,000
An undirected road network has these roads (with lengths): - A–B: 3 - B–D: 9 - F–G: 5 - B–F: 11 - D–E: 9 - A–F: 12 - G–C: 10 - E–B: 2 - A–G: 3 - A–D: 8 - C–E: 3 - B–C: 1 What is the length of the shortest route from A to G? Final line: `ANSWER: <answer>`.
An undirected road network has these roads (with lengths): - A–B: 3 - B–D: 9 - F–G: 5 - B–F: 11 - D–E: 9 - A–F: 12 - G–C: 10 - E–B: 2 - A–G: 3 - A–D: 8 - C–E: 3 - B–C: 1 What is the length of the shortest route from A to G?
3
integer
dijkstra
true
beam
Ollama Cloud (OpenAI-compatible endpoint), model tag 'beam'
medium
0.7
0.99
We need solve shortest path undirected weighted graph. Need final answer. Need compute carefully. Graph nodes A,B,C,D,E,F,G. Edges weights. Need shortest A to G. Let's list edges: A-B 3 B-D 9 F-G 5 B-F 11 D-E 9 A-F 12 G-C 10 E-B 2 A-G 3 A-D 8 C-E 3 B-C 1 Undirected. Need shortest route from A to G. Direct A-G 3. So ...
The direct road A–G has length 3. Since all road lengths are positive, no indirect route can be shorter than 3. ANSWER: 3
3
true
true
stop
180
240
1.02
v3
16,000
1
5
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Beam Verified Reasoning Traces

by Marshoot Lab

7,632 reasoning traces from Reflection's Beam-1.0-501B-A23B on 3,595 procedurally generated problems across 13 task families and 7 difficulty levels. Every answer key is computed by code and re-derived by a second, independent solver, so every trace carries a trustworthy correct/incorrect label.

The dataset is packaged four ways, so you can use it for supervised fine-tuning, preference training, reinforcement learning with verifiable rewards, or simply as a fine-grained evaluation of Beam. The generators, the independent verifier and the audit scripts are included in code/, so every number on this page can be reproduced.

Quickstart

from datasets import load_dataset

repo = "MarshootLab/beam-verified-reasoning-traces"
full  = load_dataset(repo, "full_traces")       # every Beam attempt, right or wrong
sft   = load_dataset(repo, "sft_verified")      # one verified trace per problem
pairs = load_dataset(repo, "preference_pairs")  # filter by pair_type
rl    = load_dataset(repo, "rlvr_prompts")      # prompt + verified answer

hard = rl["train"].filter(lambda x: x["beam_pass_rate"] < 1.0)  # problems Beam sometimes failed

Ready for TRL out of the box

from trl import SFTTrainer, SFTConfig, DPOTrainer, DPOConfig

# SFT on verified reasoning (assistant turn = <think>reasoning</think> + final answer)
sft_ds = sft["train"].map(lambda x: {"messages": x["messages_with_reasoning"]},
                          remove_columns=sft["train"].column_names)
SFTTrainer(model="your-model", train_dataset=sft_ds, args=SFTConfig(output_dir="sft"))

# DPO on correct-vs-incorrect pairs: `prompt`, `chosen`, `rejected` columns are already in TRL's standard format
dpo_ds = pairs["train"].filter(lambda x: x["pair_type"] == "correctness")
DPOTrainer(model="your-model", train_dataset=dpo_ds, args=DPOConfig(output_dir="dpo"))

Use messages instead of messages_with_reasoning if you only want the short final answers (median 25 characters) without the reasoning.

Why this dataset

  • Labels you can trust. Answers are not judged by another LLM. Each problem is generated together with its exact answer, and a separate solver that only reads the prompt text (and uses a different algorithm) must agree. Result: 0 disagreements on 3,595 problems.
  • Real failures, not just successes. Beam is right 96.5% of the time overall, but the remaining errors are concentrated and reproducible: combinatorics, date arithmetic and multi-step string transformations at low reasoning effort. These are exactly the examples useful for preference and RL training.
  • Controlled variation. Each problem has a family, difficulty level, prompt style and (for some) distractor sentences, and the same core problem is sometimes asked in 4 styles or at 5 reasoning efforts. This lets you measure what actually changes model behaviour.
  • Leak-free split. Train/test are split by core problem (style variants and near-duplicates stay together), so no test problem has a paraphrase in train.

At a glance

Model Beam-1.0-501B-A23B as served by Ollama Cloud's OpenAI-compatible API under the tag beam (serving precision not published by the provider; see Limitations)
Sampling temperature 0.7, top_p 0.99 (the settings in Beam's model card), max_tokens 16,000 (32,768 for the v4 rescue subset)
Traces 7,632 (6,859 train / 773 test)
Unique problems 3,595 (3,237 train / 358 test)
Task families 13
Difficulty levels 1-5 for all families, 6-7 for the 7 families whose generators scale further
Reasoning efforts low, high (main grid, hard tier v2); low, medium, high, xhigh, max (Pareto subset); high, max (rescue subset)
Prompt styles concise, standard, case_study, trap_distractor
Answer keys independently re-verified 3,595 / 3,595 (0 mismatches)
Beam accuracy (all traces) 96.5% (lower than v3's 96.9% because v4 deliberately adds harder problems)
Language English only

v4 additions (October 2026)

v4 adds 322 new Beam traces, all generated through Ollama Cloud (tag beam) with the same sampling settings, and every new answer key re-derived by the independent solver (0 mismatches).

Hard tier v2 (subset = hard_tier_v2): 135 new problems at difficulty 5-7 in the three families where Beam still fails (combinatorics_count, date_arithmetic, string_pipeline, 45 each), each solved at low and high effort.

Family Low effort High effort
combinatorics_count 68.9% (n=45) 86.7% (n=45)
date_arithmetic 84.4% (n=45) 100.0% (n=45)
string_pipeline 68.9% (n=45) 97.8% (n=45)
All 74.1% (median 631 tokens) 94.8% (median 1,544 tokens, 6 truncated at 16k)

These are the main source of the new correct-vs-incorrect preference pairs.

Rescue subset (subset = rescue_32k): problems that had no correct trace in v3 were re-asked at high and max effort with max_tokens = 32,768. Of the 28 problems reached so far, 26 now have a correct trace (high 25/27, max 24/25 correct). This subset is partial: the remaining 25 problems produce answers close to the 32k-token limit and repeatedly exceeded our client timeout, so they were not completed for this release. They stay in rlvr_prompts with their v3 pass rate.

Results

Beam error rate by task family

Beam error rate by difficulty level

All intervals are Wilson 95% confidence intervals. Numbers in this section come from the v3 traces in full_traces (both splits); v4 results are reported separately above.

By reasoning effort (main grid, 2,600 traces per effort, identical problems):

Effort Accuracy (95% CI) Median completion tokens Median latency
low 95.2% (94.3-95.9) 433 1.8 s
high 99.0% (98.6-99.4) 811 3.0 s

High effort removes about 80% of low-effort errors for roughly 1.9x the tokens.

Pareto subset (the same 130 problems, 10 per family, each solved at all 5 efforts):

Effort Accuracy (95% CI) Median completion tokens Mean completion tokens Median latency Truncated
low 95.4% (90.3-97.9) 430 534 2.0 s 0
medium 97.7% (93.4-99.2) 695 835 2.8 s 0
high 99.2% (95.8-99.9) 738 1,004 2.7 s 1
xhigh 97.7% (93.4-99.2) 660 923 2.6 s 1
max 97.7% (93.4-99.2) 608 936 2.5 s 1

Two observations, both stated with caution. First, xhigh and max did not spend more tokens than high on these problems; their medians were lower. On short, well-defined tasks the higher settings do not appear to translate into longer reasoning. Second, with 130 problems per effort the accuracy differences among medium, high, xhigh and max are not statistically significant: high made 1 error, xhigh and max made 3 each. One error at each of these three levels was the same kind: a combinatorics answer cut off at the 16,000-token limit (19 of the 20 truncations in the whole dataset are combinatorics). We do not claim xhigh or max are worse than high; on these tasks, going beyond high brought no measurable gain in accuracy or token use. Latency depends on the serving endpoint and load and should be read as indicative only.

By prompt style: concise 96.9%, standard 97.0%, case_study 97.0%, trap_distractor 96.8%. Beam is robust to rewording and to irrelevant distractor sentences on these tasks; no style effect is detectable.

Hardest cells (low + high pooled): combinatorics level 7 (73%, n=30), combinatorics level 5 (75%, n=106), combinatorics level 4 (81%, n=106), date arithmetic level 7 (83%, n=30), string pipelines level 7 (83%, n=30), string pipelines level 6 (87%, n=30).

Failure case studies

Two real examples from the data, where Beam failed at low effort and succeeded at high effort on the identical prompt. Excerpts are verbatim apart from trimming.

1. Combinatorics, level 3: correct method, wrong subtraction (instance_id 544e5cddf2a4eded45fb)

How many ordered sequences of 4 integers, each between 2 and 6 inclusive, have a sum of exactly 21?

Verified answer: 20.

Low effort (398 tokens), answered 60:

Total without upper bound: C(16,3)=560. [...] subtract 4*165=660. But 560-660 negative; need higher intersections. Two variables >=5: [...] add 6*20=120. [...] Total = 560 - 660 + 120 = 60. Check. Answer 60.

High effort (667 tokens), answered 20:

[...] So total 560 -660 +120 =20. Need check. Alternatively enumerate. Answer 20.

Both runs set up the same inclusion-exclusion with identical terms. The low-effort run even noticed the intermediate value was negative, then made a plain arithmetic slip in the final line and said "Check" without re-checking. The error is in execution, not in understanding.

2. Date arithmetic, level 7: right date, weekday shifted the wrong way (instance_id 2c26d2bf51a5f4253497)

Start from Thursday, August 14, 2003. Subtract 162 days, then add 89 days, then subtract 139 days, then add 294 days, then subtract 24 days, then add 40 days, then add 8 days, then subtract 154 days. What is the resulting date and weekday?

Verified answer: 2003-06-27 Friday.

Low effort (356 tokens), answered 2003-06-27 Wednesday:

Weekday: start Thursday. -48 days mod 7 = -48+49=1, so one day before Thursday = Wednesday. [...] I think yes.

High effort (898 tokens), answered 2003-06-27 Friday:

-48 days ≡ +1 day modulo 7. Thursday +1 = Friday? Need check. [...] subtract 6 more days [...] Thu -1 Wed, -2 Tue, -3 Mon, -4 Sun, -5 Sat, -6 Fri. Yes Friday.

The low-effort run computed the residue correctly (+1) and then applied it in the wrong direction. The high-effort run hit the same doubt, verified with a second method (counting back day by day) and caught it. This pattern, a correct intermediate value followed by a sign or direction slip that only an explicit second check catches, is typical of the low-effort failures in dates and combinatorics.

Where it tops out: shortest path, Venn counting and work rates were solved 100% at both efforts, and inventory and modular arithmetic were above 99.5%. These families are saturated for Beam at the difficulties our generators can produce; they remain useful as clean SFT data and as regression checks, but they do not separate strong models.

The four configurations

Config Rows (train / test) One row is Use it for
full_traces 6,859 / 773 one Beam attempt, correct or not, with all metadata evaluation, analysis, filtering your own subsets
sft_verified 3,200 / 357 the shortest correct, complete, strictly formatted trace per problem, as messages (answer only) and messages_with_reasoning (reasoning in <think> tags + answer) supervised fine-tuning on verified reasoning
preference_pairs 1,380 / 155 two Beam answers to the same prompt, labelled by pair_type, with TRL-ready prompt / chosen / rejected columns (reasoning in <think> tags) DPO / reward modelling
rlvr_prompts 3,237 / 358 a problem with its verified answer and Beam's empirical pass rate, no model output RL with verifiable rewards, curriculum by difficulty

Because sft_verified keeps the shortest correct trace, it is mostly low-effort reasoning (2,593 of 3,064 train rows are low, 448 high, 23 medium/xhigh/max). Filter on reasoning_effort if you want longer, more self-checking traces. sft_verified covers 3,557 of the 3,595 problems; the other 38 never received a correct, complete, strictly formatted answer from Beam. beam_pass_rate in rlvr_prompts is the fraction of Beam attempts on that problem that were correct (2 to 5 attempts, see beam_attempts), a ready-made difficulty signal.

Preference pair types

pair_type Train / test Chosen Rejected Notes
correctness 206 / 17 correct, cleanly finished incorrect (wrong, empty or truncated) the hard signal; mostly date arithmetic, combinatorics and strings
concise_reasoning 1,174 / 138 correct, strict format, at most half the tokens correct, strict format, longer for training shorter reasoning; in 1,198 of 1,246 pairs chosen is low effort and rejected is high effort

Both answers in a concise_reasoning pair are correct, so these pairs teach brevity, not accuracy; use them only if that is what you want. We also considered format-compliance pairs but did not include them: 209 of the 212 correct answers without a strict ANSWER: line were work-rate answers written as ANSWER: 120 minutes instead of ANSWER: 120, and since the prompts never forbid a unit, preferring one over the other would not be justified.

Key fields (full_traces)

Field Meaning
instance_id unique id of the exact prompt
core_problem_id id of the underlying problem; style variants share it
split_group_id grouping used for the train/test split (merges near-duplicates)
subset main_grid, pareto_5efforts, robustness_4styles or hard_tier
family, difficulty, style, has_distractors how the problem was generated
prompt exact text sent to Beam (includes the answer-format instruction)
core_prompt the problem without styling or format instruction
answer, answer_format verified answer and its format (integer, fraction, date, string, list...)
solver_type, key_verified_independently how the key was computed; always true here
reasoning the reasoning text returned by the API's reasoning field
response Beam's visible answer
extracted_answer answer parsed from the final ANSWER: line (or a lenient fallback)
is_correct extracted answer equals the key after canonical normalisation
is_correct_strict_format correct and given on a proper ANSWER: line
finish_reason, prompt_tokens, completion_tokens, latency_s generation metadata (completion_tokens includes reasoning; the endpoint did not report a separate reasoning-token count)
beam_pass_rate, beam_attempts fraction of Beam attempts on this exact prompt that were correct, and how many attempts there were

Task families

Each answer key is computed twice by two separate code paths: once by the generator, which knows the problem's internal structure, and once by the verifier, which only sees the prompt text, parses it back into a problem, and solves it with a different method.

Family What the model must do Levels Generator solver Independent verifier (prompt text only)
Inventory word problems track a quantity through a sequence of operations 1-7 state simulation on the internal operation list re-parses each sentence and simulates
Date arithmetic add or subtract days across month and year boundaries 1-7 Python datetime ordinal-day arithmetic, plus a check of the stated start weekday
Ordering logic find the unique order satisfying clues 1-5 brute force over permutations (internal constraints) re-parses clues and searches permutations
Code tracing predict the output of a short Python program 1-7 execution of the generated program executes the code as printed in the prompt
Combinatorics count sequences with constraints 1-7 forward dynamic programming brute-force enumeration, or memoised recursion when enumeration is too large
String pipelines apply a chain of string transformations 1-7 built-in transformation functions separately written interpreter of the English instructions
Work rates combined-work timing 1-5 exact fractions LCM of the individual times
Modular arithmetic large powers and residues 1-5 Python pow(a, b, m) hand-written square-and-multiply
Shortest path weighted shortest route in a graph 1-7 Dijkstra Floyd-Warshall
Probability exact probability as a fraction 1-7 closed-form hypergeometric with exact fractions brute-force enumeration of all draws
Knights & knaves identify truth-tellers and liars 1-5 truth-table enumeration on internal statements re-parses the statements and enumerates
Meeting scheduling earliest common free slot 1-5 interval scan minute-by-minute bitmap
Venn counting inclusion-exclusion counting 1-5 explicit set enumeration region decomposition from the stated counts

For a few families (inventory, ordering, knights & knaves) both sides use a similar algorithm; their independence comes from the verifier re-reading the English text rather than trusting the generator's internal data, which catches wording errors such as an ambiguous or misleading sentence.

Ordering logic, work rates, modular arithmetic, knights & knaves, meeting scheduling and Venn counting are capped at level 5: beyond that our generators either stop producing meaningfully harder instances or produce prompts too long to be natural.

How it was built

Code for every step is in code/: tasks.py and tasks_v2.py (generators and canonical grading), verify.py (independent verifier), run.py (resumable generation), audit.py (quality audit), package.py (splits and configurations), charts.py (figures), check_release.py (one-command re-check of the published files) and reward_fn.py (verifiable reward for GRPO/RLVR).

  1. Generate. Deterministic, seeded generators produce each problem and its exact answer. Names (80), items (40) and words (40) are varied, with 8-10 narrative contexts per family and 15 distractor sentence types.
  2. Verify the key. A second solver parses only the prompt text and solves it with a different algorithm. Any disagreement blocks release; the final run had none.
  3. Ask Beam. Each prompt asks for a final line ANSWER: <answer>. Calls used the official reasoning-effort levels, temperature 0.7, top_p 0.99 and max_tokens 16,000, one request at a time.
  4. Grade. Answers are normalised by format (integers, fractions, dates, lists, strings) and compared to the key. Grading was re-run from scratch during the audit with 0 changes.
  5. Audit. Schema checks, exact and MinHash near-duplicate detection, manual review of failures, and a check that no core problem appears in two subsets.
  6. Split. About 10% of split groups go to test, by hash of split_group_id.

Reproduce the audit

Everything needed is in this repo. From a clone (or with nothing but the scripts, which then fetch the data from the Hub):

pip install -r requirements.txt
python code/check_release.py

It re-derives all 3,595 answer keys with the independent prompt-only verifier, re-grades all 7,632 Beam responses, and checks train/test leakage. Expected output (about a minute on a laptop CPU):

traces            7,632 (6,859 train / 773 test)
unique problems   3,595
key mismatches    0 / 3,595
regrade changes   0 / 7,632
train/test leaks  cores 0, split groups 0
Beam accuracy     96.46%

Reward function for GRPO / RLVR

code/reward_fn.py wraps the same canonical grader as TRL-style reward functions (correctness_reward, 1.0 or 0.0, and an optional format_reward bonus of 0.2), reading the answer, answer_format and family columns of rlvr_prompts:

import sys; sys.path.append("code")
from datasets import load_dataset
from trl import GRPOTrainer, GRPOConfig
from reward_fn import correctness_reward, format_reward

ds = load_dataset("MarshootLab/beam-verified-reasoning-traces", "rlvr_prompts", split="train")
trainer = GRPOTrainer(model="your-model", reward_funcs=[correctness_reward, format_reward],
                      args=GRPOConfig(output_dir="out"), train_dataset=ds)

The reward functions are tested on example completions; we have not run a training job with them.

Quality audit (final)

Check Result
Answer keys disagreeing with the independent solver 0 / 3,595
Missing fields 0
Exact duplicate prompts across different problems 0
Core problems shared across subsets 0
Train/test leakage (core problems or split groups) 0
Near-duplicate problem pairs (MinHash) 13, all same-template problems with different numbers; kept and grouped into the same split
Empty responses / no ANSWER: line 19 / 19 (kept in full_traces, labelled incorrect; excluded from sft_verified)
Truncated at the 16,000-token limit (finish_reason = length) 20 (same treatment); 19 of them are the 19 empty responses. 18 were at high effort or above, 1 at low. 19 of the 20 are combinatorics problems
Raw records outside the final generation plan (superseded runs) 460, dropped before packaging
Distractor sentences that happen to contain the answer number 14 of 444 distractor problems with an integer answer; kept, flagged here so you can filter them
Strict-format compliance 94.0%; of the correct answers not counted as strict, 209 of 212 are work-rate answers with a unit added (120 minutes)

Ambiguity found and fixed. During failure review we found that "remove all vowels (a, e, i, o, u)" was ambiguous for uppercase letters, and several "errors" were Beam using the other reasonable reading. The wording was changed to "in either upper or lower case" and every affected trace was regenerated. Old traces were discarded, not relabelled. In meeting scheduling, one failure matched an alternative reading of a slot boundary; the other failures are genuine model errors.

Limitations

  • Synthetic and templated. Problems come from templates. They test precise multi-step reasoning, not world knowledge, open-ended writing or long-context skills. A model trained only on this data may learn the templates.
  • One model, one sampling setting, one provider. All traces are Beam at temperature 0.7 via Ollama Cloud (tag beam). The provider does not publish the precision it serves Beam at, so if it uses a quantised build, accuracy through Reflection's own API or Hugging Face Inference Providers may differ.
  • Reasoning text. reasoning is what the API returned in its reasoning field. We make no claim that it is the model's complete internal computation, and a correct final answer does not guarantee every reasoning step is correct.
  • Small subsets have wide intervals. The Pareto (130 problems per effort) and hard-tier (105 traces per level per effort) results should be read with their confidence intervals.
  • Saturated families. Several families are near 100% for Beam and add little evaluation signal.
  • Few correctness pairs. Because Beam is accurate, only 223 correct-vs-incorrect pairs exist (182 before v4), concentrated in the hardest families. The larger concise_reasoning set teaches brevity, not accuracy.
  • Pass rates are coarse. beam_pass_rate comes from 2 to 5 attempts, usually at different reasoning efforts, so treat it as a difficulty hint rather than a precise probability.
  • No training experiments. We did not fine-tune any model on this data, so we make no claims about downstream gains.

Licence and credit

Released under Apache-2.0, matching Beam's licence. Model outputs are from Reflection's Beam; problems, answer keys, verification and packaging are by Marshoot Lab.

@misc{marshootlab2026beamtraces,
  title  = {Beam Verified Reasoning Traces},
  author = {Marshoot Lab},
  year   = {2026},
  url    = {https://huggingface.co/datasets/MarshootLab/beam-verified-reasoning-traces}
}
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