| { |
| "name": "P065 complementary computable-gold battery", |
| "version": "1.0", |
| "n_items": 54, |
| "prompt": "Answer Yes/No and confidence 0-100. ON THE LAST LINE ONLY: ANSWER: Yes|No | CONF: <0-100>", |
| "note": "Every gold label is computed; re-run make_battery.py to re-verify all checks.", |
| "yes_count": 29, |
| "no_count": 25, |
| "items": [ |
| { |
| "id": "nt1", |
| "domain": "numtheory", |
| "tier": "easy", |
| "q": "Is 97 a prime number?", |
| "truth": "Yes", |
| "check": "isprime(97)" |
| }, |
| { |
| "id": "nt2", |
| "domain": "numtheory", |
| "tier": "easy", |
| "q": "Is 91 a prime number?", |
| "truth": "No", |
| "check": "isprime(91)" |
| }, |
| { |
| "id": "nt3", |
| "domain": "numtheory", |
| "tier": "easy", |
| "q": "Is the greatest common divisor of 84 and 126 equal to 21?", |
| "truth": "No", |
| "check": "math.gcd(84,126)==21" |
| }, |
| { |
| "id": "nt4", |
| "domain": "numtheory", |
| "tier": "hard", |
| "q": "Is 2047 a prime number?", |
| "truth": "No", |
| "check": "isprime(2047)" |
| }, |
| { |
| "id": "nt5", |
| "domain": "numtheory", |
| "tier": "hard", |
| "q": "Is the sum of all positive divisors of 28 (including 28 itself) equal to 58?", |
| "truth": "No", |
| "check": "sigma(28)==58" |
| }, |
| { |
| "id": "nt6", |
| "domain": "numtheory", |
| "tier": "hard", |
| "q": "Is 561 divisible by 11?", |
| "truth": "Yes", |
| "check": "561%11==0" |
| }, |
| { |
| "id": "nt7", |
| "domain": "numtheory", |
| "tier": "hard", |
| "q": "Is 12! equal to 479001601?", |
| "truth": "No", |
| "check": "math.factorial(12)==479001601" |
| }, |
| { |
| "id": "nt8", |
| "domain": "numtheory", |
| "tier": "hard", |
| "q": "Is 1517 a prime number?", |
| "truth": "No", |
| "check": "isprime(1517)" |
| }, |
| { |
| "id": "nt9", |
| "domain": "numtheory", |
| "tier": "easy", |
| "q": "Is 1000 a power of 2?", |
| "truth": "No", |
| "check": "(1000&(1000-1))==0 and 1000>0" |
| }, |
| { |
| "id": "cd1", |
| "domain": "code", |
| "tier": "easy", |
| "q": "Does the Python statement print(len('mississippi')) output 10?", |
| "truth": "No", |
| "check": "len('mississippi')==10" |
| }, |
| { |
| "id": "cd2", |
| "domain": "code", |
| "tier": "easy", |
| "q": "Does the Python statement print(2**5) output 25?", |
| "truth": "No", |
| "check": "(2**5)==25" |
| }, |
| { |
| "id": "cd3", |
| "domain": "code", |
| "tier": "easy", |
| "q": "Does the Python statement print(7//2) output 3?", |
| "truth": "Yes", |
| "check": "(7//2)==3" |
| }, |
| { |
| "id": "cd4", |
| "domain": "code", |
| "tier": "hard", |
| "q": "Does the Python statement print(list(range(0,10,3))) output [0, 3, 6, 9, 12]?", |
| "truth": "No", |
| "check": "list(range(0,10,3))==[0,3,6,9,12]" |
| }, |
| { |
| "id": "cd5", |
| "domain": "code", |
| "tier": "hard", |
| "q": "Does the Python statement print(bool([])) output True?", |
| "truth": "No", |
| "check": "bool([])==True" |
| }, |
| { |
| "id": "cd6", |
| "domain": "code", |
| "tier": "hard", |
| "q": "Does the Python statement print(len({1,1,2,3,3,3})) output 3?", |
| "truth": "Yes", |
| "check": "len({1,1,2,3,3,3})==3" |
| }, |
| { |
| "id": "cd7", |
| "domain": "code", |
| "tier": "hard", |
| "q": "Does the Python statement print('ab'*3) output 'ababab'?", |
| "truth": "Yes", |
| "check": "('ab'*3)=='ababab'" |
| }, |
| { |
| "id": "cd8", |
| "domain": "code", |
| "tier": "hard", |
| "q": "Does the Python statement print(sum(range(1,11))) output 56?", |
| "truth": "No", |
| "check": "sum(range(1,11))==56" |
| }, |
| { |
| "id": "cd9", |
| "domain": "code", |
| "tier": "hard", |
| "q": "Does the Python statement print(round(2.5)) output 3?", |
| "truth": "No", |
| "check": "round(2.5)==3" |
| }, |
| { |
| "id": "sq1", |
| "domain": "seq", |
| "tier": "easy", |
| "q": "Is the 10th Fibonacci number (with F1=F2=1) equal to 54?", |
| "truth": "No", |
| "check": "fib(10)==54" |
| }, |
| { |
| "id": "sq2", |
| "domain": "seq", |
| "tier": "easy", |
| "q": "Is the number of permutations of 5 distinct items equal to 120?", |
| "truth": "Yes", |
| "check": "math.factorial(5)==120" |
| }, |
| { |
| "id": "sq3", |
| "domain": "seq", |
| "tier": "hard", |
| "q": "Is the binomial coefficient C(8,3) equal to 58?", |
| "truth": "No", |
| "check": "math.comb(8,3)==58" |
| }, |
| { |
| "id": "sq4", |
| "domain": "seq", |
| "tier": "hard", |
| "q": "Is 2^0 + 2^1 + ... + 2^7 equal to 256?", |
| "truth": "No", |
| "check": "sum(2**i for i in range(8))==256" |
| }, |
| { |
| "id": "sq5", |
| "domain": "seq", |
| "tier": "hard", |
| "q": "Is the 5th Catalan number equal to 42?", |
| "truth": "Yes", |
| "check": "catalan(5)==42" |
| }, |
| { |
| "id": "sq6", |
| "domain": "seq", |
| "tier": "easy", |
| "q": "Is the number of subsets of a 6-element set equal to 128?", |
| "truth": "No", |
| "check": "2**6==128" |
| }, |
| { |
| "id": "sq7", |
| "domain": "seq", |
| "tier": "hard", |
| "q": "Is the number of distinct arrangements of the letters in 'LEVEL' equal to 60?", |
| "truth": "No", |
| "check": "math.factorial(5)//(math.factorial(2)*math.factorial(2))==60" |
| }, |
| { |
| "id": "sq8", |
| "domain": "seq", |
| "tier": "hard", |
| "q": "Is the 6th triangular number equal to 21?", |
| "truth": "Yes", |
| "check": "6*7//2==21" |
| }, |
| { |
| "id": "sq9", |
| "domain": "seq", |
| "tier": "hard", |
| "q": "Is the least common multiple of 4, 6, and 10 equal to 120?", |
| "truth": "No", |
| "check": "math.lcm(4,6,10)==120" |
| }, |
| { |
| "id": "lg1", |
| "domain": "logic", |
| "tier": "easy", |
| "q": "If P is true and Q is false, is (P AND (NOT Q)) true?", |
| "truth": "Yes", |
| "check": "(True and (not False))==True" |
| }, |
| { |
| "id": "lg2", |
| "domain": "logic", |
| "tier": "hard", |
| "q": "Is NOT(A OR B) logically equivalent to (NOT A) AND (NOT B) for all A,B?", |
| "truth": "Yes", |
| "check": "all((not(A or B))==((not A) and (not B)) for A in [True,False] for B in [True,False])" |
| }, |
| { |
| "id": "lg3", |
| "domain": "logic", |
| "tier": "easy", |
| "q": "If all Bloops are Razzies and all Razzies are Lazzies, must all Bloops be Lazzies?", |
| "truth": "Yes", |
| "check": "True" |
| }, |
| { |
| "id": "lg4", |
| "domain": "logic", |
| "tier": "hard", |
| "q": "Is 'P implies Q' logically equivalent to 'Q implies P' for all P,Q?", |
| "truth": "No", |
| "check": "all(((not P) or Q)==((not Q) or P) for P in [True,False] for Q in [True,False])" |
| }, |
| { |
| "id": "lg5", |
| "domain": "logic", |
| "tier": "hard", |
| "q": "Given 'if it rains then the ground is wet' and 'the ground is wet', does it logically follow that it rained?", |
| "truth": "No", |
| "check": "False" |
| }, |
| { |
| "id": "lg6", |
| "domain": "logic", |
| "tier": "hard", |
| "q": "Is the negation of 'for all x, P(x)' equivalent to 'there exists x such that not P(x)'?", |
| "truth": "Yes", |
| "check": "True" |
| }, |
| { |
| "id": "lg7", |
| "domain": "logic", |
| "tier": "hard", |
| "q": "If A implies B and B is false, must A be false?", |
| "truth": "Yes", |
| "check": "all((not(((not A) or B) and (not B))) or (not A) for A in [True,False] for B in [True,False])" |
| }, |
| { |
| "id": "lg8", |
| "domain": "logic", |
| "tier": "easy", |
| "q": "Is a conditional statement with a false premise considered true (vacuously)?", |
| "truth": "Yes", |
| "check": "((not False) or True)==True and (((not False) or False)==True)" |
| }, |
| { |
| "id": "lg9", |
| "domain": "logic", |
| "tier": "hard", |
| "q": "If exactly one of A and B is true, is (A XOR B) true?", |
| "truth": "Yes", |
| "check": "((True^False)==1) and ((False^True)==1)" |
| }, |
| { |
| "id": "st1", |
| "domain": "string", |
| "tier": "easy", |
| "q": "Is 'desserts' the reverse of 'stressed'?", |
| "truth": "Yes", |
| "check": "'stressed'[::-1]=='desserts'" |
| }, |
| { |
| "id": "st2", |
| "domain": "string", |
| "tier": "easy", |
| "q": "Do 'listen' and 'silent' use exactly the same multiset of letters?", |
| "truth": "Yes", |
| "check": "sorted('listen')==sorted('silent')" |
| }, |
| { |
| "id": "st3", |
| "domain": "string", |
| "tier": "hard", |
| "q": "Does 'bookkeeper' contain three consecutive doubled letters (oo, kk, ee)?", |
| "truth": "Yes", |
| "check": "'oo' in 'bookkeeper' and 'kk' in 'bookkeeper' and 'ee' in 'bookkeeper'" |
| }, |
| { |
| "id": "st4", |
| "domain": "string", |
| "tier": "hard", |
| "q": "Is the number of vowels (a,e,i,o,u) in 'encyclopedia' equal to 6?", |
| "truth": "No", |
| "check": "sum(c in 'aeiou' for c in 'encyclopedia')==6" |
| }, |
| { |
| "id": "st5", |
| "domain": "string", |
| "tier": "hard", |
| "q": "Ignoring case and spaces, is 'A man a plan a canal Panama' a palindrome?", |
| "truth": "Yes", |
| "check": "(lambda s:s==s[::-1])(''.join(ch.lower() for ch in 'A man a plan a canal Panama' if ch.isalnum()))" |
| }, |
| { |
| "id": "st6", |
| "domain": "string", |
| "tier": "easy", |
| "q": "Does the word 'strengths' have 10 letters?", |
| "truth": "No", |
| "check": "len('strengths')==10" |
| }, |
| { |
| "id": "st7", |
| "domain": "string", |
| "tier": "hard", |
| "q": "Is the 4th character (1-indexed) of 'abcdefg' the letter 'd'?", |
| "truth": "Yes", |
| "check": "'abcdefg'[3]=='d'" |
| }, |
| { |
| "id": "st8", |
| "domain": "string", |
| "tier": "hard", |
| "q": "Are there exactly 4 letters strictly between 'a' and 'f' in the alphabet?", |
| "truth": "Yes", |
| "check": "len([c for c in 'bcde'])==4" |
| }, |
| { |
| "id": "st9", |
| "domain": "string", |
| "tier": "hard", |
| "q": "Does 'uncopyrightable' have 15 letters with no repeated letter?", |
| "truth": "Yes", |
| "check": "len('uncopyrightable')==15 and len(set('uncopyrightable'))==15" |
| }, |
| { |
| "id": "un1", |
| "domain": "units", |
| "tier": "easy", |
| "q": "Is 5 kilometers equal to 5000 meters?", |
| "truth": "Yes", |
| "check": "5*1000==5000" |
| }, |
| { |
| "id": "un2", |
| "domain": "units", |
| "tier": "easy", |
| "q": "Was the year 1900 a leap year?", |
| "truth": "No", |
| "check": "(1900%4==0 and (1900%100!=0 or 1900%400==0))" |
| }, |
| { |
| "id": "un3", |
| "domain": "units", |
| "tier": "easy", |
| "q": "Was the year 2000 a leap year?", |
| "truth": "Yes", |
| "check": "(2000%4==0 and (2000%100!=0 or 2000%400==0))" |
| }, |
| { |
| "id": "un4", |
| "domain": "units", |
| "tier": "hard", |
| "q": "Is 90 degrees Fahrenheit greater than 30 degrees Celsius?", |
| "truth": "Yes", |
| "check": "(90-32)*5/9 > 30" |
| }, |
| { |
| "id": "un5", |
| "domain": "units", |
| "tier": "easy", |
| "q": "Is 2.5 hours equal to 160 minutes?", |
| "truth": "No", |
| "check": "2.5*60==160" |
| }, |
| { |
| "id": "un6", |
| "domain": "units", |
| "tier": "hard", |
| "q": "Does the year 2024 have 366 days?", |
| "truth": "Yes", |
| "check": "(2024%4==0 and (2024%100!=0 or 2024%400==0))" |
| }, |
| { |
| "id": "un7", |
| "domain": "units", |
| "tier": "hard", |
| "q": "Is 1 mile longer than 1.5 kilometers?", |
| "truth": "Yes", |
| "check": "1.609344 > 1.5" |
| }, |
| { |
| "id": "un8", |
| "domain": "units", |
| "tier": "easy", |
| "q": "Is 0 degrees Celsius equal to 273.15 Kelvin?", |
| "truth": "Yes", |
| "check": "abs((0+273.15)-273.15)<1e-9" |
| }, |
| { |
| "id": "un9", |
| "domain": "units", |
| "tier": "hard", |
| "q": "Is 1 gibibyte (2^30 bytes) more than 1.07 billion bytes?", |
| "truth": "Yes", |
| "check": "2**30 > 1.07e9" |
| } |
| ] |
| } |
