Update Automated MNLP evaluation report (2026-05-23)

EVAL_REPORT.md

@@ -2,7 +2,7 @@
 
 - **Model repo:** [`cs-552-2026-mvte/math_model`](https://huggingface.co/cs-552-2026-mvte/math_model)
 - **Owner(s):** group **mvte**
-- **Generated at:** 2026-05-22T03:04:12+00:00 (UTC)
+- **Generated at:** 2026-05-23T14:37:35+00:00 (UTC)
 - **Pipeline:** [mnlp-project-ci](https://github.com/eric11eca/mnlp-project-ci)
 
 _This PR is opened automatically by the course CI. It is **non-blocking** — you do not need to merge it. The next nightly run will refresh this file._
@@ -11,17 +11,110 @@ _This PR is opened automatically by the course CI. It is **non-blocking** — yo
 
 | Benchmark | Accuracy | Status |
 |---|---:|---|
-| Math | — | error (generation_config) |
+| Math | 0.3400 | ok |
 | Knowledge | — | not run |
 | Multilingual | — | not run |
 | Safety | — | not run |
 
-## Errors
+## Sample completions
 
-### math — `generation_config`
+_Prompts are intentionally omitted to avoid revealing benchmark contents. For multi-completion problems, only one completion is shown per sample._
 
-```
-generation_config.json not found: 404 Client Error. (Request ID: Root=1-6a0bd32f-6c0874061110bc1f60075356;f2a3614d-255d-44a4-876b-9db1da0b6b23)
+### Math
 
-Entry Not Found for url: https://huggingface.co/cs-552-2026-mvte/math_model/resolve/main/generation_config.json.
-```
+**Correct** (1 shown)
+
+- **reference**: `1`
+- **overall** (1/8 completions correct)
+- **extracted** (✓): `1`
+- **completion**:
+
+    ```text
+    1. **Define the Problem**: Given positive integers \( n \) and \( k \) with \( n > 2k \), the leader of a Vietnamese Olympiad team provides these values to both the deputy leader and a contestant. The leader then shows the deputy leader a binary string of length \( n \). The deputy leader records every binary string of length \( n \) that differs from the leader's string in exactly \( k \) positio
+    
+    ... [truncated 823 chars] ...
+    
+    number of binary strings that differ from a given string in exactly \( k \) positions and also differ from another given string in exactly \( k \) positions.
+    
+    5. **Counting the Intersections**: For any binary string \( A \) and another binary string \( B \), the intersection of their lists is the set of binary strings that differ from both in exactly \( k \) positions. This can be calculated as \( \binom{n}{k} \times \binom{n}{k} \) because each position in the first string can independently differ in \( k \) positions and each position in the second string can independently differ in \( k \) positions.
+    
+    6. **Determining the Minimum Number of Guesses**: The minimum number of guesses needed to guarantee identifying the leader's original string is given by the formula:
+       \[
+       \left\lceil \frac{\binom{n}{k}}{\binom{n}{k} \times \binom{n}{k}} \right\rceil = \left\lceil \frac{1}{\binom{n}{k}} \right\rceil
+       \]
+       Simplifying, we get:
+       \[
+       \left\lceil \frac{1}{\binom{n}{k}} \right\rceil = 1
+       \]
+       Therefore, the minimum number of guesses needed is 1.
+    
+    7. **Conclusion**: The minimum number of guesses needed to guarantee identifying the leader's original string is \( \boxed{1} \).
+    ```
+
+**Incorrect** (1 shown)
+
+- **reference**: `$g(x)=c, g(x)=\lceil x \rceil, g(x)=\lfloor x \rfloor$`
+- **overall** (0/8 completions correct)
+- **extracted** (✗): `h(x) = 0`
+- **completion**:
+
+    ```text
+    1. **Initial Observation**: Given the functional equation:
+       \[
+       h(x) = h\left(\frac{h(bx - a) + a}{b}\right),
+       \]
+       we need to find all mappings \( h : \mathbb{Q} \to \mathbb{Z} \).
+    
+    2. **Substituting \( a = 0 \)**: Setting \( a = 0 \) in the given equation, we get:
+       \[
+       h(x) = h\left(\frac{h(bx) + 0}{b}\right) = h\left(\frac{h(bx)}{b}\right).
+       \]
+       This simplifies to:
+       \[
+       h(x)
+    
+    ... [truncated 284 chars] ...
+    
+    \) in the equation:
+       \[
+       h(x) = h\left(\frac{h(bx) + h(x)}{b}\right).
+       \]
+       This implies:
+       \[
+       h(x) = h\left(\frac{h(bx)}{b} + h(x)\right).
+       \]
+    
+    5. **Substituting \( x = 0 \)**: Setting \( x = 0 \) in the equation:
+       \[
+       h(0) = h\left(\frac{h(0) + a}{b}\right).
+       \]
+       This simplifies to:
+       \[
+       h(0) = h\left(\frac{h(0) + a}{b}\right).
+       \]
+    
+    6. **Substituting \( b = 0 \)**: Setting \( b = 0 \) in the equation:
+       \[
+       h(x) = h\left(\frac{h(0) + a}{0}\right),
+       \]
+       which is undefined since division by zero is not allowed.
+    
+    7. **Substituting \( a = 0 \) and \( b = 0 \)**: Setting \( a = 0 \) and \( b = 0 \):
+       \[
+       h(x) = h\left(\frac{h(0) + 0}{0}\right),
+       \]
+       which is also undefined.
+    
+    8. **General Case**: For general \( x \in \mathbb{Q} \), we can use the functional equation to show that:
+       \[
+       h(x) = h\left(\frac{h(bx)}{b}\right).
+       \]
+       This implies that \( h(x) \) must be constant for all \( x \).
+    
+    9. **Conclusion**: The only constant mapping that satisfies the given functional equation for all \( x \in \mathbb{Q} \) and for all \( a \in \mathbb{Z} \) and positive integers \( b \) is \( h(x) = 0 \).
+    
+    Thus, the solution is:
+    \[
+    \boxed{h(x) = 0}
+    \]
+    ```