results: 76
This data as json
| id | model_name | task_name | sample_id | prompt_actual | prompt_full | gold_answer | is_correct | extracted_answers | stop_reasons | response_1 |
|---|---|---|---|---|---|---|---|---|---|---|
| 76 | grpo-gsm8k-train-13ep-success_global_step_50 | gsm8k_main(0) | 75 | Question: Luke is spending time at the beach building sandcastles. He eventually notices that each level of a sandcastle will have half the square footage as the level below it. If he makes a 4 leveled sandcastle where the top level has a square footage of 16, what is the average square footage of a level? Answer: | <|im_start|>system You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|> <|im_start|>user Output format: end your response with \boxed{<answer>} where <answer> is the final answer. Question: Luke is spending time at the beach building sandcastles. He eventually notices that each level of a sandcastle will have half the square footage as the level below it. If he makes a 4 leveled sandcastle where the top level has a square footage of 16, what is the average square footage of a level? Answer:<|im_end|> <|im_start|>assistant | 60 | 0 | [7.5] | [stop:-] | To find the average square footage of a level in Luke's 4-level sandcastle, we need to determine the square footage of each level and then calculate the average. Given: - The top level (4th level) has a square footage of 16. - Each level below has half the square footage of the level above it. Let's denote the square footage of the 4th level as \( A_4 = 16 \). The square footage of the 3rd level (\( A_3 \)) is: \[ A_3 = \frac{A_4}{2} = \frac{16}{2} = 8 \] The square footage of the 2nd level (\( A_2 \)) is: \[ A_2 = \frac{A_3}{2} = \frac{8}{2} = 4 \] The square footage of the 1st level (\( A_1 \)) is: \[ A_1 = \frac{A_2}{2} = \frac{4}{2} = 2 \] Now, we sum the square footages of all four levels: \[ A_1 + A_2 + A_3 + A_4 = 2 + 4 + 8 + 16 = 30 \] To find the average square footage per level, we divide the total square footage by the number of levels: \[ \text{Average} = \frac{30}{4} = 7.5 \] Thus, the average square footage of a level is: \[ \boxed{7.5} \] |