RL Iteration 7

This HTML log was generated by logtree during RL training. It shows rollouts and rewards for a subset of trajectory groups in this iteration. To customize what gets logged, modify the logtree calls in your Env implementation (see examples in tinker_cookbook/recipes/).

Group Rollout

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Tomas is hoping to run a marathon next year, which is 26.3 miles. He knows that each month he trains, he can run twice as far as the month before. If he can run 3 miles during the first month of training, how many total months before the marathon should he start training to ensure he can run far enough?

Policy Response

assistant:

Tomas runs 3 miles in the first month. Each month he trains, he can run twice as far as the month before. We need to find the month where he can run at least 26.3 miles. Month 1: $3$ miles Month 2: $3 \times 2 = 6$ miles Month 3: $6 \times 2 = 12$ miles Month 4: $12 \times 2 = 24$ miles Month 5: $24 \times 2 = 48$ miles Since 24 miles is less than 26.3 miles, he needs to train for a 5th month to ensure he can run far enough. \boxed{5}

Reward

Reward components

key	value
reference_answer	5
format_valid	True
correct	True
format_coef	0.1
reward	1.000

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Policy Response

assistant:

Tomas can run 3 miles in the first month. Each subsequent month, he runs twice as far as the previous month. We need to find the month when his distance is greater than or equal to 26.3 miles. Month 1: $3$ miles Month 2: $3 \times 2 = 6$ miles Month 3: $6 \times 2 = 12$ miles Month 4: $12 \times 2 = 24$ miles Month 5: $24 \times 2 = 48$ miles The distance after 4 months is 24 miles, which is less than 26.3. The distance after 5 months is 48 miles, which is greater than 26.3. Therefore, he should start training 5 months before the marathon. \boxed{5}

Reward

Reward components

key	value
reference_answer	5
format_valid	True
correct	True
format_coef	0.1
reward	1.000

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Policy Response

assistant:

Tomas wants to run a marathon, which is 26.3 miles. He runs twice as far each month, starting with 3 miles. Month 1: $3$ miles (Total: 3) Month 2: $3 \times 2 = 6$ miles (Total: $3 + 6 = 9$) Month 3: $6 \times 2 = 12$ miles (Total: $9 + 12 = 21$) Month 4: $12 \times 2 = 24$ miles (Total: $21 + 24 = 45$) After 3 months, he has run 21 miles, which is not enough. After 4 months, he has run 45 miles, which is more than enough. To ensure he can run far enough, he should train for 4 months. \boxed{4}

Reward

Reward components

key	value
reference_answer	5
format_valid	True
correct	False
format_coef	0.1
reward	0.000

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Policy Response

assistant:

Tomas starts by running 3 miles during the first month. Each subsequent month, he runs twice as far as the month before. We need to find when he runs at least 26.3 miles. - Month 1: $3$ miles - Month 2: $3 \times 2 = 6$ miles - Month 3: $6 \times 2 = 12$ miles - Month 4: $12 \times 2 = 24$ miles In Month 4, he runs 24 miles, which is less than 26.3 miles. - Month 5: $24 \times 2 = 48$ miles In Month 5, he runs 48 miles, which is sufficient to complete the marathon distance. He should have started training 5 months before the marathon. \boxed{5}

Reward

Reward components

key	value
reference_answer	5
format_valid	True
correct	True
format_coef	0.1
reward	1.000

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Policy Response

assistant:

Tomas starts by running 3 miles in the first month. Each subsequent month, he runs twice as far as the month before. He needs to run at least 26.3 miles. Month 1: $3$ miles Month 2: $3 \times 2 = 6$ miles Month 3: $6 \times 2 = 12$ miles Month 4: $12 \times 2 = 24$ miles Month 5: $24 \times 2 = 48$ miles To ensure he can run far enough, he needs to reach a capacity of at least 26.3 miles. After month 4, he runs 24 miles, which is not enough. After month 5, he runs 48 miles, which is more than enough. He should start training 5 months before the marathon. \boxed{5}

Reward

Reward components

key	value
reference_answer	5
format_valid	True
correct	True
format_coef	0.1
reward	1.000

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Policy Response

assistant:

Tomas starts training for the marathon at 3 miles during the first month. Each subsequent month, he doubles his distance. He needs to run at least 26.3 miles during the first month of operation (or as close as possible to ensure he has enough distance). Let $d_n$ be the distance run in month $n$. Month 1: $d_1 = 3$ miles. Control: $3 < 26.3$. Month 2: $d_2 = 3 \times 2 = 6$ miles. Control: $6 < 26.3$. Month 3: $d_3 = 6 \times 2 = 12$ miles. Control: $12 < 26.3$. Month 4: $d_4 = 12 \times 2 = 24$ miles. Control: $24 < 26.3$. Month 5: $d_5 = 24 \times 2 = 48$ miles. Control: $48 \ge 26.3$. Since he can run 48 miles in the fifth month, he has reached his goal. He should start training 5 months before the marathon (assuming he starts training for the marathon that month). \boxed{4} Wait, let me re-read. "How many total months before the marathon should he start training to ensure he can run far enough?" If he needs to start training for the

Reward

Reward components

key	value
reference_answer	5
format_valid	False
correct	False
format_coef	0.1
reward	-0.100

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Policy Response

assistant:

Tomas runs 3 miles in the first month. Each subsequent month, he runs twice as far as the month before. The marathon is 26.3 miles. Month 1: $3$ miles Month 2: $3 \times 2 = 6$ miles Month 3: $6 \times 2 = 12$ miles Month 4: $12 \times 2 = 24$ miles Month 5: $24 \times 2 = 48$ miles After 4 months, he has run $3 + 6 + 12 + 24 = 45$ miles. After 5 months, he will be capable of running 48 miles in that month alone, but the question asks "how many total months before the marathon should he start training". Usually, this implies the number of months required until his capability meets the requirement, or the cumulative total. However, context for "start training to ensure he can run far enough" usually means having accumulated enough distance or having the capability for the distance. Given he runs twice as far each month, after 5 months he can definitely run the marathon (since the distance in month 5 is sufficient). Assuming he needs to run the distance over the course of training months, 45 miles in 4 months leaves a deficit. With month 5, he adds 48 miles. Since he can run huge distances in month 5 after training, he would need minimum 5 months to be capable

Reward

Reward components

key	value
reference_answer	5
format_valid	False
correct	True
format_coef	0.1
reward	0.900

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Policy Response

assistant:

Tomas starts by running 3 miles in the first month. Each month he can double the distance from the previous month. We need to calculate the cumulative distance until he has run at least 26.3 miles. Month 1: Runs 3 miles. Total: 3 miles. Month 2: Runs $3 \times 2 = 6$ miles. Total: $3 + 6 = 9$ miles. Month 3: Runs $6 \times 2 = 12$ miles. Total: $9 + 12 = 21$ miles. Month 4: Runs $12 \times 2 = 24$ miles. Total: $21 + 24 = 45$ miles. After 3 months, he has run 21 miles, which is less than 26.3 miles. After 4 months, he has run 45 miles, which is enough. Therefore, he should start training 4 months before the marathon. \boxed{4}

Reward

Reward components

key	value
reference_answer	5
format_valid	True
correct	False
format_coef	0.1
reward	0.000

Trajectory Details

Trajectory 0 Episode

Episode Details

Turn 1

Step stats

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step_reward	1.000

Step Metrics

Metrics emitted by env.step

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Episode totals

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Trajectory 1 Episode

Episode Details

Turn 1

Step stats

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Step Metrics

Metrics emitted by env.step

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Episode totals

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Trajectory 2 Episode

Episode Details

Turn 1

Step stats

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Step Metrics

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Trajectory 3 Episode

Episode Details

Turn 1

Step stats

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Trajectory 4 Episode

Episode Details

Turn 1

Step stats

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Step Metrics

Metrics emitted by env.step

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Trajectory 5 Episode

Episode Details

Turn 1

Step stats

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Step Metrics

Metrics emitted by env.step

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Trajectory 6 Episode

Episode Details

Turn 1

Step stats

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Step Metrics

Metrics emitted by env.step

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Episode totals

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Trajectory 7 Episode

Episode Details

Turn 1

Step stats

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step_reward	1.000

Step Metrics

Metrics emitted by env.step

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Group Rollout

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Hazel and Razel are twins who share everything they receive. If Hazel received 6 shirts, while Razel received twice the number of shirts as Hazel. How many shirts do they have in total?

Policy Response

assistant:

Hazel received 6 shirts. Razel received twice the number of shirts as Hazel, which is $6 \times 2 = 12$ shirts. Together, they have $6 + 12 = 18$ shirts. \boxed{18}

Reward

Reward components

key	value
reference_answer	18
format_valid	True
correct	True
format_coef	0.1
reward	1.000

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Hazel and Razel are twins who share everything they receive. If Hazel received 6 shirts, while Razel received twice the number of shirts as Hazel. How many shirts do they have in total?

Policy Response

assistant:

Hazel received 6 shirts. Razel received twice the number of shirts as Hazel, which means Razel received $2 \times 6 = 12$ shirts. Since they share everything they receive, the total number of shirts is $6 + 12$. $6 + 12 = 18$ \boxed{18}

Reward

Reward components

key	value
reference_answer	18
format_valid	True
correct	True
format_coef	0.1
reward	1.000

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Hazel and Razel are twins who share everything they receive. If Hazel received 6 shirts, while Razel received twice the number of shirts as Hazel. How many shirts do they have in total?

Policy Response

assistant:

Hazel received 6 shirts. Razel received twice the number of shirts as Hazel, which is $2 \times 6 = 12$ shirts. Since they share everything they receive, the total number of shirts is the sum of their shirts. Total shirts = $6 + 12 = 18$. \boxed{18}

Reward

Reward components

key	value
reference_answer	18
format_valid	True
correct	True
format_coef	0.1
reward	1.000

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Hazel and Razel are twins who share everything they receive. If Hazel received 6 shirts, while Razel received twice the number of shirts as Hazel. How many shirts do they have in total?

Policy Response

assistant:

Hazel received 6 shirts. Razel received twice the number of shirts as Hazel, which is $2 \times 6 = 12$ shirts. They share everything they receive, so we add the shirts together: $6 + 12 = 18$ shirts in total. \boxed{18}

Reward

Reward components

key	value
reference_answer	18
format_valid	True
correct	True
format_coef	0.1
reward	1.000

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Hazel and Razel are twins who share everything they receive. If Hazel received 6 shirts, while Razel received twice the number of shirts as Hazel. How many shirts do they have in total?

Policy Response

assistant:

Reward

Reward components

key	value
reference_answer	18
format_valid	True
correct	True
format_coef	0.1
reward	1.000

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Hazel and Razel are twins who share everything they receive. If Hazel received 6 shirts, while Razel received twice the number of shirts as Hazel. How many shirts do they have in total?

Policy Response

assistant:

Hazel received 6 shirts. Razel received twice the number of shirts as Hazel, so Razel received $2 \times 6 = 12$ shirts. Since they share everything, the total number of shirts is $6 + 12 = 18$. \boxed{18}

Reward

Reward components

key	value
reference_answer	18
format_valid	True
correct	True
format_coef	0.1
reward	1.000

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Hazel and Razel are twins who share everything they receive. If Hazel received 6 shirts, while Razel received twice the number of shirts as Hazel. How many shirts do they have in total?

Policy Response

assistant:

Hazel received 6 shirts. Razel received twice the number of shirts as Hazel, which is $2 \times 6 = 12$ shirts. They share everything they receive. The total number of shirts is $6 + 12 = 18$. \boxed{18}

Reward

Reward components

key	value
reference_answer	18
format_valid	True
correct	True
format_coef	0.1
reward	1.000

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Hazel and Razel are twins who share everything they receive. If Hazel received 6 shirts, while Razel received twice the number of shirts as Hazel. How many shirts do they have in total?

Policy Response

assistant:

Hazel received 6 shirts. Razel received twice the number of shirts as Hazel, so Razel received $2 \times 6 = 12$ shirts. They share everything they receive, but the question asks for the total number of shirts they have. Total shirts = Hazel's shirts + Razel's shirts Total shirts = $6 + 12$ Total shirts = $18$ \boxed{18}

Reward

Reward components

key	value
reference_answer	18
format_valid	True
correct	True
format_coef	0.1
reward	1.000

Trajectory Details

Trajectory 0 Episode

Episode Details

Turn 1

Step stats

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Step Metrics

Metrics emitted by env.step

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Episode totals

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Trajectory 1 Episode

Episode Details

Turn 1

Step stats

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Step Metrics

Metrics emitted by env.step

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Trajectory 2 Episode

Episode Details

Turn 1

Step stats

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Step Metrics

Metrics emitted by env.step

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Trajectory 3 Episode

Episode Details

Turn 1

Step stats

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Step Metrics

Metrics emitted by env.step

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Trajectory 4 Episode

Episode Details

Turn 1

Step stats

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Step Metrics

Metrics emitted by env.step

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Trajectory 5 Episode

Episode Details

Turn 1

Step stats

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Step Metrics

Metrics emitted by env.step

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Trajectory 6 Episode

Episode Details

Turn 1

Step stats

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Step Metrics

Metrics emitted by env.step

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Trajectory 7 Episode

Episode Details

Turn 1

Step stats

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Step Metrics

Metrics emitted by env.step

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Group Rollout

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Tara has a shoebox that is 4 inches tall and 6 inches wide. She puts a square block inside that is 4 inches per side. How many square inches of the box are left uncovered?

Policy Response

assistant:

The shoebox has a height of 4 inches and a width of 6 inches. Assume the base is a rectangle with area $4 \text{ inches} \times 6 \text{ inches} = 24 \text{ square inches}$. Tara puts a square block inside that is 4 inches per side. Assuming she places it on the bottom of the box facing one of the sides so it fits within the dimensions (since $4 \le 6$ and $4 \le 4$), the block has an area of $4 \text{ inches} \times 4 \text{ inches} = 16 \text{ square inches}$. The amount of area left uncovered is the area of the base minus the area of the block: $24 - 16 = 8 \text{ square inches}$. \boxed{8}

Reward

Reward components

key	value
reference_answer	8
format_valid	True
correct	True
format_coef	0.1
reward	1.000

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Tara has a shoebox that is 4 inches tall and 6 inches wide. She puts a square block inside that is 4 inches per side. How many square inches of the box are left uncovered?

Policy Response

assistant:

The shoebox has a height of 4 inches and a width of 6 inches. Assuming the depth is sufficient to hold the block, the base of the shoebox is a rectangle with dimensions $4 \text{ inches} \times 6 \text{ inches}$. The area of the box base is $4 \times 6 = 24 \text{ square inches}$. Tara places a square block with a side of 4 inches inside. The area of the block is $4 \times 4 = 16 \text{ square inches}$. The uncovered area is the base area minus the block area: $24 - 16 = 8 \text{ square inches}$. \boxed{8}

Reward

Reward components

key	value
reference_answer	8
format_valid	True
correct	True
format_coef	0.1
reward	1.000

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Tara has a shoebox that is 4 inches tall and 6 inches wide. She puts a square block inside that is 4 inches per side. How many square inches of the box are left uncovered?

Policy Response

assistant:

Tara has a shoebox that is 4 inches tall and 6 inches wide. Since the problem describes a block placed inside a shoebox with these dimensions while the depth of the shoebox isn't explicitly stated but implied to be sufficient to contain the block, we typically assume the shoebox covers the area defined by its height and width. The block is a square with side length 4 inches. Area of the box: $4 \text{ inches} \times 6 \text{ inches} = 24 \text{ square inches}$. Area of the square block: $4 \text{ inches} \times 4 \text{ inches} = 16 \text{ square inches}$. Uncovered area: $24 - 16 = 8 \text{ square inches}$. \boxed{8}

Reward

Reward components

key	value
reference_answer	8
format_valid	True
correct	True
format_coef	0.1
reward	1.000

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Tara has a shoebox that is 4 inches tall and 6 inches wide. She puts a square block inside that is 4 inches per side. How many square inches of the box are left uncovered?

Policy Response

assistant:

Tara puts a square block with side length 4 inches into a shoebox. First, we need to calculate the area of the block and the area of the box. 1. Calculate the area of the square block. Area of block = side $\times$ side = $4 \times 4 = 16$ square inches. 2. Calculate the area of the shoebox. Area of box = height $\times$ width = $4 \times 6 = 24$ square inches. 3. Calculate the uncovered area. Uncovered area = Area of box - Area of block = $24 - 16 = 8$ square inches. \boxed{8}

Reward

Reward components

key	value
reference_answer	8
format_valid	True
correct	True
format_coef	0.1
reward	1.000

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Tara has a shoebox that is 4 inches tall and 6 inches wide. She puts a square block inside that is 4 inches per side. How many square inches of the box are left uncovered?

Policy Response

assistant:

The shoebox has a height of 4 inches and a width of 6 inches. The block is a square with sides of 4 inches. To find the total area of the box, we calculate the area of the side containing the block (usually assuming it sits on the bottom). The dimensions are $4 \text{ inches} \times 6 \text{ inches}$. The area is $4 \times 6 = 24$ square inches. The block covers an area of $4 \text{ inches} \times 4 \text{ inches} = 16$ square inches. To find the area left uncovered, we subtract the covered area from the total area: $24 - 16 = 8$ square inches. \boxed{8}

Reward

Reward components

key	value
reference_answer	8
format_valid	True
correct	True
format_coef	0.1
reward	1.000

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Tara has a shoebox that is 4 inches tall and 6 inches wide. She puts a square block inside that is 4 inches per side. How many square inches of the box are left uncovered?

Policy Response

assistant:

The shoebox has dimensions 4 inches tall and 6 inches wide. Assuming the shoebox is a rectangular prism with a square base in cross-section or referring to the footprint area of 4 inches by 6 inches for the purpose of the puzzle. The square block is 4 inches per side. To find the uncovered area, first calculate the total area of the box. Assuming the shoebox has a square footprint of 4 inches by 6 inches is incorrect because 4x6 is rectangular. However, usually shoebox problems imply the box holds the block tightly at the top. Let's assume the question refers to the area defined by the box's footprint. If the box is 4 tall and 6 wide, usually height is depth. But for area problems, it's typically base area. Let's assume the base is 4 inches by 6 inches. The block is $4 \times 4$. Total area = $4 \text{ inches} \times 6 \text{ inches} = 24 \text{ square inches}$. Area covered by the block = $4 \text{ inches} \times 4 \text{ inches} = 16 \text{ square inches}$. Uncovered area = Total area - Covered area = $24 - 16 = 8 \text{ square inches}$. \boxed{8}

Reward

Reward components

key	value
reference_answer	8
format_valid	True
correct	True
format_coef	0.1
reward	1.000

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Tara has a shoebox that is 4 inches tall and 6 inches wide. She puts a square block inside that is 4 inches per side. How many square inches of the box are left uncovered?

Policy Response

assistant:

Tara has a shoebox that is 4 inches tall and 6 inches wide. Assuming the shoebox has a standard depth required to fit a 4-inch side block, or at least that problem asks about the top surface area, we calculate as follows: The height of the box is $4$ inches and the width is $6$ inches. Assuming a standard square unit squared depth (or just asking about the surface), let's assume depth is sufficient. Wait, usually these problems imply the block takes up space on the floor. If we assume the box is $4$ tall and $6$ wide and unknown depth $d$. It says "square block". Usually blocks have some depth. If the block is 4 inches per side, and the box is 4 inches tall, then the block must lie flat on the bottom (usually). The question asks "How many square inches of the box are left uncovered?" This usually implies surface area of the base. If the box is $4$ tall and $6$ wide, and depth is unknown. However often these problems assume a standard form or the block covers the floor area $4 \times 4$ or $6 \times 6$. Let's assume the shoebox dimensions are simply handled as the footprint area is $4 \times 6 = 24$ square inches. She puts a square block inside that is $4$ inches per side. This block takes up $4 \times 4 = 16$ square inches. The box has a footprint of $2

Reward

Reward components

key	value
reference_answer	8
format_valid	False
correct	False
format_coef	0.1
reward	-0.100

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Tara has a shoebox that is 4 inches tall and 6 inches wide. She puts a square block inside that is 4 inches per side. How many square inches of the box are left uncovered?

Policy Response

assistant:

The shoebox has dimensions of 4 inches tall and 6 inches wide. To find the area of the box, we assume the box is essentially a 1x1 inch prism (or we are only considering the horizontal surface area, as no height for the box length is given, but typically such problems refer to the floor area). Area of the box = Height $\times$ Width = $4 \text{ inches} \times 6 \text{ inches} = 24 \text{ square inches}$. Tara places a square block that is 4 inches per side inside. The area of the block = Side $\times$ Side = $4 \text{ inches} \times 4 \text{ inches} = 16 \text{ square inches}$. To find the area left uncovered, subtract the block's area from the box's area: Uncovered Area = $24 \text{ square inches} - 16 \text{ square inches} = 8 \text{ square inches}$. \boxed{8}

Reward

Reward components

key	value
reference_answer	8
format_valid	True
correct	True
format_coef	0.1
reward	1.000

Trajectory Details

Trajectory 0 Episode

Episode Details

Turn 1

Step stats

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step_reward	1.000

Step Metrics

Metrics emitted by env.step

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Episode totals

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Trajectory 1 Episode

Episode Details

Turn 1

Step stats

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ob_len	96
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step_reward	1.000

Step Metrics

Metrics emitted by env.step

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Episode totals

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final_ob_len	0
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total_return	1.000

Trajectory 2 Episode

Episode Details

Turn 1

Step stats

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ob_len	96
ac_len	157
step_reward	1.000

Step Metrics

Metrics emitted by env.step

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Episode totals

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num_turns	1
final_ob_len	0
sum_step_rewards	1.000
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total_return	1.000

Trajectory 3 Episode

Episode Details

Turn 1

Step stats

key	value
ob_len	96
ac_len	166
step_reward	1.000

Step Metrics

Metrics emitted by env.step

key	value
format	1.000
correct	1.000

Episode totals

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num_turns	1
final_ob_len	0
sum_step_rewards	1.000
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total_return	1.000

Trajectory 4 Episode

Episode Details

Turn 1

Step stats

key	value
ob_len	96
ac_len	149
step_reward	1.000

Step Metrics

Metrics emitted by env.step

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format	1.000
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Episode totals

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num_turns	1
final_ob_len	0
sum_step_rewards	1.000
final_group_reward	0.000
total_return	1.000

Trajectory 5 Episode

Episode Details

Turn 1

Step stats

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ob_len	96
ac_len	222
step_reward	1.000

Step Metrics

Metrics emitted by env.step

key	value
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Episode totals

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num_turns	1
final_ob_len	0
sum_step_rewards	1.000
final_group_reward	0.000
total_return	1.000

Trajectory 6 Episode

Episode Details

Turn 1

Step stats

key	value
ob_len	96
ac_len	186
step_reward	1.000

Step Metrics

Metrics emitted by env.step

key	value
format	1.000
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Episode totals

key	value
num_turns	1
final_ob_len	0
sum_step_rewards	1.000
final_group_reward	0.000
total_return	1.000

Trajectory 7 Episode

Episode Details

Turn 1

Step stats

key	value
ob_len	96
ac_len	320
step_reward	-0.100

Step Metrics

Metrics emitted by env.step

key	value
format	0.000
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Episode totals

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num_turns	1
final_ob_len	0
sum_step_rewards	-0.100
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total_return	-0.100

Group Rollout

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Uncle Jude baked 256 cookies. He gave 15 cookies to Tim, 23 cookies to Mike, kept some in the fridge and gave the rest to Anna. How many cookies did he put in the fridge if he gave twice as many cookies as he gave Tim to Anna?

Policy Response

assistant:

Uncle Jude baked 256 cookies. He gave 15 cookies to Tim and 23 cookies to Mike. First, find the total number of cookies given to Tim and Mike: $15 + 23 = 38$ cookies. He gave the rest to Anna. Anna received twice as many cookies as he gave Tim, which means Anna received $2 \times 15 = 30$ cookies. Let $x$ be the number of cookies kept in the fridge. The sum must be 256: $38 + 30 + x = 256$ $68 + x = 256$ $x = 256 - 68$ $x = 188$ Uncle Jude put 188 cookies in the fridge. \boxed{188}

Reward

Reward components

key	value
reference_answer	188
format_valid	True
correct	True
format_coef	0.1
reward	1.000

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Policy Response

assistant:

Uncle Jude baked 256 cookies. He gave 15 cookies to Tim and 23 cookies to Mike. First, calculate the total cookies given to Tim and Mike: $15 + 23 = 38$ cookies. Let $F$ be the cookies kept in the fridge and $A$ be the cookies given to Anna. Jude gave twice as many cookies to Anna as Tim. Cookies for Anna = $2 \times 15 = 30$. The remaining cookies are $256 - 38 - 30$. $256 - 38 = 218$ $218 - 30 = 188$ Uncle Jude put 188 cookies in the fridge. \boxed{188}

Reward

Reward components

key	value
reference_answer	188
format_valid	True
correct	True
format_coef	0.1
reward	1.000

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Policy Response

assistant:

Uncle Jude baked 256 cookies. He gave 15 cookies to Tim and 23 cookies to Mike. First, calculate the cookies given away before Anna: Cookies given to Tim and Mike = $15 + 23 = 38$. Let $x$ be the cookies given to Anna. Anna received twice as many cookies as Tim, so $x = 2 \times 15 = 30$. The cookies kept in the fridge are the total minus those given away: Cookies in fridge = $256 - 38 - 30$. $256 - 38 = 218$ $218 - 30 = 188$ He put 188 cookies in the fridge. \boxed{188}

Reward

Reward components

key	value
reference_answer	188
format_valid	True
correct	True
format_coef	0.1
reward	1.000

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Policy Response

assistant:

Uncle Jude baked 256 cookies. He gave 15 cookies to Tim and 23 cookies to Mike. Cookies given to Tim and Mike = $15 + 23 = 38$. Let $x$ be the number of cookies given to Anna. The problem states he gave twice as many cookies as he gave Tim to Anna. Since he gave Tim 15 cookies, Anna received $2 \times 15 = 30$ cookies. The cookies kept in the fridge = Total cookies - Cookies given to Tim, Mike, and Anna Cookies in fridge = $256 - 38 - 30$ Cookies in fridge = $256 - 68$ Cookies in fridge = $188$ \boxed{188}

Reward

Reward components

key	value
reference_answer	188
format_valid	True
correct	True
format_coef	0.1
reward	1.000

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Policy Response

assistant:

Uncle Jude baked 256 cookies. He gave 15 to Tim and 23 to Mike. The sum of cookies given to Tim and Mike is $15 + 23 = 38$. He gave the rest to Anna and some cookies were kept in the fridge. He gave twice as many cookies as he gave Tim to Anna. Let $x$ be the number of cookies given to Anna. Then $x = 2 \times 15 = 30$. To find the number of cookies in the fridge, we first subtract the cookies given to Tim, Mike, and Anna from the total. The sum given so far is $38 + 30 = 68$. The remaining cookies are $256 - 68 = 188$. Uncle Jude put 188 cookies in the fridge. \boxed{188}

Reward

Reward components

key	value
reference_answer	188
format_valid	True
correct	True
format_coef	0.1
reward	1.000

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Policy Response

assistant:

Uncle Jude started with 256 cookies. He gave 15 cookies to Tim and 23 cookies to Mike. He kept some cookies in the fridge and gave the rest to Anna. First, calculate the total number of cookies given to Tim and Mike: $15 + 23 = 38$ cookies. Let $x$ be the number of cookies Anna received. The problem states he gave twice as many cookies as he gave Tim to Anna. Tim received 15 cookies, so Anna received $2 \times 15 = 30$ cookies. Uncle Jude gave Tim 15 cookies and Mike 23 cookies. Anna received 30 cookies. The refrigerator cookies are the remainder. Total cookies given out = $15 + 23 + 30 = 68$ cookies. Cookies in the fridge = Total cookies - Cookies given out = $256 - 68$. $256 - 68 = 188$. \boxed{188}

Reward

Reward components

key	value
reference_answer	188
format_valid	True
correct	True
format_coef	0.1
reward	1.000

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Policy Response

assistant:

Uncle Jude baked 256 cookies. He gave 15 cookies to Tim and 23 cookies to Mike. First, calculate the cookies given away: Tim: 15 Mike: 23 Total given = $15 + 23 = 38$. He kept some and gave the rest to Anna. He gave twice as many cookies as he gave Tim to Anna. Let $x$ be the number of cookies given to Anna. Then Anna received $2 \times 15 = 30$ cookies. Uncle Jude put the rest in the fridge. Cookies kept + Cookies for Anna = Remaining cookies. Remaining cookies = Total cookies - Cookies given to Tim and Mike. Since all remaining were given to Anna, Total cookies - Cookies given = Cookies for Anna. $256 - 38 = 218$. Anna received 30 cookies. The rest are in the fridge. Wait, re-reading the sentence: "gave twice as many cookies as he gave Tim to Anna". Tim got 15, Anna got 30. The rest were "kept some in the fridge and gave the rest to Anna". Usually this phrasing means flour was given to Tim, Mike, and Anna until all cookies were gone, or Anna got the rest. Let's assume Anna got everyone else. Cookies given to Tim = 15 Cookies given to Mike = 23 Cookies given to Anna = 30 Cookies used so far = $

Reward

Reward components

key	value
reference_answer	188
format_valid	False
correct	False
format_coef	0.1
reward	-0.100

Prompt

system:

You are a careful math assistant. Solve the grade-school math problem step by step, then give the final numeric answer on its own line in the form \boxed{ANSWER}.

user:

Policy Response

assistant:

Uncle Jude started with 256 cookies. He gave 15 cookies to Tim and 23 cookies to Mike. The rest were divided between Anna and the fridge. First, calculate the number of cookies given away initially: $15 + 23 = 38$ cookies. Uncle Jude gave twice as many cookies to Anna as he gave Tim to Anna. Let $A_T$ be the cookies given to Anna and Tim. Then $A_T$ must be an even number because Anna got twice as many as Tim. Since they received the rest of the cookies, the sum must be integer cookies. Let $t$ be the number of cookies given to Tim and Anna combined (wait, the phrasing is "Anna" and the problem says "gave twice as many cookies as he gave Tim to Anna". This is slightly ambiguous phrasing. Assuming Tim got $x$ cookies and Anna got $2x$ cookies. But Tim already received cookies, and Anna received cookies. Let's denote cookies given to Anna and Tim as $a$ and $t'$. The problem says "he gave twice as many cookies as he gave Tim to Anna". This usually implies Anna received $2 \times$ cookies given to Tim. Wait, Tim already got cookies, but unrelated to Anna's total. Let's assume the statement means Anna's share was twice Tim's share. Wait, but Tim received cookies "from Uncle Jude" in a specific amount. Let's assume Anna received twice as many cookies as Tim. Tim received

Reward

Reward components

key	value
reference_answer	188
format_valid	False
correct	False
format_coef	0.1
reward	-0.100

Trajectory Details

Trajectory 0 Episode

Episode Details

Turn 1

Step stats

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ob_len	114
ac_len	172
step_reward	1.000

Step Metrics

Metrics emitted by env.step

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Episode totals

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Trajectory 1 Episode

Episode Details

Turn 1

Step stats

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ob_len	114
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step_reward	1.000

Step Metrics

Metrics emitted by env.step

key	value
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Episode totals

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Trajectory 2 Episode

Episode Details

Turn 1

Step stats

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ob_len	114
ac_len	320
step_reward	-0.100

Step Metrics

Metrics emitted by env.step

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Episode totals

key	value
num_turns	1
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Trajectory 3 Episode

Episode Details

Turn 1

Step stats

key	value
ob_len	114
ac_len	320
step_reward	-0.100

Step Metrics

Metrics emitted by env.step

key	value
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Episode totals

key	value
num_turns	1
final_ob_len	0
sum_step_rewards	-0.100
final_group_reward	0.000
total_return	-0.100

Trajectory 4 Episode

Episode Details

Turn 1

Step stats

key	value
ob_len	114
ac_len	192
step_reward	1.000

Step Metrics

Metrics emitted by env.step

key	value
format	1.000
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Episode totals

key	value
num_turns	1
final_ob_len	0
sum_step_rewards	1.000
final_group_reward	0.000
total_return	1.000

Trajectory 5 Episode

Episode Details

Turn 1

Step stats

key	value
ob_len	114
ac_len	225
step_reward	1.000

Step Metrics

Metrics emitted by env.step

key	value
format	1.000
correct	1.000

Episode totals

key	value
num_turns	1
final_ob_len	0
sum_step_rewards	1.000
final_group_reward	0.000
total_return	1.000

Trajectory 6 Episode

Episode Details

Turn 1

Step stats

key	value
ob_len	114
ac_len	188
step_reward	1.000

Step Metrics

Metrics emitted by env.step

key	value
format	1.000
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Episode totals

key	value
num_turns	1
final_ob_len	0
sum_step_rewards	1.000
final_group_reward	0.000
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Trajectory 7 Episode

Episode Details

Turn 1

Step stats

key	value
ob_len	114
ac_len	179
step_reward	1.000

Step Metrics

Metrics emitted by env.step

key	value
format	1.000
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Episode totals

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final_ob_len	0
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final_group_reward	0.000
total_return	1.000