RL Iteration 8

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:

Yuko likes to play board games. He decides to play a game with his brother Yuri. They must roll 3 dice at the same time and move the squares corresponding to the value of the 3 dice. Yuri started and his dice had the following combination: 2, 4, and 5. On Yuko's turn, he rolled 1, 5, and X. How many squares must Yuko's last die move him so that he is in front of his brother?

Policy Response

assistant:

Yuri started with dice showing 2, 4, and 5. The squares moved are the values of the dice. Yuri's total movement is $2 + 4 + 5 = 11$. Yuko rolled 1, 5, and X. Yuko's movement is $1 + 5 + X = 6 + X$. For Yuko to be in front of his brother, Yuko's total movement must be strictly greater than Yuri's total movement. $6 + X > 11$ Subtracting 6 from both sides gives: $X > 5$ Assuming X is a die roll, X can be 1, 2, 3, 4, or 6. Since X must be greater than 5, the only possible value is 6. \boxed{6}

Reward

Reward components

key	value
reference_answer	6
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:

Yuri started with dice values 2, 4, and 5. The total value for Yuri's turn is $2 + 4 + 5 = 11$. Yuko rolled 1, 5, and X. The total value for Yuko is $1 + 5 + X = 6 + X$. To be in front of his brother, Yuko's total must be greater than Yuri's total. $6 + X > 11$ $X > 5$ Yuko must roll a die that results in a value greater than 5. The possible values for a die roll are integers from 1 to 6. The only integer greater than 5 is 6. \boxed{6}

Reward

Reward components

key	value
reference_answer	6
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:

Yuri started with dice showing 2, 4, and 5. The sum of Yuri's dice is $2 + 4 + 5 = 11$. Yuko rolled 1, 5, and X. Yuko needs to move his last die so that he is in front of his brother. Yuko's sum after rolling all dice must be at least $11 + 1$ squares ahead. Yuri moved 11 squares. Yuko's current sum without the last die is $1 + 5 + X = 6 + X$. Yuko needs to be ahead, meaning his total sum $S_Y > S_X$. Since Yuri started, Yuri is currently at position 11. Yuko needs to be at position $11 + k$ where $k \ge 1$. Yuko must roll X to make his position strictly greater than 11. $6 + X + \text{movement} > 11$ $X + \text{movement} > 5$ The problem asks "How many squares must Yuko's last die move him...". Usually, this implies the minimum movement required. The value of X is not specified, but typically in such problems, X is a single digit die result (1 to 6) or the sum depends on X being a specific value required to create a valid situation. Assuming X is minimized or standard, let's assume X must be such that Yuko *can* be ahead or the question implies finding the minimum movement

Reward

Reward components

key	value
reference_answer	6
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:

Yuri started with dice values 2, 4, and 5. Yuri moved his first squares. To find Yuko's position relative to Yuri, we first need to determine Yuri's total movement distance and assume Yuri moved all his values forward since no backward movements or stopping conditions were mentioned, nor was a game board length specified. Yuri's total movement is $2 + 4 + 5 = 11$ squares. Yuko rolled 1, 5, and X. To find Yuko's movement, he sums these values. Yuko must move him in front of Yuri. Assuming they are on a linear board starting from 0. Yuko's movement is $1 + 5 + X = 6 + X$. For Yuko to be in front of Yuri, Yuko's total distance must be greater than Yuri's total distance. Yuko needs to move him $1 + 5 + X = 6 + X$ squares in total. Yuri moved 11 squares. The problem asks "How many squares must Yuko's last die move him". This phrasing usually implies finding the minimum value for X such that Yuko wins, or finding the required movement if X is fixed, but here X is the variable die rolled. Wait, X is the value of the last die rolled. The question asks how many squares must Yuko's last die move him. This phrasing suggests finding the value of X from the conditions, assuming he needs to win or tie? No, typically in these problems,

Reward

Reward components

key	value
reference_answer	6
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:

Yuri started with dice showing 2, 4, and 5. To find the sum Yuri moved initially: $2 + 4 + 5 = 11$. Yuko rolled 1, 5, and X. Yuko needs to reach a higher square number than Yuri. Yuko's current sum is $1 + 5 + X = 6 + X$. Yuko must move forward. The condition "in front of his brother" usually means strictly ahead on the board, assuming they start at the same position and move based on the sum of the dice values. Yuri is at position 11. Yuko is at position $6 + X$. For Yuko to be in front of Yuri, $6 + X > 11$. $X > 5$. The problem asks for "How many squares must Yuko's last die move him". Yuko rolled 3 dice, meaning there was no "last die" to control movement from a specific spot relative to the previous sum, each die contributed equally to the total sum. The question implies finding a valid integer value for X, likely from a standard die roll (1 to 6). The square values on a board might be sequential. Assuming standard dice, X can be 6. If X is 6, Yuko's sum is $6 + 6 = 12$. Since $12 > 11$, Yuko is in front of Yuri. \boxed{6}

Reward

Reward components

key	value
reference_answer	6
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:

Yuri started with dice showing 2, 4, and 5. The current position of Yuri is the sum of these values. Yuri's position = $2 + 4 + 5 = 11$. Yuko rolled 1, 5, and $X$ on his turn. The current position after his roll will be the sum of these values. However, Yuuko has already moved the squares corresponding to the value of the 3 dice. To be in front of his brother, Yuko must be further along the board. The question implies finding the value $X$ that ensures Yuko is ahead. Usually, these problems imply moving forward by the sum of the dice values. Assuming Yuuko rolled $X$, his move sum is $1 + 5 + X = 6 + X$. Yuko needs his new position to be greater than Yuri's current position of 11. Yuko's new position = $11 + (6 + X)$ (assuming Yuuko already moved or started from position 0 and added dice values sequentially, but typically board games start at 0 and players move forward). Let's assume they start at 0. Yuri moved $2+4+5=11$. Yuko must move forward $1+5+X = 6+X$. For Yuko to be in front, Yuko's position must be $> 11$. $6 + X > 11$ (assuming they move squares relative to a starting

Reward

Reward components

key	value
reference_answer	6
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:

Yuri started with a dice combination of 2, 4, and 5. The sum of these values is $2 + 4 + 5 = 11$. On Yuko's turn, he rolled 1, 5, and X. For Yuko to be in front of his brother, his sum must be greater than Yuri's sum. Let $S_Y$ be Yuko's sum and $S_{Yu}$ be Yuri's sum. $S_Y = 1 + 5 + X = 6 + X$. Yuko needs to move X squares such that $6 + X > 11$. $X > 11 - 6$ $X > 5$ Since the problem implies X is a number resulting from rolling a standard die (values 1 through 6), X can be 6. If X were lower than 6 (e.g., 5), the sum would be 11, placing them tie, meaning Yuri would not have lost. The question asks "How many squares must Yuko's last die move him", which refers to the value X of the last die roll or potentially the distance required if there was a board? Assuming X represents the value rolled, we look for the smallest integer value X that makes Yuko ahead. $X$ must be greater than 5. The possible values for a die roll are 1, 2, 3, 4, 5, 6. The only value greater than 5 is 6

Reward

Reward components

key	value
reference_answer	6
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:

Yuri started with dice values 2, 4, and 5. Yuko rolled 1, 5, and X. The problem implicitly assumes that Yuri moves his opponent (Yuko) or Yuri moves first. Let's re-read carefully: "Yuri started and his dice had the following combination... Yuri started and his dice had... On Yuko's turn, he rolled... How many squares must Yuko's last die move him so that he is in front of his brother?" First, calculate Yuri's total distance moved. Yuri's dice sum $S_Y = 2 + 4 + 5 = 11$. Yuko's current dice sum depends on X. Yuko's dice are 1, 5, and X. Sum $S_Yuko = 1 + 5 + X = 6 + X$. Yuri started. This usually means Yuri moved first. However, the problem asks how many squares Yuko's last die must move him to be in front. "Front" typically means a greater distance traveled on a board game where players move towards a fixed endpoint or end of the board. The question doesn't specify the board length or starting position relative to moves. Assuming both started at position 0 and trying to reach position $L$, or simply trying to have a higher sum. For Yuko to be in front, $S_Yuko$ must be greater than $S_Y$. $6 + X > 11$ $X > 5$ Since dice usually have

Reward

Reward components

key	value
reference_answer	6
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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step_reward	-0.100

Step Metrics

Metrics emitted by env.step

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Episode totals

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sum_step_rewards	-0.100
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total_return	-0.100

Trajectory 1 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 2 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 3 Episode

Episode Details

Turn 1

Step stats

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step_reward	-0.100

Step Metrics

Metrics emitted by env.step

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Episode totals

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Trajectory 4 Episode

Episode Details

Turn 1

Step stats

key	value
ob_len	154
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step_reward	0.900

Step Metrics

Metrics emitted by env.step

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Episode totals

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final_ob_len	0
sum_step_rewards	0.900
final_group_reward	0.000
total_return	0.900

Trajectory 5 Episode

Episode Details

Turn 1

Step stats

key	value
ob_len	154
ac_len	320
step_reward	0.900

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	0.900
final_group_reward	0.000
total_return	0.900

Trajectory 6 Episode

Episode Details

Turn 1

Step stats

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ob_len	154
ac_len	320
step_reward	-0.100

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

key	value
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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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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:

Sarah starts saving $5.00 a week for 4 weeks. Then she saves $10.00 a week for the next 4 weeks. Then she saves $20.00 a week for the next 4 weeks. How much money has she saved over 12 weeks?

Policy Response

assistant:

Sarah saves $5.00 a week for the first 4 weeks. The total savings for these 4 weeks is $5.00 * 4 weeks = $20.00. Sarah saves $10.00 a week for the next 4 weeks. The total savings for these 4 weeks is $10.00 * 4 weeks = $40.00. Sarah saves $20.00 a week for the next 4 weeks. The total savings for these 4 weeks is $20.00 * 4 weeks = $80.00. The total money saved over 12 weeks is $20.00 + $40.00 + $80.00 = $140.00. \boxed{140.00}

Reward

Reward components

key	value
reference_answer	140
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:

Sarah starts saving $5.00 a week for 4 weeks. Then she saves $10.00 a week for the next 4 weeks. Then she saves $20.00 a week for the next 4 weeks. How much money has she saved over 12 weeks?

Policy Response

assistant:

Sarah saves $5.00 a week for 4 weeks. The total amount for the first 4 weeks is $5.00 * 4 weeks = $20.00. Sarah saves $10.00 a week for the next 4 weeks. The total amount for the next 4 weeks is $10.00 * 4 weeks = $40.00. Sarah saves $20.00 a week for the next 4 weeks. The total amount for the last 4 weeks is $20.00 * 4 weeks = $80.00. The total money saved over 12 weeks is $20.00 + $40.00 + $80.00 = $140.00. \boxed{140}

Reward

Reward components

key	value
reference_answer	140
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:

Sarah starts saving $5.00 a week for 4 weeks. Then she saves $10.00 a week for the next 4 weeks. Then she saves $20.00 a week for the next 4 weeks. How much money has she saved over 12 weeks?

Policy Response

assistant:

Sarah saves $5.00 a week for the first 4 weeks. Amount saved in the first 4 weeks = $5.00 * 4 weeks = $20.00 Sarah saves $10.00 a week for the next 4 weeks. Amount saved in the next 4 weeks = $10.00 * 4 weeks = $40.00 Sarah saves $20.00 a week for the next 4 weeks. Amount saved in the last 4 weeks = $20.00 * 4 weeks = $80.00 To find the total money saved over 12 weeks, add the amounts from each period: Total = $20.00 + $40.00 + $80.00 = $140.00 \boxed{140}

Reward

Reward components

key	value
reference_answer	140
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:

Sarah starts saving $5.00 a week for 4 weeks. Then she saves $10.00 a week for the next 4 weeks. Then she saves $20.00 a week for the next 4 weeks. How much money has she saved over 12 weeks?

Policy Response

assistant:

Sarah saves $5.00 a week for the first 4 weeks. She saves $10.00 a week for the next 4 weeks. She saves $20.00 a week for the next 4 weeks. To find the total amount saved, we calculate the savings for each period and sum them up. First period: $5.00 a week for 4 weeks $5.00 * 4 = $20.00 Second period: $10.00 a week for 4 weeks $10.00 * 4 = $40.00 Third period: $20.00 a week for 4 weeks $20.00 * 4 = $80.00 Total savings: $20.00 + $40.00 + $80.00 = $140.00 \boxed{140}

Reward

Reward components

key	value
reference_answer	140
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:

Sarah starts saving $5.00 a week for 4 weeks. Then she saves $10.00 a week for the next 4 weeks. Then she saves $20.00 a week for the next 4 weeks. How much money has she saved over 12 weeks?

Policy Response

assistant:

Sarah saves $5.00 a week for the first 4 weeks. The total amount saved in the first 4 weeks is $5.00 * 4 = $20.00. She saves $10.00 a week for the next 4 weeks. The total amount saved in the next 4 weeks is $10.00 * 4 = $40.00. She saves $20.00 a week for the next 4 weeks. The total amount saved in the last 4 weeks is $20.00 * 4 = $80.00. To find the total money saved over 12 weeks, sum these amounts: $20.00 + $40.00 + $80.00 = $140.00. \boxed{140.00}

Reward

Reward components

key	value
reference_answer	140
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:

Sarah starts saving $5.00 a week for 4 weeks. Then she saves $10.00 a week for the next 4 weeks. Then she saves $20.00 a week for the next 4 weeks. How much money has she saved over 12 weeks?

Policy Response

assistant:

Sarah saves $5.00 a week for the first 4 weeks. The total amount saved in the first 4 weeks is $5.00 * 4 weeks = $20.00. She saves $10.00 a week for the next 4 weeks. The total amount saved in the next 4 weeks is $10.00 * 4 weeks = $40.00. She saves $20.00 a week for the next 4 weeks. The total amount saved in the last 4 weeks is $20.00 * 4 weeks = $80.00. To find the total money saved over 12 weeks, we sum these amounts: $20.00 + $40.00 + $80.00 = $140.00 \boxed{140.00}

Reward

Reward components

key	value
reference_answer	140
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:

Sarah starts saving $5.00 a week for 4 weeks. Then she saves $10.00 a week for the next 4 weeks. Then she saves $20.00 a week for the next 4 weeks. How much money has she saved over 12 weeks?

Policy Response

assistant:

Sarah saves $5.00 a week for the first 4 weeks. Sarah saves $10.00 a week for the next 4 weeks. Sarah saves $20.00 a week for the next 4 weeks. For the first 4 weeks, she saves $5.00 a week: $5.00 * 4 weeks = $20.00. For the next 4 weeks, she saves $10.00 a week: $10.00 * 4 weeks = $40.00. For the next 4 weeks, she saves $20.00 a week: $20.00 * 4 weeks = $80.00. To find the total money saved over 12 weeks, we sum these amounts: $20.00 + $40.00 + $80.00 = $140.00 \boxed{140.00}

Reward

Reward components

key	value
reference_answer	140
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:

Sarah starts saving $5.00 a week for 4 weeks. Then she saves $10.00 a week for the next 4 weeks. Then she saves $20.00 a week for the next 4 weeks. How much money has she saved over 12 weeks?

Policy Response

assistant:

Sarah saves $5.00 a week for the first 4 weeks. Sarah saves $10.00 a week for the next 4 weeks. Sarah saves $20.00 a week for the next 4 weeks. First, calculate the amount saved in the first 4 weeks: $5.00/week * 4 weeks = $20.00 Next, calculate the amount saved in the next 4 weeks: $10.00/week * 4 weeks = $40.00 Then, calculate the amount saved in the next 4 weeks: $20.00/week * 4 weeks = $80.00 To find the total money saved over 12 weeks, sum these amounts: $20.00 + $40.00 + $80.00 = $140.00 Sarah has saved $140.00 over 12 weeks. \boxed{140.00}

Reward

Reward components

key	value
reference_answer	140
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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ob_len	119
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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_reward	1.000

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_reward	1.000

Step Metrics

Metrics emitted by env.step

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Episode totals

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Trajectory 3 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 4 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 5 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 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 Metrics

Metrics emitted by env.step

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Episode totals

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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:

Karen bakes 50 chocolate chip cookies. She keeps 10 for herself, and she gives 8 to her grandparents. If Karen wants to give everyone in her class cookies, and there are 16 people in her class, how many cookies will each person receive?

Policy Response

assistant:

Karen starts with 50 cookies. She keeps 10 for herself and gives 8 to her grandparents. First, calculate the cookies remaining after she feeds her grandparents. $50 - 10 - 8 = 32$ cookies remaining. Karen wants to give everyone in her class cookies, and there are 16 people in her class. Next, divide the remaining cookies by the number of people. $32 \div 16 = 2$ cookies each. \boxed{2}

Reward

Reward components

key	value
reference_answer	2
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:

Karen bakes 50 chocolate chip cookies. She keeps 10 for herself and gives 8 to her grandparents. To find the number of cookies available for her class, first subtract the cookies she keeps and gives away from the total. Cookies available = $50 - 10 - 8 = 32$. There are 16 people in her class. Each person receives the same number of cookies. Cookies per person = $32 / 16 = 2$. \boxed{2}

Reward

Reward components

key	value
reference_answer	2
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:

Karen bakes 50 chocolate chip cookies. She keeps 10 for herself and gives 8 to her grandparents. Cookies remaining: $50 - 10 - 8 = 32$. She wants to give everyone in her class cookies, and there are 16 people in her class. Cookies per person: $32 \div 16 = 2$. Each person will receive 2 cookies. \boxed{2}

Reward

Reward components

key	value
reference_answer	2
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:

Karen starts with 50 chocolate chip cookies. She keeps 10 for herself and gives 8 to her grandparents. To find the number of cookies left for her class, subtract these amounts from the total: $50 - 10 - 8 = 32$. There are 16 people in her class. To distribute the cookies equally, divide 32 cookies by 16 people: $32 / 16 = 2$. Each person will receive 2 cookies. \boxed{2}

Reward

Reward components

key	value
reference_answer	2
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:

Karen bakes 50 chocolate chip cookies. She keeps 10 for herself and gives 8 to her grandparents. First, calculate the number of cookies given away or kept: $50 - 10 - 8 = 32$ cookies. Karen wants to give everyone in her class cookies, and there are 16 people in her class. Each person will receive $32 \div 16 = 2$ cookies. \boxed{2}

Reward

Reward components

key	value
reference_answer	2
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:

Karen bakes 50 chocolate chip cookies. She keeps 10 for herself and gives 8 to her grandparents. First, find the number of cookies given to her class: $50 - 10 - 8 = 32$ cookies. There are 16 people in her class. She wants to give everyone cookies. Divide the cookies by the number of people: $32 \div 16 = 2$ Each person will receive 2 cookies. \boxed{2}

Reward

Reward components

key	value
reference_answer	2
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:

Karen bakes 50 chocolate chip cookies. She keeps 10 for herself and gives 8 to her grandparents. First, find the total number of cookies Karen gives away. She gave herself 10 and gave her grandparents 8. Wait, she keeps cookies for herself. This means she does not distribute these. So she distributes only the cookies not kept. Cookies distributed = Initial cookies - Cookies kept Cookies distributed = $50 - 10 = 40$ She gives 8 cookies to her grandparents as well. The problem states she gives them cookies and wants to give everyone in her class cookies. Usually, cookies given to family members are removed from the pool available for the class. Cookies distributed = $50 - 10 - 8 = 32$ Assuming she gives the class cookies evenly: $32 \div 16$ $32 \div 16 = 2$ Each person receives 2 cookies. \boxed{2}

Reward

Reward components

key	value
reference_answer	2
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:

Karen initially bakes 50 chocolate chip cookies. She keeps 10 for herself and gives 8 to her grandparents. First, calculate the number of cookies used for herself and her grandparents: $10 + 8 = 18$. Next, subtract this from the initial amount to find the cookies available for her class: $50 - 18 = 32$. There are 16 people in her class. To find how many cookies each person receives, divide the cookies by the number of people: $32 / 16 = 2$. Each person receives 2 cookies. \boxed{2}

Reward

Reward components

key	value
reference_answer	2
format_valid	True
correct	True
format_coef	0.1
reward	1.000

Trajectory Details

Trajectory 0 Episode

Episode Details

Turn 1

Step stats

key	value
ob_len	110
ac_len	101
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 1 Episode

Episode Details

Turn 1

Step stats

key	value
ob_len	110
ac_len	111
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 2 Episode

Episode Details

Turn 1

Step stats

key	value
ob_len	110
ac_len	137
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 3 Episode

Episode Details

Turn 1

Step stats

key	value
ob_len	110
ac_len	113
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 4 Episode

Episode Details

Turn 1

Step stats

key	value
ob_len	110
ac_len	100
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 5 Episode

Episode Details

Turn 1

Step stats

key	value
ob_len	110
ac_len	114
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	110
ac_len	213
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 7 Episode

Episode Details

Turn 1

Step stats

key	value
ob_len	110
ac_len	113
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

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:

Tom catches crabs for a living. He has 8 crab buckets that he checks every day. Each crab bucket gets 12 crabs. He sells each of these crabs for $5 each. How much money does he make per week?

Policy Response

assistant:

Tom has 8 crab buckets and each bucket gets 12 crabs every day. To find the money made per week, first calculate the total number of crabs per day. Crabs per day = $8 \text{ buckets} \times 12 \text{ crabs/bucket} = 96 \text{ crabs}$. Tom sells each crab for $5. Money per day = $96 \text{ crabs} \times \$5 \text{/crab} = \$480$. There are 7 days in a week. Money per week = $480 \text{ / day} \times 7 \text{ days} = \$3360$. Tom makes $3360 per week. \boxed{3360}

Reward

Reward components

key	value
reference_answer	3360
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:

Tom catches crabs for a living. He has 8 crab buckets that he checks every day. Each crab bucket gets 12 crabs. He sells each of these crabs for $5 each. How much money does he make per week?

Policy Response

assistant:

Tom catches crabs every day using 8 crab buckets. Each bucket gets 12 crabs. First, calculate the total number of crabs caught each day: $8 \text{ buckets} \times 12 \text{ crabs/bucket} = 96 \text{ crabs per day}$. Next, he sells each crab for $5. The money made per day is: $96 \text{ crabs} \times \$5 \text{ per crab} = \$480 \text{ per day}$. He makes money per week over 7 days. $\$480 \text{ per day} \times 7 \text{ days} = \$3360$. \boxed{3360}

Reward

Reward components

key	value
reference_answer	3360
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:

Tom catches crabs for a living. He has 8 crab buckets that he checks every day. Each crab bucket gets 12 crabs. He sells each of these crabs for $5 each. How much money does he make per week?

Policy Response

assistant:

Tom catches crabs every day using 8 crab buckets. Each bucket gets 12 crabs. He sells each crab for $5. First, find the total number of crabs per day: $8 \text{ buckets} \times 12 \text{ crabs/bucket} = 96 \text{ crabs/day}$. Next, find the money made per day. Each crab sells for $5: $96 \text{ crabs} \times \$5 \text{/ crab} = \$480 \text{ per day}$. He makes this money every day for a week (7 days): $\$480 \text{ per day} \times 7 \text{ days} = \$3360$. Tom makes $3360 per week. \boxed{3360}

Reward

Reward components

key	value
reference_answer	3360
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:

Tom catches crabs for a living. He has 8 crab buckets that he checks every day. Each crab bucket gets 12 crabs. He sells each of these crabs for $5 each. How much money does he make per week?

Policy Response

assistant:

Tom catches crabs using 8 crab buckets every day. Each bucket gets 12 crabs. He sells each crab for $5 each. First, calculate the total number of crabs per day: $8 \text{ buckets} \times 12 \text{ crabs/bucket} = 96 \text{ crabs per day}$. Next, calculate the earnings per day. Each crab sells for $5: $96 \text{ crabs} \times \$5 \text{ each} = \$480 \text{ per day}$. To find the money made per week, assume there are 7 days in a week: $\$480 \text{ per day} \times 7 \text{ days} = \$3360 \text{ per week}$. \boxed{3360}

Reward

Reward components

key	value
reference_answer	3360
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:

Tom catches crabs for a living. He has 8 crab buckets that he checks every day. Each crab bucket gets 12 crabs. He sells each of these crabs for $5 each. How much money does he make per week?

Policy Response

assistant:

Tom checks 8 crab buckets every day. Each bucket gets 12 crabs. He sells each crab for $5. First, find the number of crabs each day: $8 \text{ buckets} \times 12 \text{ crabs/bucket} = 96 \text{ crabs/day}$ Next, assume he sells all the crabs each day. He sells each for $5: $96 \text{ crabs} \times \$5 \text{/ crab} = \$480 \text{ per day}$ To find the money made per week, assume he works every day for 7 days: $480 \text{ dollars/day} \times 7 \text{ days/week} = \$3360 \text{ per week}$ \boxed{3360}

Reward

Reward components

key	value
reference_answer	3360
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:

Tom catches crabs for a living. He has 8 crab buckets that he checks every day. Each crab bucket gets 12 crabs. He sells each of these crabs for $5 each. How much money does he make per week?

Policy Response

assistant:

Tom catches crabs for a living. He has 8 crab buckets that he checks every day. Each crab bucket gets 12 crabs. He sells each of these crabs for $5 each. First, calculate the number of crabs caught each day: $8 \text{ buckets} \times 12 \text{ crabs/bucket} = 96 \text{ crabs/day}$. Each crab sells for $5. The money made each day is: $96 \text{ crabs} \times \$5 \text{/ crab} = \$480 \text{/ day}$. He sells crabs for a week, which has 7 days. The money made per week is: $\$480 \text{/ day} \times 7 \text{ days} = \$3360$. \boxed{3360}

Reward

Reward components

key	value
reference_answer	3360
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:

Tom catches crabs for a living. He has 8 crab buckets that he checks every day. Each crab bucket gets 12 crabs. He sells each of these crabs for $5 each. How much money does he make per week?

Policy Response

assistant:

Tom catches crabs for a living. He has 8 crab buckets that he checks every day. Each crab bucket gets 12 crabs. He sells each of these crabs for $5 each. To find the money made per week, follow these steps: 1. Calculate the crabs per day: $8 \text{ buckets} \times 12 \text{ crabs/bucket} = 96 \text{ crabs/day}$ 2. Calculate crabs per week (assuming 7 days per week): $96 \text{ crabs/day} \times 7 \text{ days/week} = 672 \text{ crabs/week}$ 3. Calculate money per week: $672 \text{ crabs} \times \$5 \text{ each} = \$3360$ Tom makes $3360 per week. \boxed{3360}

Reward

Reward components

key	value
reference_answer	3360
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:

Tom catches crabs for a living. He has 8 crab buckets that he checks every day. Each crab bucket gets 12 crabs. He sells each of these crabs for $5 each. How much money does he make per week?

Policy Response

assistant:

Tom catches crabs every day. He has 8 crab buckets, and each bucket gets 12 crabs. He sells each crab for $5. First, calculate the total number of crabs caught in one day: $8 \text{ buckets} \times 12 \text{ crabs/bucket} = 96 \text{ crabs per day}$ Next, calculate the total number of crabs in one week. Tom checks every day, and there are 7 days in a week: $96 \text{ crabs/day} \times 7 \text{ days} = 672 \text{ crabs per week}$ Finally, calculate the total money made per week. Each crab sells for $5: $672 \text{ crabs} \times \$5 \text{/ crab} = \$3360$ Tom makes $3360 per week. \boxed{3360}

Reward

Reward components

key	value
reference_answer	3360
format_valid	True
correct	True
format_coef	0.1
reward	1.000

Trajectory Details

Trajectory 0 Episode

Episode Details

Turn 1

Step stats

key	value
ob_len	108
ac_len	187
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 1 Episode

Episode Details

Turn 1

Step stats

key	value
ob_len	108
ac_len	174
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 2 Episode

Episode Details

Turn 1

Step stats

key	value
ob_len	108
ac_len	168
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 3 Episode

Episode Details

Turn 1

Step stats

key	value
ob_len	108
ac_len	187
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 4 Episode

Episode Details

Turn 1

Step stats

key	value
ob_len	108
ac_len	203
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 5 Episode

Episode Details

Turn 1

Step stats

key	value
ob_len	108
ac_len	208
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	108
ac_len	192
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 7 Episode

Episode Details

Turn 1

Step stats

key	value
ob_len	108
ac_len	183
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