RL Iteration 11

Generated 2026-06-11T16:37:23

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:
There are 30 pieces of popcorn in a serving. Jared can eat 90 pieces of popcorn and his three other friends can each eat 60 pieces of popcorn. How many servings of popcorn should Jared order for all of them?

Policy Response

assistant:
Jared eats 90 pieces. His three friends each eat 60 pieces, so the friends eat $3 \times 60 = 180$ pieces. Total popcorn eaten: $90 + 180 = 270$ pieces. Servings: $270 / 30 = 9$. \boxed{9}

Reward

Reward components
key value
reference_answer 9
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:
There are 30 pieces of popcorn in a serving. Jared can eat 90 pieces of popcorn and his three other friends can each eat 60 pieces of popcorn. How many servings of popcorn should Jared order for all of them?

Policy Response

assistant:
Jared eats 90 pieces of popcorn. Each of his 3 friends eats 60 pieces. Total popcorn = $90 + 3 \times 60 = 90 + 180 = 270$ pieces. Servings = $270 / 30 = 9$. \boxed{9}

Reward

Reward components
key value
reference_answer 9
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:
There are 30 pieces of popcorn in a serving. Jared can eat 90 pieces of popcorn and his three other friends can each eat 60 pieces of popcorn. How many servings of popcorn should Jared order for all of them?

Policy Response

assistant:
Jared eats 90 pieces of popcorn. His three friends each eat 60 pieces, so they eat $3 \times 60 = 180$ pieces total. Total popcorn eaten: $90 + 180 = 270$ pieces. Servings: $270 / 30 = 9$. \boxed{9}

Reward

Reward components
key value
reference_answer 9
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:
There are 30 pieces of popcorn in a serving. Jared can eat 90 pieces of popcorn and his three other friends can each eat 60 pieces of popcorn. How many servings of popcorn should Jared order for all of them?

Policy Response

assistant:
Jared eats 90 pieces of popcorn. His three friends each eat 60 pieces. Total pieces = $90 + 3 \times 60 = 90 + 180 = 270$ pieces. Servings = $270 / 30 = 9$. \boxed{9}

Reward

Reward components
key value
reference_answer 9
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:
There are 30 pieces of popcorn in a serving. Jared can eat 90 pieces of popcorn and his three other friends can each eat 60 pieces of popcorn. How many servings of popcorn should Jared order for all of them?

Policy Response

assistant:
Jared and his three friends eat a total of $90 + 3 \times 60 = 90 + 180 = 270$ pieces of popcorn. Each serving has 30 pieces. The number of servings needed is $270 / 30 = 9$. \boxed{9}

Reward

Reward components
key value
reference_answer 9
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:
There are 30 pieces of popcorn in a serving. Jared can eat 90 pieces of popcorn and his three other friends can each eat 60 pieces of popcorn. How many servings of popcorn should Jared order for all of them?

Policy Response

assistant:
Jared eats 90 pieces. Each of his three friends eats 60 pieces. Total pieces eaten = $90 + 3 \times 60 = 90 + 180 = 270$. Servings needed = $270 / 30 = 9$. \boxed{9}

Reward

Reward components
key value
reference_answer 9
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:
There are 30 pieces of popcorn in a serving. Jared can eat 90 pieces of popcorn and his three other friends can each eat 60 pieces of popcorn. How many servings of popcorn should Jared order for all of them?

Policy Response

assistant:
Jared eats 90 pieces, and each of his three friends eats 60 pieces. Each friend eats $3 \times 60 = 180$ pieces. The total number of pieces is $90 + 180 = 270$ pieces. The number of servings is $270 / 30 = 9$. \boxed{9}

Reward

Reward components
key value
reference_answer 9
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:
There are 30 pieces of popcorn in a serving. Jared can eat 90 pieces of popcorn and his three other friends can each eat 60 pieces of popcorn. How many servings of popcorn should Jared order for all of them?

Policy Response

assistant:
Jared eats 90 pieces, and his three friends each eat 60 pieces. Total pieces = $90 + 3 \times 60 = 90 + 180 = 270$. Servings = $270 / 30 = 9$. \boxed{9}

Reward

Reward components
key value
reference_answer 9
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 102
ac_len 73
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 102
ac_len 84
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 102
ac_len 83
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 102
ac_len 72
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 102
ac_len 81
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 102
ac_len 77
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 102
ac_len 75
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 102
ac_len 73
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:
Bill and Ted went into the forest to gather some wild mushrooms. Bill gathered 12 red mushrooms and 6 brown mushrooms. Ted gathered 14 green mushrooms and 6 blue mushrooms. If half of the blue mushrooms, two-thirds of the red mushrooms, and all of the brown mushrooms have white spots, how many white-spotted mushrooms did they gather?

Policy Response

assistant:
Bill gathered 12 red mushrooms and 6 brown mushrooms. Ted gathered 14 green mushrooms and 6 blue mushrooms. Mushrooms with white spots: * Blue mushrooms: Half of 6 is $6/2 = 3$. * Red mushrooms: Two-thirds of 12 is $12 \times 2/3 = 8$. * Brown mushrooms: All 6 mushrooms. Total white-spotted mushrooms = $3 + 8 + 6 = 17$. \boxed{17}

Reward

Reward components
key value
reference_answer 17
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:
Bill and Ted went into the forest to gather some wild mushrooms. Bill gathered 12 red mushrooms and 6 brown mushrooms. Ted gathered 14 green mushrooms and 6 blue mushrooms. If half of the blue mushrooms, two-thirds of the red mushrooms, and all of the brown mushrooms have white spots, how many white-spotted mushrooms did they gather?

Policy Response

assistant:
Bill gathered 6 brown mushrooms. Ted gathered 6 blue mushrooms. White-spotted mushrooms: - Blue: half of 6 = 3 - Red: two-thirds of 12 = 8 - Brown: all of 6 = 6 Total white-spotted mushrooms = 3 + 8 + 6 = 17. \boxed{17}

Reward

Reward components
key value
reference_answer 17
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:
Bill and Ted went into the forest to gather some wild mushrooms. Bill gathered 12 red mushrooms and 6 brown mushrooms. Ted gathered 14 green mushrooms and 6 blue mushrooms. If half of the blue mushrooms, two-thirds of the red mushrooms, and all of the brown mushrooms have white spots, how many white-spotted mushrooms did they gather?

Policy Response

assistant:
Bill gathered 12 red mushrooms and 6 brown mushrooms. Ted gathered 14 green mushrooms and 6 blue mushrooms. Mushrooms with white spots: - Blue mushrooms: half of 6 = 3 - Red mushrooms: two-thirds of 12 = 8 - Brown mushrooms: all 6 Total white-spotted mushrooms = 3 + 8 + 6 = 17. \boxed{17}

Reward

Reward components
key value
reference_answer 17
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:
Bill and Ted went into the forest to gather some wild mushrooms. Bill gathered 12 red mushrooms and 6 brown mushrooms. Ted gathered 14 green mushrooms and 6 blue mushrooms. If half of the blue mushrooms, two-thirds of the red mushrooms, and all of the brown mushrooms have white spots, how many white-spotted mushrooms did they gather?

Policy Response

assistant:
Bill gathered 12 red mushrooms and 6 brown mushrooms. Ted gathered 14 green mushrooms and 6 blue mushrooms. Mushrooms with white spots: - Blue mushrooms with spots: $14 / 2 = 7$ - Red mushrooms with spots: $12 * (2/3) = 8$ - Brown mushrooms with spots: $6$ Total white-spotted mushrooms: $7 + 8 + 6 = 21$ \boxed{21}

Reward

Reward components
key value
reference_answer 17
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:
Bill and Ted went into the forest to gather some wild mushrooms. Bill gathered 12 red mushrooms and 6 brown mushrooms. Ted gathered 14 green mushrooms and 6 blue mushrooms. If half of the blue mushrooms, two-thirds of the red mushrooms, and all of the brown mushrooms have white spots, how many white-spotted mushrooms did they gather?

Policy Response

assistant:
Bill gathered $12$ red mushrooms and $6$ brown mushrooms. Ted gathered $14$ green mushrooms and $6$ blue mushrooms. Mushrooms with white spots: - Blue mushrooms with white spots: $\frac{1}{2} \times 6 = 3$ - Red mushrooms with white spots: $\frac{2}{3} \times 12 = 8$ - Brown mushrooms with white spots: $6$ Total mushrooms with white spots: $3 + 8 + 6 = 17$. \boxed{17}

Reward

Reward components
key value
reference_answer 17
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:
Bill and Ted went into the forest to gather some wild mushrooms. Bill gathered 12 red mushrooms and 6 brown mushrooms. Ted gathered 14 green mushrooms and 6 blue mushrooms. If half of the blue mushrooms, two-thirds of the red mushrooms, and all of the brown mushrooms have white spots, how many white-spotted mushrooms did they gather?

Policy Response

assistant:
Bill gathered 12 red mushrooms and 6 brown mushrooms. Ted gathered 14 green mushrooms and 6 blue mushrooms. Mushrooms with white spots: * Half of the blue mushrooms: $1/2 * 6 = 3$. * Two-thirds of the red mushrooms: $2/3 * 12 = 8$. * All of the brown mushrooms: $6$. Total white-spotted mushrooms = $3 + 8 + 6 = 17$. \boxed{17}

Reward

Reward components
key value
reference_answer 17
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:
Bill and Ted went into the forest to gather some wild mushrooms. Bill gathered 12 red mushrooms and 6 brown mushrooms. Ted gathered 14 green mushrooms and 6 blue mushrooms. If half of the blue mushrooms, two-thirds of the red mushrooms, and all of the brown mushrooms have white spots, how many white-spotted mushrooms did they gather?

Policy Response

assistant:
Bill gathered $12$ red mushrooms and $6$ brown mushrooms. Ted gathered $14$ green mushrooms and $6$ blue mushrooms. White-spotted mushrooms: - Blue: $1/2$ of $6 = 3$ - Red: $2/3$ of $12 = 8$ - Brown: $6$ Total white-spotted mushrooms: $3 + 8 + 6 = 17$. \boxed{17}

Reward

Reward components
key value
reference_answer 17
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:
Bill and Ted went into the forest to gather some wild mushrooms. Bill gathered 12 red mushrooms and 6 brown mushrooms. Ted gathered 14 green mushrooms and 6 blue mushrooms. If half of the blue mushrooms, two-thirds of the red mushrooms, and all of the brown mushrooms have white spots, how many white-spotted mushrooms did they gather?

Policy Response

assistant:
Bill gathered 12 red mushrooms, 6 brown mushrooms, and Ted gathered 14 green mushrooms and 6 blue mushrooms. Mushrooms with white spots: - Blue mushrooms: $14 / 2 = 7$ - Red mushrooms: $(2/3) * 12 = 8$ - Brown mushrooms: 6 Total white-spotted mushrooms: $7 + 8 + 6 = 21$. \boxed{21}

Reward

Reward components
key value
reference_answer 17
format_valid True
correct False
format_coef 0.1
reward 0.000

Trajectory Details

Trajectory 0 Episode

Episode Details
Turn 1
Step stats
key value
ob_len 128
ac_len 103
step_reward 0.000
Step Metrics
Metrics emitted by env.step
key value
format 1.000
correct 0.000
Episode totals
key value
num_turns 1
final_ob_len 0
sum_step_rewards 0.000
final_group_reward 0.000
total_return 0.000

Trajectory 1 Episode

Episode Details
Turn 1
Step stats
key value
ob_len 128
ac_len 96
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 128
ac_len 124
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 128
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 128
ac_len 118
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 128
ac_len 83
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 128
ac_len 109
step_reward 0.000
Step Metrics
Metrics emitted by env.step
key value
format 1.000
correct 0.000
Episode totals
key value
num_turns 1
final_ob_len 0
sum_step_rewards 0.000
final_group_reward 0.000
total_return 0.000

Trajectory 7 Episode

Episode Details
Turn 1
Step stats
key value
ob_len 128
ac_len 104
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:
Alex was having a cookout Friday night and planned to serve burgers to his guests. He planned to cook 3 burgers for each guest and had invited 10 friends over. 1 of his friends didn't eat meat and said they would bring their own food. Another one of his friends didn't eat bread and would not need the buns. The burger buns came 8 to a pack. How many packs of buns did Alex need to buy?

Policy Response

assistant:
Alex invited 10 friends. 1 friend didn't eat meat (no burger), and another didn't eat bread (no bun). Burgers without buns: $10 - 1 - 1 = 8$ burgers. Buns needed: $10 - 1 = 9$ buns. The buns came 8 to a pack. Packs needed: $\lceil 9 / 8 \rceil = \lceil 1.125 \rceil = 2$. \boxed{2}

Reward

Reward components
key value
reference_answer 3
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:
Alex was having a cookout Friday night and planned to serve burgers to his guests. He planned to cook 3 burgers for each guest and had invited 10 friends over. 1 of his friends didn't eat meat and said they would bring their own food. Another one of his friends didn't eat bread and would not need the buns. The burger buns came 8 to a pack. How many packs of buns did Alex need to buy?

Policy Response

assistant:
Alex invited 10 friends. Each guest was served 3 burgers. Total burgers = $10 \text{ friends} \times 3 \text{ burgers/friend} = 30 \text{ burgers}$. Buns needed = 30 burgers (each burger needs 1 bun). Buns per pack = 8. Packs needed = $\lceil 30 / 8 \rceil = \lceil 3.75 \rceil = 4$. \boxed{4}

Reward

Reward components
key value
reference_answer 3
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:
Alex was having a cookout Friday night and planned to serve burgers to his guests. He planned to cook 3 burgers for each guest and had invited 10 friends over. 1 of his friends didn't eat meat and said they would bring their own food. Another one of his friends didn't eat bread and would not need the buns. The burger buns came 8 to a pack. How many packs of buns did Alex need to buy?

Policy Response

assistant:
Alex invited 10 friends. He plans to cook 3 burgers for each guest. One friend didn't eat meat, and another didn't eat bread. Burghers needed: $10 \text{ friends} \times 3 \text{ burgers} = 30 \text{ burgers}$. Buns needed: $30 \text{ burgers} \times 1 \text{ bun} = 30 \text{ buns}$. Packs needed: $30 / 8 = 3.75$. Alex needs to buy 4 packs. \boxed{4}

Reward

Reward components
key value
reference_answer 3
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:
Alex was having a cookout Friday night and planned to serve burgers to his guests. He planned to cook 3 burgers for each guest and had invited 10 friends over. 1 of his friends didn't eat meat and said they would bring their own food. Another one of his friends didn't eat bread and would not need the buns. The burger buns came 8 to a pack. How many packs of buns did Alex need to buy?

Policy Response

assistant:
Alex invited 10 friends. Each guest was planned to get 3 burgers. Total burgers = $10 \text{ friends} \times 3 \text{ burgers} = 30$ burgers. Burgers without buns: 1 friend didn't eat bread. Buns needed = $30 - 3 = 27$ buns. Buns came 8 to a pack. Packs needed = $27 / 8 = 3.375$. Alex needs 4 packs. \boxed{4}

Reward

Reward components
key value
reference_answer 3
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:
Alex was having a cookout Friday night and planned to serve burgers to his guests. He planned to cook 3 burgers for each guest and had invited 10 friends over. 1 of his friends didn't eat meat and said they would bring their own food. Another one of his friends didn't eat bread and would not need the buns. The burger buns came 8 to a pack. How many packs of buns did Alex need to buy?

Policy Response

assistant:
Alex invited 10 friends. One friend didn't eat meat, leaving 9 guests who ate burgers. He planned to cook 3 burgers for each guest, so he cooked $9 \text{ guests} \times 3 \text{ burgers} = 27$ burgers. He needed 27 buns. The buns came 8 to a pack, so he needed $\lceil 27 / 8 \rceil$ packs. $27 / 8 = 3.375$. Rounding up, Alex needed 4 packs. \boxed{4}

Reward

Reward components
key value
reference_answer 3
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:
Alex was having a cookout Friday night and planned to serve burgers to his guests. He planned to cook 3 burgers for each guest and had invited 10 friends over. 1 of his friends didn't eat meat and said they would bring their own food. Another one of his friends didn't eat bread and would not need the buns. The burger buns came 8 to a pack. How many packs of buns did Alex need to buy?

Policy Response

assistant:
Alex invited 10 friends. 3 burgers per guest means $10 \text{ guests} \times 3 \text{ burgers} = 30 \text{ burgers}$. 1 of 10 friends didn't eat meat, 1 friend didn't eat bread. The burger bun comes with bread, so this friend needs 2 fewer burgers. He served 29 burgers. Burger buns came 8 to a pack. $29 \div 8 = 3.625$ packs. Alex needs to buy 4 packs. \boxed{4}

Reward

Reward components
key value
reference_answer 3
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:
Alex was having a cookout Friday night and planned to serve burgers to his guests. He planned to cook 3 burgers for each guest and had invited 10 friends over. 1 of his friends didn't eat meat and said they would bring their own food. Another one of his friends didn't eat bread and would not need the buns. The burger buns came 8 to a pack. How many packs of buns did Alex need to buy?

Policy Response

assistant:
Alex invited 10 friends, but 1 friend would not eat the burgers. Alex cooks 3 burgers for each guest. Guests eating burgers: $10 - 1 = 9$. Total burgers: $9 \text{ guests} \times 3 \text{ burgers} = 27 \text{ burgers}$. Buns needed: Each burger needs a bun, so 27 buns. The buns come 8 to a pack. Packs needed: $27 / 8 = 3.375$. Alex needs 4 packs of buns. \boxed{4}

Reward

Reward components
key value
reference_answer 3
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:
Alex was having a cookout Friday night and planned to serve burgers to his guests. He planned to cook 3 burgers for each guest and had invited 10 friends over. 1 of his friends didn't eat meat and said they would bring their own food. Another one of his friends didn't eat bread and would not need the buns. The burger buns came 8 to a pack. How many packs of buns did Alex need to buy?

Policy Response

assistant:
Alex invited 10 friends. 1 friend didn't eat meat and 1 friend didn't eat bread. 3 burgers for each guest were planned. Burgers for meat eaters: $10 \text{ friends} - 1 \text{ friend} = 9 \text{ friends}$. Burgers total: $9 \text{ friends} \times 3 \text{ burgers} = 27 \text{ burgers}$. He does not need buns for bread eaters. The number of buns is $9 \text{ friends} \times 3 \text{ burgers} = 27 \text{ buns}$. The buns came 8 to a pack. Packs needed: $\lceil 27 / 8 \rceil$. $27 / 8 = 3.375$. $\lceil 3.375 \rceil = 4$. \boxed{4}

Reward

Reward components
key value
reference_answer 3
format_valid True
correct False
format_coef 0.1
reward 0.000

Trajectory Details

Trajectory 0 Episode

Episode Details
Turn 1
Step stats
key value
ob_len 152
ac_len 126
step_reward 0.000
Step Metrics
Metrics emitted by env.step
key value
format 1.000
correct 0.000
Episode totals
key value
num_turns 1
final_ob_len 0
sum_step_rewards 0.000
final_group_reward 0.000
total_return 0.000

Trajectory 1 Episode

Episode Details
Turn 1
Step stats
key value
ob_len 152
ac_len 132
step_reward 0.000
Step Metrics
Metrics emitted by env.step
key value
format 1.000
correct 0.000
Episode totals
key value
num_turns 1
final_ob_len 0
sum_step_rewards 0.000
final_group_reward 0.000
total_return 0.000

Trajectory 2 Episode

Episode Details
Turn 1
Step stats
key value
ob_len 152
ac_len 114
step_reward 0.000
Step Metrics
Metrics emitted by env.step
key value
format 1.000
correct 0.000
Episode totals
key value
num_turns 1
final_ob_len 0
sum_step_rewards 0.000
final_group_reward 0.000
total_return 0.000

Trajectory 3 Episode

Episode Details
Turn 1
Step stats
key value
ob_len 152
ac_len 120
step_reward 0.000
Step Metrics
Metrics emitted by env.step
key value
format 1.000
correct 0.000
Episode totals
key value
num_turns 1
final_ob_len 0
sum_step_rewards 0.000
final_group_reward 0.000
total_return 0.000

Trajectory 4 Episode

Episode Details
Turn 1
Step stats
key value
ob_len 152
ac_len 118
step_reward 0.000
Step Metrics
Metrics emitted by env.step
key value
format 1.000
correct 0.000
Episode totals
key value
num_turns 1
final_ob_len 0
sum_step_rewards 0.000
final_group_reward 0.000
total_return 0.000

Trajectory 5 Episode

Episode Details
Turn 1
Step stats
key value
ob_len 152
ac_len 208
step_reward 0.000
Step Metrics
Metrics emitted by env.step
key value
format 1.000
correct 0.000
Episode totals
key value
num_turns 1
final_ob_len 0
sum_step_rewards 0.000
final_group_reward 0.000
total_return 0.000

Trajectory 6 Episode

Episode Details
Turn 1
Step stats
key value
ob_len 152
ac_len 128
step_reward 0.000
Step Metrics
Metrics emitted by env.step
key value
format 1.000
correct 0.000
Episode totals
key value
num_turns 1
final_ob_len 0
sum_step_rewards 0.000
final_group_reward 0.000
total_return 0.000

Trajectory 7 Episode

Episode Details
Turn 1
Step stats
key value
ob_len 152
ac_len 135
step_reward 0.000
Step Metrics
Metrics emitted by env.step
key value
format 1.000
correct 0.000
Episode totals
key value
num_turns 1
final_ob_len 0
sum_step_rewards 0.000
final_group_reward 0.000
total_return 0.000

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:
Josh has 85 marbles. There are three times as many blue marbles as red while the rest are yellow. If there are 14 red marbles, how many yellow marbles are there?

Policy Response

assistant:
There are three times as many blue marbles as red marbles. Blue marbles = $3 \times 14 = 42$. Total marbles - Red marbles - Blue marbles = Yellow marbles $85 - 14 - 42 = 29$. \boxed{29}

Reward

Reward components
key value
reference_answer 29
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:
Josh has 85 marbles. There are three times as many blue marbles as red while the rest are yellow. If there are 14 red marbles, how many yellow marbles are there?

Policy Response

assistant:
There are 3 times as many blue marbles as red marbles. Red marbles: 14. Blue marbles: $3 \times 14 = 42$. Total marbles: 85. Yellow marbles: $85 - 14 - 42 = 85 - 56 = 29$. \boxed{29}

Reward

Reward components
key value
reference_answer 29
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:
Josh has 85 marbles. There are three times as many blue marbles as red while the rest are yellow. If there are 14 red marbles, how many yellow marbles are there?

Policy Response

assistant:
There are 3 times as many blue marbles as red marbles. Red marbles = 14. Blue marbles = $3 \times 14 = 42$. Total marbles used for red and blue = $14 + 42 = 56$. Yellow marbles = $85 - 56 = 29$. \boxed{29}

Reward

Reward components
key value
reference_answer 29
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:
Josh has 85 marbles. There are three times as many blue marbles as red while the rest are yellow. If there are 14 red marbles, how many yellow marbles are there?

Policy Response

assistant:
There are three times as many blue marbles as red marbles. Red marbles = 14. Blue marbles = $3 \times 14 = 42$. Total marbles for blue and red = $14 + 42 = 56$. Yellow marbles = $85 - 56 = 29$. \boxed{29}

Reward

Reward components
key value
reference_answer 29
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:
Josh has 85 marbles. There are three times as many blue marbles as red while the rest are yellow. If there are 14 red marbles, how many yellow marbles are there?

Policy Response

assistant:
There are three times as many blue marbles as red marbles. Since there are 14 red marbles, there are $3 \times 14 = 42$ blue marbles. The total number of blue and red marbles is $14 + 42 = 56$. The rest are yellow marbles, so there are $85 - 56 = 29$ yellow marbles. \boxed{29}

Reward

Reward components
key value
reference_answer 29
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:
Josh has 85 marbles. There are three times as many blue marbles as red while the rest are yellow. If there are 14 red marbles, how many yellow marbles are there?

Policy Response

assistant:
There are 3 times as many blue marbles as red marbles. Red marbles = 14. Blue marbles = $3 \times 14 = 42$. Total marbles = Red + Blue + Yellow = $14 + 42 + \text{Yellow} = 56 + \text{Yellow}$. The rest are yellow: $\text{Yellow} = 85 - 56 = 29$. \boxed{29}

Reward

Reward components
key value
reference_answer 29
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:
Josh has 85 marbles. There are three times as many blue marbles as red while the rest are yellow. If there are 14 red marbles, how many yellow marbles are there?

Policy Response

assistant:
There are 3 times as many blue marbles as red marbles. Red marbles = 14. Blue marbles = $3 \times 14 = 42$. Marbles not yellow = Red marbles + Blue marbles = $14 + 42 = 56$. Yellow marbles = 85 - 56 = 29. \boxed{29}

Reward

Reward components
key value
reference_answer 29
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:
Josh has 85 marbles. There are three times as many blue marbles as red while the rest are yellow. If there are 14 red marbles, how many yellow marbles are there?

Policy Response

assistant:
There are 3 times as many blue marbles as red marbles. Blue marbles = $3 \times 14 = 42$. Total marbles = Blue + Red + Yellow. $85 = 42 + 14 + \text{Yellow}$ $85 = 56 + \text{Yellow}$ $\text{Yellow} = 85 - 56 = 29$ \boxed{29}

Reward

Reward components
key value
reference_answer 29
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 96
ac_len 90
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 96
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 2 Episode

Episode Details
Turn 1
Step stats
key value
ob_len 96
ac_len 72
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 96
ac_len 106
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 96
ac_len 84
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 96
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 6 Episode

Episode Details
Turn 1
Step stats
key value
ob_len 96
ac_len 84
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 96
ac_len 86
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