RL Iteration 13

Generated 2026-06-11T16:37:45

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:
Seth bought some boxes of oranges. He gave a box to his mother. He then gave away half of the remaining boxes. If Seth has 4 boxes of oranges left, how many boxes did he buy in the first place?

Policy Response

assistant:
💭 Thinking
Seth bought $x$ boxes of oranges.

1. He gave 1 box to his mother.
2. Remaining after mother: $x - 1$ boxes.
3. He gave away half of the remaining: $\frac{x - 1}{2}$ boxes.
4. Boxes left after that: $(x - 1) - \frac{x - 1}{2} = \frac{x - 1}{2}$ boxes.

He has 4 boxes left:

$\frac{x - 1}{2} = 4$

$x - 1 = 8$

$x = 9$

\boxed{9}
Seth bought 9 boxes of oranges. 1. He gave 1 box to his mother, leaving $9 - 1 = 8$ boxes. 2. He gave away half of 8, which is 4 boxes. 3. He had $8 - 4 = 4$ boxes left. \boxed{9} </think> Seth bought 9 boxes of oranges. 1. He gave 1 box to his mother, leaving $9 - 1 = 8$ boxes. 2. He gave away half of 8, which is 4 boxes. 3. Remaining boxes: $8 - 4 = 4$ boxes. \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:
Seth bought some boxes of oranges. He gave a box to his mother. He then gave away half of the remaining boxes. If Seth has 4 boxes of oranges left, how many boxes did he buy in the first place?

Policy Response

assistant:
💭 Thinking
Let $x$ be the initial number of boxes.

1. He gave 1 box to his mother. Remaining: $x - 1$.
2. He gave away half of the remaining boxes. Given away: $(x - 1) / 2$.
3. Boxes left after step 2: $(x - 1) - (x - 1) / 2 = (x - 1) / 2$.
4. Seth has 4 boxes left.

$(x - 1) / 2 = 4$

$x - 1 = 8$

$x = 9$

\boxed{9}
Seth bought a total of 9 boxes. 1. After giving one box to his mother, there were $x - 1$ boxes left. 2. He gave away half of these, leaving $(x - 1) / 2$ boxes. 3. Setting $(x - 1) / 2 = 4$ gives $x - 1 = 8$, so $x = 9$. \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:
Seth bought some boxes of oranges. He gave a box to his mother. He then gave away half of the remaining boxes. If Seth has 4 boxes of oranges left, how many boxes did he buy in the first place?

Policy Response

assistant:
<think> Let $x$ be the total number of boxes bought. 1. One box was given to his mother: $x - 1$. 2. Half of the remaining boxes were given away: $\frac{1}{2}(x - 1)$. 3. Boxes left: $x - 1 - \frac{1}{2}(x - 1) = \frac{1}{2}(x - 1)$. We are given that 4 boxes are left: $\frac{1}{2}(x - 1) = 4$ $x - 1 = 8$ $x = 9$ \boxed{9} </think> Seth bought a total of $x$ boxes. 1. He gave 1 box to his mother. 2. He gave away half of the remaining boxes ($x - 1$). The boxes given away are $\frac{1}{2}(x - 1)$. 3. boxes left = $x - 1 - \frac{1}{2}(x - 1) = \frac{1}{2}(x - 1)$. $ \frac{1}{2}(x - 1) = 4 $ $ x - 1 = 8 $ $ x = 9 $ \boxed{9} </think> Seth bought $x$ boxes. He gave 1 box to his mother, leaving $x - 1$ boxes. He gave half of these away, leaving half

Reward

Reward components
key value
reference_answer 9
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:
Seth bought some boxes of oranges. He gave a box to his mother. He then gave away half of the remaining boxes. If Seth has 4 boxes of oranges left, how many boxes did he buy in the first place?

Policy Response

assistant:
💭 Thinking
Let $x$ be the initial number of boxes.

1. He gave 1 box to his mother. Remaining after giving to mother: $x - 1$.

2. He gave away half of the remaining boxes. Boxes given away: $\frac{1}{2}(x - 1)$.

3. Boxes left after giving to mother and giving away half: $(x - 1) - \frac{1}{2}(x - 1) = \frac{1}{2}(x - 1)$.

4. He has 4 boxes left.

5. Set up the equation: $\frac{1}{2}(x - 1) = 4$.

6. Multiply both sides by 2: $x - 1 = 8$.

7. Add 1 to both sides: $x = 9$.

Seth bought 9 boxes of oranges.

\boxed{9}
He gave 1 box to his mother, leaving $x - 1$ boxes. He gave away half of the remaining boxes, leaving half of $x - 1$ boxes. The boxes left were 4. $\frac{1}{2}(x - 1) = 4$ $x - 1 = 8$ $x = 9$ \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:
Seth bought some boxes of oranges. He gave a box to his mother. He then gave away half of the remaining boxes. If Seth has 4 boxes of oranges left, how many boxes did he buy in the first place?

Policy Response

assistant:
<think> Seth gave 1 box to his mother. Remaining boxes before half were given away: $X - 1$ Half of remaining boxes given away: $\frac{X - 1}{2}$ Boxes left: $X - 1 - \frac{X - 1}{2} = \frac{X - 1}{2}$ We know the boxes left is 4. $X - 1 - \frac{X - 1}{2} = 4$ $X - 1 - (X/2 - 1/2) = 4$ $X/2 + 1/2 = 4$ $X/2 = 7/2$ $X = 7$ \boxed{7} </think> Seth gave 1 box to his mother. The remaining boxes were $X - 1$. He gave away half of these, so $\frac{X - 1}{2}$ boxes were given away. The boxes left are $(X - 1) - \frac{X - 1}{2} = \frac{X - 1}{2}$. Setting this equal to 4: $\frac{X - 1}{2} = 4$ $X - 1 = 8$ $X = 9$ \boxed{9} \boxed{9} \boxed{9} \boxed{9} \boxed{9} \boxed{9}

Reward

Reward components
key value
reference_answer 9
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:
Seth bought some boxes of oranges. He gave a box to his mother. He then gave away half of the remaining boxes. If Seth has 4 boxes of oranges left, how many boxes did he buy in the first place?

Policy Response

assistant:
<think> Step 1: Seth gave a box to his mother. Remaining boxes = Total - 1. Step 2: He gave away half of the remaining boxes. Step 3: Boxes given away = (Total - 1) / 2. Step 4: Boxes left = (Total - 1) - (Total - 1) / 2 = (Total - 1) / 2. Step 5: We know Boxes left = 4. 6: 4 = (Total - 1) / 2 7: 8 = Total - 1 8: Total = 9 \boxed{9} </think> Seth gave 1 box to his mother. He gave away half of the remaining boxes. 1. Boxes after mother: $T - 1$ 2. Boxes given away: $(T - 1) / 2$ 3. Boxes left: $(T - 1) - (T - 1) / 2 = (T - 1) / 2$ $4 = (T - 1) / 2$ $8 = T - 1$ $T = 9$ \boxed{9} Seth bought 9 boxes of oranges. \boxed{9} \boxed{9} \boxed{9} \boxed{9} \boxed{9} \boxed{9} \boxed{9} \boxed{9} \

Reward

Reward components
key value
reference_answer 9
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:
Seth bought some boxes of oranges. He gave a box to his mother. He then gave away half of the remaining boxes. If Seth has 4 boxes of oranges left, how many boxes did he buy in the first place?

Policy Response

assistant:
<think> Let $x$ be the initial number of boxes. 1. He gave 1 box to his mother. Remaining boxes: $x - 1$. 2. He gave away half of the remaining boxes. Boxes given away: $\frac{x - 1}{2}$. 3. Boxes left: $(x - 1) - \frac{x - 1}{2} = \frac{x - 1}{2}$. 4. We are given that boxes left = 4. $\frac{x - 1}{2} = 4$ $x - 1 = 8$ $x = 9$ \boxed{9} </think> Seth bought $x$ boxes. 1. After giving a box to his mother, he had $x - 1$ boxes left. 2. He gave away half of these, leaving him with $\frac{x - 1}{2}$ boxes. 3. We set this equal to 4: $\frac{x - 1}{2} = 4$. Solving for $x$: $x - 1 = 8$ $x = 9$ \boxed{9} Seth bought 9 boxes of oranges. \boxed{9} Seth bought 9 boxes of oranges. \boxed{9} Seth bought 9 boxes of oranges. \boxed{9} Seth bought 9 boxes of oranges. \boxed{9} Seth bought 9 boxes of

Reward

Reward components
key value
reference_answer 9
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:
Seth bought some boxes of oranges. He gave a box to his mother. He then gave away half of the remaining boxes. If Seth has 4 boxes of oranges left, how many boxes did he buy in the first place?

Policy Response

assistant:
<think> Let $B$ be the number of boxes Seth bought. 1. He gave 1 box to his mother. Remaining: $B - 1$. 2. He gave away half of the remaining boxes. Remaining after step 2: $\frac{1}{2} (B - 1)$. 3. He has 4 boxes left. $4 = \frac{1}{2} (B - 1)$ $8 = B - 1$ $B = 9$ \boxed{9} </think> Seth bought $B$ boxes. After giving 1 to his mother, $B-1$ boxes remained. He gave half of those away, so $1/2(B-1)$ were given away, leaving $1/2(B-1)$ boxes. $1/2(B-1) = 4$ $B-1 = 8$ $B = 9$ \boxed{9} \boxed{9} \boxed{9} \boxed{9} \boxed{9} \boxed{9} \boxed{9} \boxed{9} \boxed{9} \boxed{9} \boxed{9} \boxed{9} \boxed{9} \boxed{9} \boxed{9} \boxed{9} \boxed{9} \boxed{9} \boxed{9} \boxed{9}

Reward

Reward components
key value
reference_answer 9
format_valid False
correct True
format_coef 0.1
reward 0.900

Trajectory Details

Trajectory 0 Episode

Episode Details
Turn 1
Step stats
key value
ob_len 100
ac_len 291
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 100
ac_len 320
step_reward 0.900
Step Metrics
Metrics emitted by env.step
key value
format 0.000
correct 1.000
Episode totals
key value
num_turns 1
final_ob_len 0
sum_step_rewards 0.900
final_group_reward 0.000
total_return 0.900

Trajectory 2 Episode

Episode Details
Turn 1
Step stats
key value
ob_len 100
ac_len 237
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 100
ac_len 320
step_reward 0.900
Step Metrics
Metrics emitted by env.step
key value
format 0.000
correct 1.000
Episode totals
key value
num_turns 1
final_ob_len 0
sum_step_rewards 0.900
final_group_reward 0.000
total_return 0.900

Trajectory 4 Episode

Episode Details
Turn 1
Step stats
key value
ob_len 100
ac_len 320
step_reward 0.900
Step Metrics
Metrics emitted by env.step
key value
format 0.000
correct 1.000
Episode totals
key value
num_turns 1
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 100
ac_len 283
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 100
ac_len 320
step_reward 0.900
Step Metrics
Metrics emitted by env.step
key value
format 0.000
correct 1.000
Episode totals
key value
num_turns 1
final_ob_len 0
sum_step_rewards 0.900
final_group_reward 0.000
total_return 0.900

Trajectory 7 Episode

Episode Details
Turn 1
Step stats
key value
ob_len 100
ac_len 320
step_reward -0.100
Step Metrics
Metrics emitted by env.step
key value
format 0.000
correct 0.000
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

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:
Brandon has been fired from half the businesses in town and has quit from a third of them. If there are 72 business in town, how many businesses can he still apply to?

Policy Response

assistant:
💭 Thinking
Brandon has been fired from half the businesses: 1/2 * 72 = 36.

He has quit from a third of them: 1/3 * 72 = 24.

Total businesses fired from or quit from: 36 + 24 = 60.

Businesses he can still apply to: 72 - 60 = 12.

\boxed{12}
Brandon has been fired from half the businesses: 1/2 * 72 = 36. He has quit from a third of them: 1/3 * 72 = 24. Total businesses fired from or quit from: 36 + 24 = 60. Businesses he can still apply to: 72 - 60 = 12. \boxed{12}

Reward

Reward components
key value
reference_answer 12
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:
Brandon has been fired from half the businesses in town and has quit from a third of them. If there are 72 business in town, how many businesses can he still apply to?

Policy Response

assistant:
💭 Thinking
Brandon was fired from half the businesses and quit a third of them.

1. Calculate the fraction of businesses left: $1 - \frac{1}{2} - \frac{1}{3} = \frac{6}{6} - \frac{3}{6} - \frac{2}{6} = \frac{1}{6}$.

2. Calculate the number of businesses: $72 \times \frac{1}{6} = 12$.

\boxed{12}
Brandon was fired from half the businesses ($\frac{1}{2}$) and quit a third of them ($\frac{1}{3}$). 1. Sum of fired businesses: $\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}$. 2. Remaining businesses: $1 - \frac{5}{6} = \frac{1}{6}$. 3. Number of businesses: $72 \times \frac{1}{6} = 12$. \boxed{12}

Reward

Reward components
key value
reference_answer 12
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:
Brandon has been fired from half the businesses in town and has quit from a third of them. If there are 72 business in town, how many businesses can he still apply to?

Policy Response

assistant:
💭 Thinking
Brandon has been fired from half the businesses and has quit from a third of them. There were 72 businesses in town.

1. Calculate the number of businesses he was fired from: $ \frac{1}{2} \times 72 = 36 $.
2. Calculate the number of businesses he quit from: $ \frac{1}{3} \times 72 = 24 $.

3. Calculate the total businesses he has been removed from: $ 36 + 24 = 60 $.

4. Calculate the businesses he can still apply to: $ 72 - 60 = 12 $.

\boxed{12}
He was fired from half the businesses and quit from a third of them. 1. Find the businesses he was fired from: $ \frac{1}{2} \times 72 = 36 $. 2. Find the businesses he quit from: $ \frac{1}{3} \times 72 = 24 $. 3. Total businesses removed: $ 36 + 24 = 60 $. 4. Businesses remaining: $ 72 - 60 = 12 $. \boxed{12}

Reward

Reward components
key value
reference_answer 12
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:
Brandon has been fired from half the businesses in town and has quit from a third of them. If there are 72 business in town, how many businesses can he still apply to?

Policy Response

assistant:
<think> Brandon has been fired from half the businesses and quit a third of them. 1. Calculate the fraction of businesses he was fired from or quit: $1/2 + 1/3 = 3/6 + 2/6 = 5/6$ 2. Calculate the number of businesses he was fired from or quit: $5/6 * 72 = 60$ 3. Calculate the businesses he can still apply to: $72 - 60 = 12$ \boxed{12} </think> Brandon was fired from a half and quit a third of the businesses. 1. Find the total fraction of businesses left: $1 - (1/2 + 1/3) = 1 - 5/6 = 1/6$. 2. Find the number of businesses: $1/6 * 72 = 12$. \boxed{12} \boxed{12} Brandon can still apply to 12 businesses. \boxed{12} \boxed{12} \boxed{12} \boxed{12} \boxed{12} \boxed{12} \boxed{12} \boxed{12} \boxed{12} \boxed{12} \boxed{12} \boxed{12} \boxed{12} \boxed{12}

Reward

Reward components
key value
reference_answer 12
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:
Brandon has been fired from half the businesses in town and has quit from a third of them. If there are 72 business in town, how many businesses can he still apply to?

Policy Response

assistant:
💭 Thinking
Brandon has been fired from half the businesses and quit from a third of them.

1. Find the total fraction of businesses he has left: $1 - \frac{1}{2} - \frac{1}{3}$.

2. Find a common denominator for 2 and 3, which is 6.
   - $1/2 = 3/6$
   - $1/3 = 2/6$

3. Sum the fractions: $3/6 + 2/6 = 5/6$.

4. Subtract from 1: $1 - 5/6 = 1/6$.

5. Calculate the number of businesses: $1/6$ of 72.

$72 / 6 = 12$

\boxed{12}
Brandon has been fired from half the businesses ($\frac{1}{2}$) and quit from a third ($\frac{1}{3}$). 1. Sum the fired/quit fractions: $\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}$. 2. The remaining fraction: $1 - \frac{5}{6} = \frac{1}{6}$. 3. Calculate the businesses: $\frac{1}{6} \times 72 = 12$. \boxed{12}

Reward

Reward components
key value
reference_answer 12
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:
Brandon has been fired from half the businesses in town and has quit from a third of them. If there are 72 business in town, how many businesses can he still apply to?

Policy Response

assistant:
💭 Thinking
Brandon has been fired from half the businesses and quit from a third of them.

1. Find the businesses he was fired from: $\frac{1}{2} * 72 = 36$
2. Find the businesses he quit from: $\frac{1}{3} * 72 = 24$
3. Find the total businesses he left: $36 + 24 = 60$
4. Find the businesses he can still apply to: $72 - 60 = 12$

\boxed{12}
Brandon has been fired from half the businesses and quit from a third of them. 1. Fired from: $1/2 * 72 = 36$ 2. Quit from: $1/3 * 72 = 24$ 3. Total left: $36 + 24 = 60$ 4. Available: $72 - 60 = 12$ \boxed{12}

Reward

Reward components
key value
reference_answer 12
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:
Brandon has been fired from half the businesses in town and has quit from a third of them. If there are 72 business in town, how many businesses can he still apply to?

Policy Response

assistant:
<think> Brandon has been fired from half the businesses and has quit from a third of them. 1. Find the fraction of businesses he has visited: $1/2 + 1/3 = 3/6 + 2/6 = 5/6$. 2. Calculate the number of businesses he has visited: $5/6 * 72 = 60$. 3. Find the businesses he can still apply to: $72 - 60 = 12$. \boxed{12} </think> Brandon has been fired from half the businesses and has quit from a third of them. 1. Calculate the total fraction of businesses visited: $1/2 + 1/3 = 5/6$. 2. Find the number of businesses visited: $5/6 * 72 = 60$. 3. Find the businesses remaining: $72 - 60 = 12$. \boxed{12} He can still apply to 12 businesses. \boxed{12} \boxed{12} \boxed{12} \boxed{12} \boxed{12} \boxed{12} \boxed{12} \boxed{12} \boxed{12} \boxed{12} \boxed{12} \boxed{12} \boxed{12} \boxed{12} \boxed{1

Reward

Reward components
key value
reference_answer 12
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:
Brandon has been fired from half the businesses in town and has quit from a third of them. If there are 72 business in town, how many businesses can he still apply to?

Policy Response

assistant:
💭 Thinking
Brandon was fired from half of the businesses and quit from a third of them.

1. Calculate the fraction of businesses from which he was fired or quit: $1/2 + 1/3 = 3/6 + 2/6 = 5/6$.

2. Calculate the number of businesses from which he was fired or quit: $72 * 5/6 = 60$.

3. Calculate the businesses he can still apply to: $72 - 60 = 12$.

\boxed{12}
Brandon was fired from $1/2$ and quit from $1/3$ of the businesses. 1. Find the total fraction of businesses: $1/2 + 1/3 = 5/6$. 2. Find the number of businesses affected: $72 * 5/6 = 60$. 3. Find the remaining businesses: $72 - 60 = 12$. \boxed{12}

Reward

Reward components
key value
reference_answer 12
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 91
ac_len 247
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 91
ac_len 217
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 91
ac_len 316
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 91
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 4 Episode

Episode Details
Turn 1
Step stats
key value
ob_len 91
ac_len 320
step_reward 0.900
Step Metrics
Metrics emitted by env.step
key value
format 0.000
correct 1.000
Episode totals
key value
num_turns 1
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 91
ac_len 320
step_reward 0.900
Step Metrics
Metrics emitted by env.step
key value
format 0.000
correct 1.000
Episode totals
key value
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
key value
ob_len 91
ac_len 267
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 91
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

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:
At peak season, 6 packs of tuna fish are sold per hour, while in a low season 4 tuna packs are sold per hour. If each tuna pack is sold at $60, How much more money is made in a day during a high season than a low season if the fish are sold for 15 hours?

Policy Response

assistant:
💭 Thinking
**High Season Sales:**
1. Packs per hour: 6
2. Sales per hour: $60 * 6 = 360
3. Total hours per day: 15
4. Sales per day: 360 * 15 = 5400

**Low Season Sales:**
1. Packs per hour: 4
2. Sales per hour: $60 * 4 = 240
3. Total hours per day: 15
4. Sales per day: 240 * 15 = 3600

**Difference:**
5400 - 3600 = 1800

\boxed{1800}
High season sales: $6 packs/hour * $60/pack * 15 hours = 5400 per day. Low season sales: $4 packs/hour * $60/pack * 15 hours = 3600 per day. Difference: 5400 - 3600 = 1800. \boxed{1800}

Reward

Reward components
key value
reference_answer 1800
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:
At peak season, 6 packs of tuna fish are sold per hour, while in a low season 4 tuna packs are sold per hour. If each tuna pack is sold at $60, How much more money is made in a day during a high season than a low season if the fish are sold for 15 hours?

Policy Response

assistant:
💭 Thinking
* **Tuna packs per hour in high season:** 6 packs
* **Tuna packs per hour in low season:** 4 packs
* **Packs per day in high season:** 6 packs/hour * 15 hours = 90 packs
* **Packs per day in low season:** 4 packs/hour * 15 hours = 60 packs
* **Total packs in high season:** 90 packs
* **Total packs in low season:** 60 packs

**Money earned in high season:**
90 packs * $60 = $5400

**Money earned in low season:**
60 packs * $60 = $3600

**Difference:**
$5400 - $3600 = $1800

\boxed{1800}
6 packs per hour * 15 hours = 90 packs per day in high season. 4 packs per hour * 15 hours = 60 packs per day in low season. 90 packs * $60 = $5400 per day in high season. 60 packs * $60 = $3600 per day in low season. $5400 - $3600 = $1800. \boxed{1800}

Reward

Reward components
key value
reference_answer 1800
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:
At peak season, 6 packs of tuna fish are sold per hour, while in a low season 4 tuna packs are sold per hour. If each tuna pack is sold at $60, How much more money is made in a day during a high season than a low season if the fish are sold for 15 hours?

Policy Response

assistant:
<think> High season tuna packs per hour: 6 Low season tuna packs per hour: 4 Tuna packs per hour difference: 6 - 4 = 2 Tuna packs per day difference: 2 packs/hour * 15 hours = 30 packs Money per day high season: 30 packs * $60 = $1800 Money per day low season: 24 packs/hour * $60 = $1440 Money difference per day: $1800 - $1440 = $360 \boxed{360} </think> 6 packs per hour * 60 dollars * 15 hours = 5400 dollars per high season day. 4 packs per hour * 60 dollars * 15 hours = 3600 dollars per low season day. 5400 - 3600 = 1800 dollars. \boxed{1800} \boxed{1800} \boxed{1800} \boxed{1800} \boxed{1800} \boxed{1800} \boxed{1800} \boxed{1800} \boxed{1800} \boxed{1800} \boxed{1800} \boxed{1800} \boxed{1

Reward

Reward components
key value
reference_answer 1800
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:
At peak season, 6 packs of tuna fish are sold per hour, while in a low season 4 tuna packs are sold per hour. If each tuna pack is sold at $60, How much more money is made in a day during a high season than a low season if the fish are sold for 15 hours?

Policy Response

assistant:
💭 Thinking
Packs sold per hour:

* High season: 6 packs
* Low season: 4 packs

Packs sold in a day (15 hours):

* High season: 6 packs/ hr * 15 hrs = 90 packs
* Low season: 4 packs/ hr * 15 hrs = 60 packs

Money earned per day:

* High season: 90 packs * $60 = $5400
* Low season: 60 packs * $60 = $3600

Difference:

$5400 - $3600 = $1800

\boxed{1800}
Packs sold per day: * High season: $6 \text{ packs/ hr} \times 15 \text{ hrs} = 90 \text{ packs}$ * Low season: $4 \text{ packs/ hr} \times 15 \text{ hrs} = 60 \text{ packs}$ Money per day: * High season: $90 \text{ packs} \times \$60 = \$5400$ * Low season: $60 \text{ packs} \times \$60 = \$3600$ Difference: $5400 - 3600 = 1800$ \boxed{1800}

Reward

Reward components
key value
reference_answer 1800
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:
At peak season, 6 packs of tuna fish are sold per hour, while in a low season 4 tuna packs are sold per hour. If each tuna pack is sold at $60, How much more money is made in a day during a high season than a low season if the fish are sold for 15 hours?

Policy Response

assistant:
<think> 1. Calculate the packs sold per hour: High season = 6, Low season = 4. 2. Calculate the packs sold in 15 hours: High season = 6 * 15 = 90, Low season = 4 * 15 = 60. 3. Calculate the total packs in a day: High season = 90 + 60 = 150. 4. Calculate the total packs sold: 150 * 60 = 9000. 5. Calculate the money made per day: 9000 * 60 = 540000. 6. Calculate the difference in money: 540000 - (Low season packs * 60) = 540000 - (60 * 60) = 540000 - 360000 = 180000. \boxed{180000} </think> High season packs per day: $6 \text{ packs/hour} \times 15 \text{ hours} = 90 \text{ packs/ day}$. Low season packs per day: $4 \text{ packs/ hour} \times 15 \text{ hours} = 60 \text{ packs/ day}$. Total packs per day: $90 + 60 = 150 \text{ packs

Reward

Reward components
key value
reference_answer 1800
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:
At peak season, 6 packs of tuna fish are sold per hour, while in a low season 4 tuna packs are sold per hour. If each tuna pack is sold at $60, How much more money is made in a day during a high season than a low season if the fish are sold for 15 hours?

Policy Response

assistant:
<think> High season tuna packs per day: $6 \text{ packs/hour} \times 15 \text{ hours} = 90 \text{ packs}$. Low season tuna packs per day: $4 \text{ packs/hour} \times 15 \text{ hours} = 60 \text{ packs}$. Total packs per day: $90 + 60 = 150 \text{ packs}$. Money per day: $150 \text{ packs} \times 60 \text{ dollars} = 9000 \text{ dollars}$. Difference: $9000 - 9000 = 0$? No, the question asks "How much more money". Low season money: $60 \text{ packs} \times 60 \text{ dollars} = 3600 \text{ dollars}$. High season money: $90 \text{ packs} \times 60 \text{ dollars} = 5400 \text{ dollars}$. Difference: $5400 - 3600 = 1800 \text{ dollars}$. \boxed{1800} </think> High season tuna packs per day: $6 \text{ packs/hour} \times 15 \text{ hours} = 90 \text{ packs}$. Low season tuna packs per day: $4 \text{

Reward

Reward components
key value
reference_answer 1800
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:
At peak season, 6 packs of tuna fish are sold per hour, while in a low season 4 tuna packs are sold per hour. If each tuna pack is sold at $60, How much more money is made in a day during a high season than a low season if the fish are sold for 15 hours?

Policy Response

assistant:
<think> 1. Calculate the tuna packs sold per day in each season: High Season: 6 packs/hour * 15 hours = 90 packs Low Season: 4 packs/hour * 15 hours = 60 packs 2. Calculate the total packs sold in each season: High Season: 90 packs * 1 day = 90 packs Low Season: 60 packs * 1 day = 60 packs 3. Calculate the money made in each season: High Season: 90 packs * $60 = $5400 Low Season: 60 packs * $60 = $3600 4. Find the difference: $5400 - $3600 = $1800 \boxed{1800} </think> High Season Packs: $6 \text{ packs/hour} \times 15 \text{ hours} = 90 \text{ packs}$ Low Season Packs: $4 \text{ packs/hour} \times 15 \text{ hours} = 60 \text{ packs}$ High Season Earnings: $90 \text{ packs} \times 60 \text{ dollars} = 5400 \text{ dollars}$ Low Season Earnings: $60 \text{ packs} \times 60 \text{ dollars} = 3600 \text

Reward

Reward components
key value
reference_answer 1800
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:
At peak season, 6 packs of tuna fish are sold per hour, while in a low season 4 tuna packs are sold per hour. If each tuna pack is sold at $60, How much more money is made in a day during a high season than a low season if the fish are sold for 15 hours?

Policy Response

assistant:
<think> **1. Tuna packs per hour:** * High Season: 6 packs per hour * Low Season: 4 packs per hour **2. Tuna packs per day (15 hours):** * High Season: $6 \text{ packs/ hour} \times 15 \text{ hours} = 90 \text{ packs}$ * Low Season: $4 \text{ packs/ hour} \times 15 \text{ hours} = 60 \text{ packs}$ **3. Money earned per day:** * High Season: $90 \text{ packs} \times 60 \text{ dollars} = 5400 \text{ dollars}$ * Low Season: $60 \text{ packs} \times 60 \text{ dollars} = 3600 \text{ dollars}$ **4. Difference in money:** $5400 - 3600 = 1800 \text{ dollars}$ \boxed{1800} </think> High season packs per day: $6 \text{ packs/ hour} \times 15 \text{ hours} = 90 \text{ packs}$. Low season packs per day: $4 \text{ packs/ hour} \times 15 \text{ hours} = 60 \text{ packs}$. High season earnings: $90 \text{ packs} \times 60 \text

Reward

Reward components
key value
reference_answer 1800
format_valid False
correct True
format_coef 0.1
reward 0.900

Trajectory Details

Trajectory 0 Episode

Episode Details
Turn 1
Step stats
key value
ob_len 121
ac_len 320
step_reward 0.900
Step Metrics
Metrics emitted by env.step
key value
format 0.000
correct 1.000
Episode totals
key value
num_turns 1
final_ob_len 0
sum_step_rewards 0.900
final_group_reward 0.000
total_return 0.900

Trajectory 1 Episode

Episode Details
Turn 1
Step stats
key value
ob_len 121
ac_len 320
step_reward 0.900
Step Metrics
Metrics emitted by env.step
key value
format 0.000
correct 1.000
Episode totals
key value
num_turns 1
final_ob_len 0
sum_step_rewards 0.900
final_group_reward 0.000
total_return 0.900

Trajectory 2 Episode

Episode Details
Turn 1
Step stats
key value
ob_len 121
ac_len 295
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 121
ac_len 320
step_reward -0.100
Step Metrics
Metrics emitted by env.step
key value
format 0.000
correct 0.000
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 121
ac_len 252
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 121
ac_len 320
step_reward -0.100
Step Metrics
Metrics emitted by env.step
key value
format 0.000
correct 0.000
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 6 Episode

Episode Details
Turn 1
Step stats
key value
ob_len 121
ac_len 320
step_reward 0.900
Step Metrics
Metrics emitted by env.step
key value
format 0.000
correct 1.000
Episode totals
key value
num_turns 1
final_ob_len 0
sum_step_rewards 0.900
final_group_reward 0.000
total_return 0.900

Trajectory 7 Episode

Episode Details
Turn 1
Step stats
key value
ob_len 121
ac_len 309
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:
A man owned 1/2 of a lot. He sold 1/10 of his share for the amount of $460. What is the worth of the entire lot?

Policy Response

assistant:
<think> He owns 1/2 of the lot. He sold 1/10 of his share. 1. Find the portion of the lot sold: (1/2) * (1/10) = 1/20 2. Find the value of the lot based on the sales amount: 460 / (1/20) = 460 * 20 = 9200 \boxed{9200} </think> He owned 1/2 of the lot. He sold 1/10 of his share. 1. Calculate the fraction of the total lot sold: $ \frac{1}{2} \times \frac{1}{10} = \frac{1}{20} $ 2. Calculate the total worth of the lot: $ \frac{460}{1/20} = 460 \times 20 = 9200 $ \boxed{9200} </think> He owned 1/2 of the lot. He sold 1/10 of his share. 1. Calculate the fraction of the total lot sold: $ \frac{1}{2} \times \frac{1}{10} = \frac{1}{20} $ 2. Calculate the total worth of the lot: $ 460 \div \frac{1}{20} = 460 \times 20 =

Reward

Reward components
key value
reference_answer 9200
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:
A man owned 1/2 of a lot. He sold 1/10 of his share for the amount of $460. What is the worth of the entire lot?

Policy Response

assistant:
💭 Thinking
A man owned 1/2 of a lot. He sold 1/10 of his share for $460.

1. Find the value of 1/10 of the share: (1/2) * (1/10) = 1/20 of the lot.

2. Find the worth of 1/20 of the lot: $460.

3. Find the worth of the entire lot: $460 * 20 = $9200.

\boxed{9200}
He owned 1/2 of the lot. He sold 1/10 of his share, which is (1/2) * (1/10) = 1/20 of the lot. The lot was worth 20 * 460 = 9200. \boxed{9200} </think> He owned 1/2 of a lot. He sold 1/10 of his share, which represents (1/2) * (1/10) = 1/20 of the lot. The worth of the lot is 20 * 460 = 9200. \boxed{9200}

Reward

Reward components
key value
reference_answer 9200
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:
A man owned 1/2 of a lot. He sold 1/10 of his share for the amount of $460. What is the worth of the entire lot?

Policy Response

assistant:
💭 Thinking
He owned 1/2 of the lot.

1. Find the share sold: 1/2 * 1/10 = 1/20 of the lot.

2. Find the worth of the sold share:

Worth of Sold Share = 460

3. Find the total worth of the lot:

Worth of Lot = Worth of Sold Share / Share Sold = 460 / (1/20) = 460 * 20 = 9200

\boxed{9200}
He owned 1/2 of the lot. He sold 1/10 of his share, which is 1/10 * 1/2 = 1/20 of the lot. The cost of 1/20 of the lot was $460. The worth of the entire lot was 460 * 20 = 9200. \boxed{9200}

Reward

Reward components
key value
reference_answer 9200
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:
A man owned 1/2 of a lot. He sold 1/10 of his share for the amount of $460. What is the worth of the entire lot?

Policy Response

assistant:
<think> He owned 1/2 of the lot. He sold 1/10 of his share. 1. Calculate the share sold: $1/2 * 1/10 = 1/20$ of the lot. 2. The cost of the share sold was $460. 3. Calculate the cost of the entire lot: $460 / (1/20) = 460 * 20 = 9200$. \boxed{9200} </think> He owned 1/2 of the lot. He sold 1/10 of his share: $1/2 * 1/10 = 1/20$ of the lot. The worth of the entire lot is $460 / (1/20) = 460 * 20 = 9200$. \boxed{9200} The worth of the entire lot is $9200. \boxed{9200} \boxed{9200} \boxed{9200} \boxed{9200} The worth of the entire lot is $9200. \boxed{9200} \boxed{9200} \boxed{9200} \boxed{9200} \boxed{9200} \boxed{9200}

Reward

Reward components
key value
reference_answer 9200
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:
A man owned 1/2 of a lot. He sold 1/10 of his share for the amount of $460. What is the worth of the entire lot?

Policy Response

assistant:
<think> He owned 1/2 of a lot. 1. Find the amount of the lot he sold: $1/10$ of his share $= 1/10 * 1/2 = 1/20$. 2. Find the worth of the lot he sold: $1/20 * Worth = 460$. 3. Find the worth of the entire lot: Worth = 460 * 20 = 9200. \boxed{9200} </think> He owned 1/2 of a lot. He sold 1/10 of his share. 1. Share sold: $1/10 * 1/2 = 1/20$ of the lot. 2. Worth of lot sold: $1/20 * W = 460$. 3. Worth of entire lot (W): $W = 460 * 20 = 9200$. \boxed{9200} </think> He owned 1/2 of the lot. He sold 1/10 of his share. 1. The share sold was $1/10 * 1/2 = 1/20$ of the lot. 2. The worth of the lot sold was $1/20$ of the total worth, which was $460. 3. The total worth of the lot was $460 * 20 =

Reward

Reward components
key value
reference_answer 9200
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:
A man owned 1/2 of a lot. He sold 1/10 of his share for the amount of $460. What is the worth of the entire lot?

Policy Response

assistant:
💭 Thinking
He owned 1/2 of a lot.

1. Find the fraction of the lot sold: 1/2 * 1/10 = 1/20.

2. Find the worth of the lot sold: 1/20 * LotWorth = 460.

3. Find the lot worth: LotWorth = 460 * 20 = 9200.

\boxed{9200}
He owned 1/2 of a lot. He sold 1/10 of his share, which is 1/2 * 1/10 = 1/20 of the lot. (1/20) * Worth = 460 Worth = 460 * 20 = 9200 \boxed{9200} </think> He owned 1/2 of a lot. He sold 1/10 of his share, which is 1/2 * 1/10 = 1/20 of the lot. Worth * 1/20 = 460 Worth = 460 * 20 = 9200 \boxed{9200}

Reward

Reward components
key value
reference_answer 9200
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:
A man owned 1/2 of a lot. He sold 1/10 of his share for the amount of $460. What is the worth of the entire lot?

Policy Response

assistant:
<think> He owned 1/2 of the lot. He sold 1/10 of his share. 1. Find the share sold: $1/2 * 1/10 = 1/20$ of the lot. 2. The value of the share sold is $460. 3. Find the value of the entire lot: $460 / (1/20) = 460 * 20 = 9200$. \boxed{9200} </think> He owned 1/2 of the lot, and he sold 1/10 of his share. 1. Share sold: $1/2 * 1/10 = 1/20$ of the lot. 2. Value of entire lot: $460 / (1/20) = 460 * 20 = 9200$. \boxed{9200} \boxed{9200} \boxed{9200} \boxed{9200} \boxed{9200} \boxed{9200} \boxed{9200} \boxed{9200} \boxed{9200} \boxed{9200} \boxed{9200} \boxed{9200} \boxed{9200} \boxed{

Reward

Reward components
key value
reference_answer 9200
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:
A man owned 1/2 of a lot. He sold 1/10 of his share for the amount of $460. What is the worth of the entire lot?

Policy Response

assistant:
💭 Thinking
He owned 1/2 of a lot. He sold 1/10 of his share.

1. Calculate the share sold: 1/2 * 1/10 = 1/20
2. Calculate the value of the share sold: 1/20 * Lot Value = 460
3. Lot Value = 460 * 20 = 9200

\boxed{9200}
He owned 1/2 of a lot. He sold 1/10 of his share, which is 1/2 * 1/10 = 1/20 of the lot. The value of the lot sold was $460. Lot Value = 460 / (1/20) = 460 * 20 = 9200. \boxed{9200} </think> He owned 1/2 of a lot. He sold 1/10 of his share. 1. Share Sold: \( \frac{1}{2} \times \frac{1}{10} = \frac{1}{20} \) 2. Lot Value: \( \frac{460}{1/20} = 460 \times 20 = 9200 \) \boxed{9200} \boxed{9200}

Reward

Reward components
key value
reference_answer 9200
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 92
ac_len 312
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 92
ac_len 217
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 92
ac_len 320
step_reward 0.900
Step Metrics
Metrics emitted by env.step
key value
format 0.000
correct 1.000
Episode totals
key value
num_turns 1
final_ob_len 0
sum_step_rewards 0.900
final_group_reward 0.000
total_return 0.900

Trajectory 3 Episode

Episode Details
Turn 1
Step stats
key value
ob_len 92
ac_len 320
step_reward 0.900
Step Metrics
Metrics emitted by env.step
key value
format 0.000
correct 1.000
Episode totals
key value
num_turns 1
final_ob_len 0
sum_step_rewards 0.900
final_group_reward 0.000
total_return 0.900

Trajectory 4 Episode

Episode Details
Turn 1
Step stats
key value
ob_len 92
ac_len 278
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 92
ac_len 320
step_reward 0.900
Step Metrics
Metrics emitted by env.step
key value
format 0.000
correct 1.000
Episode totals
key value
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
key value
ob_len 92
ac_len 275
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 92
ac_len 320
step_reward 0.900
Step Metrics
Metrics emitted by env.step
key value
format 0.000
correct 1.000
Episode totals
key value
num_turns 1
final_ob_len 0
sum_step_rewards 0.900
final_group_reward 0.000
total_return 0.900