question
stringclasses 51
values | steps
sequencelengths 1
12
| final_step_reward
float64 0
1
| metadata
dict |
|---|---|---|---|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries."
] | 0.25
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 1,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we need to find out how many countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, which is 6 / 2 = 3 countries."
] | 0.5
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 2,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we need to find out how many countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, which is 6 / 2 = 3 countries.",
"Now, we need to calculate how many countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to, so Patrick traveled to 3 * 3 = 9 countries."
] | 0.75
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 3,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we need to find out how many countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, which is 6 / 2 = 3 countries.",
"Now, we need to calculate how many countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to, so Patrick traveled to 3 * 3 = 9 countries.",
"Finally, we can calculate how many countries Zack traveled to.\nZack traveled to twice the number of countries Patrick traveled to, so Zack traveled to 2 * 9 = 18 countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 4,
"step_number": 4,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries."
] | 0.25
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 1,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we calculate the number of countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, so Joseph traveled to 6 / 2 = 3 countries."
] | 0.5
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 2,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we calculate the number of countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, so Joseph traveled to 6 / 2 = 3 countries.",
"Now, we calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to, so Patrick traveled to 3 * 3 = 9 countries."
] | 0.75
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 3,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we calculate the number of countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, so Joseph traveled to 6 / 2 = 3 countries.",
"Now, we calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to, so Patrick traveled to 3 * 3 = 9 countries.",
"Finally, we can calculate the number of countries Zack traveled to.\nZack traveled to twice the number of countries Patrick traveled to, so Zack traveled to 2 * 9 = 18 countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 4,
"step_number": 4,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries."
] | 0.25
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 1,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we need to find out how many countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, which is 6 / 2 = 3 countries."
] | 0.5
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 2,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we need to find out how many countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, which is 6 / 2 = 3 countries.",
"Now, we need to find out how many countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to, so Patrick traveled to 3 * 3 = 9 countries."
] | 0.75
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 3,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we need to find out how many countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, which is 6 / 2 = 3 countries.",
"Now, we need to find out how many countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to, so Patrick traveled to 3 * 3 = 9 countries.",
"Finally, we can find out how many countries Zack traveled to.\nZack traveled to twice the number of countries Patrick traveled to, so Zack traveled to 2 * 9 = 18 countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 4,
"step_number": 4,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGeorge traveled to 6 countries, and Joseph traveled to half that number. So, Joseph traveled to $6 / 2 = 3$ countries."
] | 0.333333
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 1,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGeorge traveled to 6 countries, and Joseph traveled to half that number. So, Joseph traveled to $6 / 2 = 3$ countries.",
"Calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to. So, Patrick traveled to $3 \\times 3 = 9$ countries."
] | 0.666667
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 2,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGeorge traveled to 6 countries, and Joseph traveled to half that number. So, Joseph traveled to $6 / 2 = 3$ countries.",
"Calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to. So, Patrick traveled to $3 \\times 3 = 9$ countries.",
"Calculate the number of countries Zack traveled to.\nZack traveled to twice the number of countries Patrick traveled to. So, Zack traveled to $2 \\times 9 = 18$ countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 3,
"step_number": 3,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries."
] | 0.333333
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 1,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries.",
"Calculate the total number of countries Patrick traveled to.\nSince Patrick traveled to three times the number of countries Joseph traveled to, Patrick's travel count = 3 * 3 = 9 countries."
] | 0.666667
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 2,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries.",
"Calculate the total number of countries Patrick traveled to.\nSince Patrick traveled to three times the number of countries Joseph traveled to, Patrick's travel count = 3 * 3 = 9 countries.",
"Calculate the number of countries Zack traveled to.\nGiven that Zack has traveled to twice the number of countries Patrick traveled to, Zack's travel count = 2 * 9 = 18 countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 3,
"step_number": 3,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries."
] | 0.25
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 1,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we need to find out how many countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, which is 6 / 2 = 3 countries."
] | 0.5
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 2,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we need to find out how many countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, which is 6 / 2 = 3 countries.",
"Now, we use the information that Patrick traveled to three times the number of countries Joseph traveled to to find out how many countries Patrick traveled to.\nPatrick traveled to 3 * 3 = 9 countries."
] | 0.75
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 3,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we need to find out how many countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, which is 6 / 2 = 3 countries.",
"Now, we use the information that Patrick traveled to three times the number of countries Joseph traveled to to find out how many countries Patrick traveled to.\nPatrick traveled to 3 * 3 = 9 countries.",
"Finally, we calculate the number of countries Zack traveled to.\nSince Zack traveled to twice the number of countries Patrick traveled to, Zack traveled to 2 * 9 = 18 countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 4,
"step_number": 4,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries."
] | 0.333333
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 1,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries.",
"Calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to. Therefore, Patrick's travel count is 3 * 3 = 9 countries."
] | 0.666667
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 2,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries.",
"Calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to. Therefore, Patrick's travel count is 3 * 3 = 9 countries.",
"Calculate the number of countries Zack traveled to.\nZack traveled to twice the number of countries Patrick traveled to. Thus, Zack's travel count is 2 * 9 = 18 countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 3,
"step_number": 3,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGeorge traveled to 6 countries, and Joseph traveled to half that number. So, Joseph traveled to $6 / 2 = 3$ countries."
] | 0.333333
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 1,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGeorge traveled to 6 countries, and Joseph traveled to half that number. So, Joseph traveled to $6 / 2 = 3$ countries.",
"Calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to. So, Patrick traveled to $3 \\times 3 = 9$ countries."
] | 0.666667
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 2,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGeorge traveled to 6 countries, and Joseph traveled to half that number. So, Joseph traveled to $6 / 2 = 3$ countries.",
"Calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to. So, Patrick traveled to $3 \\times 3 = 9$ countries.",
"Calculate the number of countries Zack traveled to.\nZach traveled to twice the number of countries Patrick traveled to. So, Zack traveled to $2 \\times 9 = 18$ countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 3,
"step_number": 3,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries."
] | 0.333333
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 1,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries.",
"Calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to, so Patrick's travel count is 3 * 3 = 9 countries."
] | 0.666667
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 2,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries.",
"Calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to, so Patrick's travel count is 3 * 3 = 9 countries.",
"Calculate the number of countries Zack traveled to.\nSince Zack traveled to twice the number of countries Patrick traveled to and Patrick traveled to 9 countries, Zack's travel count is 2 * 9 = 18 countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 3,
"step_number": 3,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries."
] | 0.25
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 1,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries.",
"Calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to. Therefore, Patrick's travel count is 3 * 3 = 9 countries."
] | 0.5
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 2,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries.",
"Calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to. Therefore, Patrick's travel count is 3 * 3 = 9 countries.",
"Calculate the number of countries Zack traveled to.\nZack traveled to twice the number of countries Patrick traveled to. Thus, Zack's travel count is 2 * 9 = 18 countries."
] | 0.75
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 3,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries.",
"Calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to. Therefore, Patrick's travel count is 3 * 3 = 9 countries.",
"Calculate the number of countries Zack traveled to.\nZack traveled to twice the number of countries Patrick traveled to. Thus, Zack's travel count is 2 * 9 = 18 countries.",
"Output the final count of countries Zack traveled to.\nBased on the calculations, Zack traveled to 18 countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 4,
"step_number": 4,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries."
] | 0.333333
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 1,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries.",
"Calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to, so Patrick's travel count is 3 * 3 = 9 countries."
] | 0.666667
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 2,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries.",
"Calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to, so Patrick's travel count is 3 * 3 = 9 countries.",
"Calculate the number of countries Zack traveled to.\nGiven that Zack has traveled to twice the number of countries Patrick traveled to, and Patrick traveled to 9 countries, Zack's travel count is 2 * 9 = 18 countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 3,
"step_number": 3,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries."
] | 0.25
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 1,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we calculate the number of countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, so Joseph traveled to 6 / 2 = 3 countries."
] | 0.5
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 2,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we calculate the number of countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, so Joseph traveled to 6 / 2 = 3 countries.",
"Then, we calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to, so Patrick traveled to 3 * 3 = 9 countries."
] | 0.75
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 3,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we calculate the number of countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, so Joseph traveled to 6 / 2 = 3 countries.",
"Then, we calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to, so Patrick traveled to 3 * 3 = 9 countries.",
"Finally, we calculate the number of countries Zack traveled to.\nZack traveled to twice the number of countries Patrick traveled to, so Zack traveled to 2 * 9 = 18 countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 4,
"step_number": 4,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries."
] | 0.25
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 1,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we need to find out how many countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, which is 6 / 2 = 3 countries."
] | 0.5
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 2,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we need to find out how many countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, which is 6 / 2 = 3 countries.",
"Now, we need to find out how many countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to, so Patrick traveled to 3 * 3 = 9 countries."
] | 0.75
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 3,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we need to find out how many countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, which is 6 / 2 = 3 countries.",
"Now, we need to find out how many countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to, so Patrick traveled to 3 * 3 = 9 countries.",
"Finally, we need to find out how many countries Zack traveled to.\nZack traveled to twice the number of countries Patrick traveled to, so Zack traveled to 2 * 9 = 18 countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 4,
"step_number": 4,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries."
] | 0.25
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 1,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we calculate the number of countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, so Joseph traveled to 6 / 2 = 3 countries."
] | 0.5
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 2,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we calculate the number of countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, so Joseph traveled to 6 / 2 = 3 countries.",
"Since Zack traveled to twice the number of countries Patrick traveled to, we calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to, so Patrick traveled to 3 * 3 = 9 countries."
] | 0.75
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 3,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we calculate the number of countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, so Joseph traveled to 6 / 2 = 3 countries.",
"Since Zack traveled to twice the number of countries Patrick traveled to, we calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to, so Patrick traveled to 3 * 3 = 9 countries.",
"Now we calculate the number of countries Zack traveled to.\nZack traveled to twice the number of countries Patrick traveled to, so Zack traveled to 2 * 9 = 18 countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 4,
"step_number": 4,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGeorge traveled to 6 countries, and Joseph traveled to half that number. So, Joseph traveled to $6 / 2 = 3$ countries."
] | 0.333333
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 1,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGeorge traveled to 6 countries, and Joseph traveled to half that number. So, Joseph traveled to $6 / 2 = 3$ countries.",
"Calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to. Since Joseph traveled to 3 countries, Patrick traveled to $3 \\times 3 = 9$ countries."
] | 0.666667
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 2,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGeorge traveled to 6 countries, and Joseph traveled to half that number. So, Joseph traveled to $6 / 2 = 3$ countries.",
"Calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to. Since Joseph traveled to 3 countries, Patrick traveled to $3 \\times 3 = 9$ countries.",
"Calculate the number of countries Zack traveled to.\nZack traveled to twice the number of countries Patrick traveled to. Since Patrick traveled to 9 countries, Zack traveled to $2 \\times 9 = 18$ countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 3,
"step_number": 3,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries."
] | 0.333333
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 1,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries.",
"Calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to. Therefore, Patrick's travel count is 3 * 3 = 9 countries."
] | 0.666667
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 2,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries.",
"Calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to. Therefore, Patrick's travel count is 3 * 3 = 9 countries.",
"Calculate the number of countries Zack traveled to.\nZack traveled to twice the number of countries Patrick traveled to. Therefore, Zack's travel count is 2 * 9 = 18 countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 3,
"step_number": 3,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries."
] | 0.333333
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 1,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries.",
"Calculate the number of countries Patrick traveled to.\nSince Patrick traveled to three times the number of countries Joseph traveled to, Patrick's travel count is 3 * 3 = 9 countries."
] | 0.666667
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 2,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries.",
"Calculate the number of countries Patrick traveled to.\nSince Patrick traveled to three times the number of countries Joseph traveled to, Patrick's travel count is 3 * 3 = 9 countries.",
"Calculate the number of countries Zack traveled to.\nKnowing Zack traveled to twice the number of countries Patrick traveled to and Patrick traveled to 9 countries, we can find Zack's travel count as 2 * 9 = 18 countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 3,
"step_number": 3,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries."
] | 0.25
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 1,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we calculate the number of countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, so Joseph traveled to 6 / 2 = 3 countries."
] | 0.5
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 2,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we calculate the number of countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, so Joseph traveled to 6 / 2 = 3 countries.",
"Since Zack traveled to twice the number of countries Patrick traveled to, we calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to, so Patrick traveled to 3 * 3 = 9 countries."
] | 0.75
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 3,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we calculate the number of countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, so Joseph traveled to 6 / 2 = 3 countries.",
"Since Zack traveled to twice the number of countries Patrick traveled to, we calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to, so Patrick traveled to 3 * 3 = 9 countries.",
"Now, we calculate the number of countries Zack traveled to.\nZack traveled to twice the number of countries Patrick traveled to, so Zack traveled to 2 * 9 = 18 countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 4,
"step_number": 4,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries."
] | 0.333333
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 1,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries.",
"Calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to, so Patrick's travel count is 3 * 3 = 9 countries."
] | 0.666667
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 2,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries.",
"Calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to, so Patrick's travel count is 3 * 3 = 9 countries.",
"Calculate the number of countries Zack traveled to.\nZack traveled to twice the number of countries Patrick traveled to, so Zack's travel count is 2 * 9 = 18 countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 3,
"step_number": 3,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries."
] | 0.333333
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 1,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries.",
"Calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to. Therefore, Patrick's travel count is 3 * 3 = 9 countries."
] | 0.666667
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 2,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries.",
"Calculate the number of countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to. Therefore, Patrick's travel count is 3 * 3 = 9 countries.",
"Calculate the number of countries Zack traveled to.\nZack traveled to twice the number of countries Patrick traveled to. So, Zack's travel count is 2 * 9 = 18 countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 3,
"step_number": 3,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGeorge traveled to 6 countries, and Joseph traveled to half that number. So, Joseph traveled to $6 / 2 = 3$ countries."
] | 0.333333
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 1,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGeorge traveled to 6 countries, and Joseph traveled to half that number. So, Joseph traveled to $6 / 2 = 3$ countries.",
"Calculate the number of countries Patrick traveled to.\nPatrol traveled to three times the number of countries Joseph traveled to. So, Patrick traveled to $3 \\times 3 = 9$ countries."
] | 0.666667
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 2,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGeorge traveled to 6 countries, and Joseph traveled to half that number. So, Joseph traveled to $6 / 2 = 3$ countries.",
"Calculate the number of countries Patrick traveled to.\nPatrol traveled to three times the number of countries Joseph traveled to. So, Patrick traveled to $3 \\times 3 = 9$ countries.",
"Calculate the number of countries Zack traveled to.\nZack traveled to twice the number of countries Patrick traveled to. So, Zack traveled to $2 \\times 9 = 18$ countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 3,
"step_number": 3,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries."
] | 0.333333
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 1,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries.",
"Calculate the total number of countries Patrick traveled to.\nSince Patrick traveled to three times the number of countries Joseph traveled to, Patrick's travel count = 3 * 3 = 9 countries."
] | 0.666667
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 2,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries.",
"Calculate the total number of countries Patrick traveled to.\nSince Patrick traveled to three times the number of countries Joseph traveled to, Patrick's travel count = 3 * 3 = 9 countries.",
"Calculate the total number of countries Zack traveled to.\nZack traveled to twice the number of countries Patrick traveled to. Since Patrick traveled to 9 countries, Zack's travel count = 2 * 9 = 18 countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 3,
"step_number": 3,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries."
] | 0.25
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 1,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we need to find out how many countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, which is 6 / 2 = 3 countries."
] | 0.5
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 2,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we need to find out how many countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, which is 6 / 2 = 3 countries.",
"Now, we need to calculate how many countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to, so Patrick traveled to 3 * 3 = 9 countries."
] | 0.75
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 3,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we need to find out how many countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, which is 6 / 2 = 3 countries.",
"Now, we need to calculate how many countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to, so Patrick traveled to 3 * 3 = 9 countries.",
"Finally, we need to find out how many countries Zack traveled to.\nZack traveled to twice the number of countries Patrick traveled to, so Zack traveled to 2 * 9 = 18 countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 4,
"step_number": 4,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries."
] | 0.25
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 1,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we need to find out how many countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, which is 6 / 2 = 3 countries."
] | 0.5
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 2,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we need to find out how many countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, which is 6 / 2 = 3 countries.",
"Now, we use the information that Patrick traveled to three times the number of countries Joseph traveled to to find out how many countries Patrick traveled to.\nPatrick traveled to 3 * 3 = 9 countries."
] | 0.75
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 3,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we need to find out how many countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, which is 6 / 2 = 3 countries.",
"Now, we use the information that Patrick traveled to three times the number of countries Joseph traveled to to find out how many countries Patrick traveled to.\nPatrick traveled to 3 * 3 = 9 countries.",
"Finally, we calculate how many countries Zack traveled to by using the information that Zack has traveled to twice the number of countries Patrick traveled to.\nZack traveled to 2 * 9 = 18 countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 4,
"step_number": 4,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGeorge traveled to 6 countries, and Joseph traveled to half that number. So, Joseph traveled to $6 / 2 = 3$ countries."
] | 0.333333
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 1,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGeorge traveled to 6 countries, and Joseph traveled to half that number. So, Joseph traveled to $6 / 2 = 3$ countries.",
"Calculate the number of countries Patrick traveled to based on Joseph's travel.\nPatrick traveled to three times the number of countries Joseph traveled to. So, Patrick traveled to $3 \\times 3 = 9$ countries."
] | 0.666667
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 2,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGeorge traveled to 6 countries, and Joseph traveled to half that number. So, Joseph traveled to $6 / 2 = 3$ countries.",
"Calculate the number of countries Patrick traveled to based on Joseph's travel.\nPatrick traveled to three times the number of countries Joseph traveled to. So, Patrick traveled to $3 \\times 3 = 9$ countries.",
"Calculate the number of countries Zack traveled to based on Patrick's travel.\nZack traveled to twice as many countries as Patrick, so Zack traveled to $2 \\times 9 = 18$ countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 3,
"step_number": 3,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries."
] | 0.25
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 1,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we need to find out how many countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, which is 6 / 2 = 3 countries."
] | 0.5
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 2,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we need to find out how many countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, which is 6 / 2 = 3 countries.",
"Now, we need to calculate how many countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to, so Patrick traveled to 3 * 3 = 9 countries."
] | 0.75
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 3,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries.",
"Next, we need to find out how many countries Joseph traveled to.\nJoseph traveled to half the number of countries George traveled to, which is 6 / 2 = 3 countries.",
"Now, we need to calculate how many countries Patrick traveled to.\nPatrick traveled to three times the number of countries Joseph traveled to, so Patrick traveled to 3 * 3 = 9 countries.",
"Finally, we need to calculate how many countries Zack traveled to.\nZack traveled to twice the number of countries Patrick traveled to, so Zack traveled to 2 * 9 = 18 countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 4,
"step_number": 4,
"raw_path_length": 6
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries."
] | 0.333333
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 1,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries.",
"Calculate the total number of countries Patrick traveled to.\nSince Patrick traveled to three times the number of countries Joseph traveled to, Patrick's travel count = 3 * 3 = 9 countries."
] | 0.666667
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 2,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGiven that Joseph traveled to half the number of countries George traveled to, and George traveled 6 countries, we can find Joseph's travel count as 6 / 2 = 3 countries.",
"Calculate the total number of countries Patrick traveled to.\nSince Patrick traveled to three times the number of countries Joseph traveled to, Patrick's travel count = 3 * 3 = 9 countries.",
"Calculate the total number of countries Zack traveled to.\nZack traveled to twice the number of countries Patrick traveled to, which is 2 * 9 = 18 countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 3,
"step_number": 3,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGeorge traveled to 6 countries, and Joseph traveled to half that number. So, Joseph traveled to $6 / 2 = 3$ countries."
] | 0.333333
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 1,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGeorge traveled to 6 countries, and Joseph traveled to half that number. So, Joseph traveled to $6 / 2 = 3$ countries.",
"Calculate the number of countries Patrick traveled to based on Joseph's travel.\nPatrick traveled to three times the number of countries Joseph traveled to. So, Patrick traveled to $3 \\times 3 = 9$ countries."
] | 0.666667
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 2,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGeorge traveled to 6 countries, and Joseph traveled to half that number. So, Joseph traveled to $6 / 2 = 3$ countries.",
"Calculate the number of countries Patrick traveled to based on Joseph's travel.\nPatrick traveled to three times the number of countries Joseph traveled to. So, Patrick traveled to $3 \\times 3 = 9$ countries.",
"Calculate the number of countries Zack traveled to based on Patrick's travel.\nZack traveled to twice the number of countries Patrick traveled to. So, Zack traveled to $2 \\times 9 = 18$ countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 3,
"step_number": 3,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGeorge traveled to 6 countries, and Joseph traveled to half that number. So, Joseph traveled to $6 / 2 = 3$ countries."
] | 0.333333
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 1,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGeorge traveled to 6 countries, and Joseph traveled to half that number. So, Joseph traveled to $6 / 2 = 3$ countries.",
"Calculate the number of countries Patrick traveled to based on Joseph's travel.\nPatrick traveled to three times the number of countries Joseph traveled to. So, Patrick traveled to $3 \\times 3 = 9$ countries."
] | 0.666667
|
{
"is_complete": false,
"is_correct": true,
"path_length": 3,
"step_number": 2,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"Calculate the number of countries Joseph traveled to.\nGeorge traveled to 6 countries, and Joseph traveled to half that number. So, Joseph traveled to $6 / 2 = 3$ countries.",
"Calculate the number of countries Patrick traveled to based on Joseph's travel.\nPatrick traveled to three times the number of countries Joseph traveled to. So, Patrick traveled to $3 \\times 3 = 9$ countries.",
"Calculate the number of countries Zack traveled to based on Patrick's travel.\nZack has traveled to twice the number of countries Patrick traveled to. So, Zack traveled to $2 \\times 9 = 18$ countries.\n\nThe final answer is: $\\boxed{18}$"
] | 1
|
{
"is_complete": true,
"is_correct": true,
"path_length": 3,
"step_number": 3,
"raw_path_length": 5
}
|
Zack has traveled to twice the number of countries Patrick traveled to. Patrick traveled to three times the number of countries Joseph traveled to. Joseph traveled to half the number of countries George traveled to. If George traveled to 6 countries, how many countries did Zack travel to?
|
[
"First, let's calculate the number of countries George traveled to.\nGeorge traveled to 6 countries."
] | 0.25
|
{
"is_complete": false,
"is_correct": true,
"path_length": 4,
"step_number": 1,
"raw_path_length": 6
}
|
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