LLMs Encode Their Failures: Predicting Success from Pre-Generation Activations
Paper • 2602.09924 • Published • 1
formatted_prompt string | generated_solutions list | ground_truth string | input_cost_usd_once float64 | k int64 | majority_vote_extracted_answer string | majority_vote_is_correct int8 | max_len int64 | model_name string | pass_at_k float64 | problem string | problem_id string | rating float64 | split string | success_rate float64 | task string | temperature float64 | total_cost_usd float64 | total_input_tokens int64 | total_output_cost_usd float64 | total_output_tokens int64 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In Professor Plum's biology class there are 40 students. Of those students, 80 percent have puppies. Of those who have puppies, 25% also have parrots. How many students have both puppies and parrots? Let... | [
{
"input_cost_usd_once": 0.0000092,
"input_tokens": 92,
"output_cost_usd": 0.0000243,
"output_tokens": 243,
"rollout_cost_usd": 0.0000243,
"score": 1,
"text": "To determine how many students have both puppies and parrots, we can follow these steps:\n\n1. Calculate the number of students ... | 8 | 0.000009 | 5 | 8 | 1 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 1 | In Professor Plum's biology class there are 40 students. Of those students, 80 percent have puppies. Of those who have puppies, 25% also have parrots. How many students have both puppies and parrots? | SW4gUHJvZmVzc29yIFBsdW0ncyBiaW9sb2d5IGNsYXNzIHRoZXJlIGFyZSA0MCBzdHVkZW50cy4gT2YgdGhvc2Ugc3R1ZGVudHMsIDgwIHBlcmNlbnQgaGF2ZSBwdXBwaWVzLiBPZiB0aG9zZSB3aG8gaGF2ZSBwdXBwaWVzLCAyNSUgYWxzbyBoYXZlIHBhcnJvdHMuIEhvdyBtYW55IHN0dWRlbnRzIGhhdmUgYm90aCBwdXBwaWVzIGFuZCBwYXJyb3RzPw== | null | train | 1 | openai_gsm8k | 0.7 | 0.000121 | 92 | 0.000111 | 1,113 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Diane bought twenty more apples than Cecile. If Cecile bought 15 apples, how many apples did they buy altogether? Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_star... | [
{
"input_cost_usd_once": 0.000007,
"input_tokens": 70,
"output_cost_usd": 0.0000173,
"output_tokens": 173,
"rollout_cost_usd": 0.0000173,
"score": 1,
"text": "To determine the total number of apples Diane and Cecile bought, we need to follow these steps:\n\n1. Identify how many apples Ce... | 50 | 0.000007 | 5 | 50 | 1 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 1 | Diane bought twenty more apples than Cecile. If Cecile bought 15 apples, how many apples did they buy altogether? | RGlhbmUgYm91Z2h0IHR3ZW50eSBtb3JlIGFwcGxlcyB0aGFuIENlY2lsZS4gSWYgQ2VjaWxlIGJvdWdodCAxNSBhcHBsZXMsIGhvdyBtYW55IGFwcGxlcyBkaWQgdGhleSBidXkgYWx0b2dldGhlcj8= | null | train | 1 | openai_gsm8k | 0.7 | 0.000107 | 70 | 0.0001 | 1,002 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Ann can skate 6 miles an hour. Her friend Glenda can skate 8 miles an hour. If they start in the same place and skate in straight lines in opposite directions for 3 hours, how many miles apart do they en... | [
{
"input_cost_usd_once": 0.0000093,
"input_tokens": 93,
"output_cost_usd": 0.0000296,
"output_tokens": 296,
"rollout_cost_usd": 0.0000296,
"score": 1,
"text": "To determine how far apart Ann and Glenda are after skating for 3 hours in opposite directions, we need to calculate the distanc... | 42 | 0.000009 | 5 | 42 | 1 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 1 | Ann can skate 6 miles an hour. Her friend Glenda can skate 8 miles an hour. If they start in the same place and skate in straight lines in opposite directions for 3 hours, how many miles apart do they end up? | QW5uIGNhbiBza2F0ZSA2IG1pbGVzIGFuIGhvdXIuIEhlciBmcmllbmQgR2xlbmRhIGNhbiBza2F0ZSA4IG1pbGVzIGFuIGhvdXIuIElmIHRoZXkgc3RhcnQgaW4gdGhlIHNhbWUgcGxhY2UgYW5kIHNrYXRlIGluIHN0cmFpZ2h0IGxpbmVzIGluIG9wcG9zaXRlIGRpcmVjdGlvbnMgZm9yIDMgaG91cnMsIGhvdyBtYW55IG1pbGVzIGFwYXJ0IGRvIHRoZXkgZW5kIHVwPw== | null | train | 1 | openai_gsm8k | 0.7 | 0.000154 | 93 | 0.000144 | 1,442 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Running for 2 hours, Jonah burnt 30 calories every hour. How many more calories would he have lost if he would have run for five hours? Let's think step by step and output the final answer within \boxed{... | [
{
"input_cost_usd_once": 0.000007499999999999999,
"input_tokens": 75,
"output_cost_usd": 0.000029999999999999997,
"output_tokens": 300,
"rollout_cost_usd": 0.000029999999999999997,
"score": 1,
"text": "To determine how many more calories Jonah would have lost if he had run for five hours... | 90 | 0.000007 | 5 | 90 | 1 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 1 | Running for 2 hours, Jonah burnt 30 calories every hour. How many more calories would he have lost if he would have run for five hours? | UnVubmluZyBmb3IgMiBob3VycywgSm9uYWggYnVybnQgMzAgY2Fsb3JpZXMgZXZlcnkgaG91ci4gSG93IG1hbnkgbW9yZSBjYWxvcmllcyB3b3VsZCBoZSBoYXZlIGxvc3QgaWYgaGUgd291bGQgaGF2ZSBydW4gZm9yIGZpdmUgaG91cnM/ | null | train | 1 | openai_gsm8k | 0.7 | 0.000157 | 75 | 0.00015 | 1,496 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
The city of Richmond has 1000 more people than Victoria. Victoria has 4 times as many people as Beacon. If Richmond has 3000 people, how many people are there in Beacon? Let's think step by step and outp... | [
{
"input_cost_usd_once": 0.0000087,
"input_tokens": 87,
"output_cost_usd": 0.00003710000000000001,
"output_tokens": 371,
"rollout_cost_usd": 0.00003710000000000001,
"score": 1,
"text": "To determine the population of Beacon, we need to follow these steps:\n\n1. Identify the population of... | 500 | 0.000009 | 5 | 500 | 1 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 1 | The city of Richmond has 1000 more people than Victoria. Victoria has 4 times as many people as Beacon. If Richmond has 3000 people, how many people are there in Beacon? | VGhlIGNpdHkgb2YgUmljaG1vbmQgaGFzIDEwMDAgbW9yZSBwZW9wbGUgdGhhbiBWaWN0b3JpYS4gVmljdG9yaWEgaGFzIDQgdGltZXMgYXMgbWFueSBwZW9wbGUgYXMgQmVhY29uLiBJZiBSaWNobW9uZCBoYXMgMzAwMCBwZW9wbGUsIGhvdyBtYW55IHBlb3BsZSBhcmUgdGhlcmUgaW4gQmVhY29uPw== | null | train | 1 | openai_gsm8k | 0.7 | 0.000144 | 87 | 0.000136 | 1,355 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
To get his fill of oysters, Crabby has to eat at least twice as many oysters as Squido does. If Squido eats 200 oysters, how many oysters do they eat altogether? Let's think step by step and output the f... | [
{
"input_cost_usd_once": 0.0000088,
"input_tokens": 88,
"output_cost_usd": 0.0000193,
"output_tokens": 193,
"rollout_cost_usd": 0.0000193,
"score": 1,
"text": "To determine how many oysters Crabby and Squido eat altogether, we need to follow these steps:\n\n1. Identify how many oysters S... | 600 | 0.000009 | 5 | 600 | 1 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 1 | To get his fill of oysters, Crabby has to eat at least twice as many oysters as Squido does. If Squido eats 200 oysters, how many oysters do they eat altogether? | VG8gZ2V0IGhpcyBmaWxsIG9mIG95c3RlcnMsIENyYWJieSBoYXMgdG8gZWF0IGF0IGxlYXN0IHR3aWNlIGFzIG1hbnkgb3lzdGVycyBhcyBTcXVpZG8gZG9lcy4gSWYgU3F1aWRvIGVhdHMgMjAwIG95c3RlcnMsIGhvdyBtYW55IG95c3RlcnMgZG8gdGhleSBlYXQgYWx0b2dldGhlcj8= | null | train | 1 | openai_gsm8k | 0.7 | 0.000116 | 88 | 0.000107 | 1,071 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
John sells 20 woodburning for $15 each. The wood cost $100. How much does he make in profit? Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| [
{
"input_cost_usd_once": 0.000007499999999999999,
"input_tokens": 75,
"output_cost_usd": 0.0000169,
"output_tokens": 169,
"rollout_cost_usd": 0.0000169,
"score": 1,
"text": "To determine John's profit, we need to follow these steps:\n\n1. Calculate the total revenue from selling the wood... | 200 | 0.000007 | 5 | 200 | 1 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 1 | John sells 20 woodburning for $15 each. The wood cost $100. How much does he make in profit? | Sm9obiBzZWxscyAyMCB3b29kYnVybmluZyBmb3IgJDE1IGVhY2guICBUaGUgd29vZCBjb3N0ICQxMDAuICBIb3cgbXVjaCBkb2VzIGhlIG1ha2UgaW4gcHJvZml0Pw== | null | train | 1 | openai_gsm8k | 0.7 | 0.000092 | 75 | 0.000085 | 846 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a field of 500 clovers, 20% have four leaves and one quarter of these are purple clovers. Assuming these proportions are exactly correct, how many clovers in the field are both purple and four-leaved?... | [
{
"input_cost_usd_once": 0.0000093,
"input_tokens": 93,
"output_cost_usd": 0.0000272,
"output_tokens": 272,
"rollout_cost_usd": 0.0000272,
"score": 1,
"text": "To determine how many clovers in the field are both purple and four-leaved, we can follow these steps:\n\n1. Calculate the numbe... | 25 | 0.000009 | 5 | 25 | 1 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 1 | In a field of 500 clovers, 20% have four leaves and one quarter of these are purple clovers. Assuming these proportions are exactly correct, how many clovers in the field are both purple and four-leaved? | SW4gYSBmaWVsZCBvZiA1MDAgY2xvdmVycywgMjAlIGhhdmUgZm91ciBsZWF2ZXMgYW5kIG9uZSBxdWFydGVyIG9mIHRoZXNlIGFyZSBwdXJwbGUgY2xvdmVycy4gQXNzdW1pbmcgdGhlc2UgcHJvcG9ydGlvbnMgYXJlIGV4YWN0bHkgY29ycmVjdCwgaG93IG1hbnkgY2xvdmVycyBpbiB0aGUgZmllbGQgYXJlIGJvdGggcHVycGxlIGFuZCBmb3VyLWxlYXZlZD8= | null | train | 1 | openai_gsm8k | 0.7 | 0.000134 | 93 | 0.000125 | 1,251 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Tony lifts weights as a form of exercise. He can lift 90 pounds with one arm in the exercise known as "the curl." In an exercise known as "the military press," he can lift over his head twice the weigh... | [
{
"input_cost_usd_once": 0.000014200000000000001,
"input_tokens": 142,
"output_cost_usd": 0.0000186,
"output_tokens": 186,
"rollout_cost_usd": 0.0000186,
"score": 1,
"text": "To determine how much weight Tony can lift in the squat exercise, we need to follow the information given step by... | 900 | 0.000014 | 5 | 900 | 1 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 1 | Tony lifts weights as a form of exercise. He can lift 90 pounds with one arm in the exercise known as "the curl." In an exercise known as "the military press," he can lift over his head twice the weight that he can curl. His favorite exercise is known as "the squat" and he can squat 5 times the weight that he can li... | VG9ueSBsaWZ0cyB3ZWlnaHRzIGFzIGEgZm9ybSBvZiBleGVyY2lzZS4gIEhlIGNhbiBsaWZ0IDkwIHBvdW5kcyB3aXRoIG9uZSBhcm0gaW4gdGhlIGV4ZXJjaXNlIGtub3duIGFzICJ0aGUgY3VybC4iICBJbiBhbiBleGVyY2lzZSBrbm93biBhcyAidGhlIG1pbGl0YXJ5IHByZXNzLCIgaGUgY2FuIGxpZnQgb3ZlciBoaXMgaGVhZCB0d2ljZSB0aGUgd2VpZ2h0IHRoYXQgaGUgY2FuIGN1cmwuICBIaXMgZmF2b3JpdGUgZXhl... | null | train | 1 | openai_gsm8k | 0.7 | 0.000107 | 142 | 0.000093 | 925 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Elsa started the day with 40 marbles. At breakfast, she lost 3 marbles while playing. At lunchtime, she gave her best friend Susie 5 marbles. In the afternoon, Elsa's mom bought her a new bag with 12 ... | [
{
"input_cost_usd_once": 0.0000136,
"input_tokens": 136,
"output_cost_usd": 0.0000345,
"output_tokens": 345,
"rollout_cost_usd": 0.0000345,
"score": 1,
"text": "To determine how many marbles Elsa ended the day with, we will go through each transaction step by step.\n\n1. **Initial number... | 54 | 0.000014 | 5 | 54 | 1 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 1 | Elsa started the day with 40 marbles. At breakfast, she lost 3 marbles while playing. At lunchtime, she gave her best friend Susie 5 marbles. In the afternoon, Elsa's mom bought her a new bag with 12 marbles. Susie came back and gave Elsa twice as many marbles as she received at lunch. How many marbles did Elsa en... | RWxzYSBzdGFydGVkIHRoZSBkYXkgd2l0aCA0MCBtYXJibGVzLiAgQXQgYnJlYWtmYXN0LCBzaGUgbG9zdCAzIG1hcmJsZXMgd2hpbGUgcGxheWluZy4gIEF0IGx1bmNodGltZSwgc2hlIGdhdmUgaGVyIGJlc3QgZnJpZW5kIFN1c2llIDUgbWFyYmxlcy4gIEluIHRoZSBhZnRlcm5vb24sIEVsc2EncyBtb20gYm91Z2h0IGhlciBhIG5ldyBiYWcgd2l0aCAxMiBtYXJibGVzLiAgU3VzaWUgY2FtZSBiYWNrIGFuZCBnYXZlIEVs... | null | train | 1 | openai_gsm8k | 0.7 | 0.000183 | 136 | 0.000169 | 1,693 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
John buys thank you cards. He decides to buy them for people who got him Christmas and birthday presents. He sent 20 for Christmas gifts and 15 for birthday gifts. If each card cost $2 how much did he... | [
{
"input_cost_usd_once": 0.0000097,
"input_tokens": 97,
"output_cost_usd": 0.000016400000000000002,
"output_tokens": 164,
"rollout_cost_usd": 0.000016400000000000002,
"score": 1,
"text": "To determine how much John spent on thank you cards, we need to follow these steps:\n\n1. Calculate ... | 70 | 0.00001 | 5 | 70 | 1 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 1 | John buys thank you cards. He decides to buy them for people who got him Christmas and birthday presents. He sent 20 for Christmas gifts and 15 for birthday gifts. If each card cost $2 how much did he spend on cards? | Sm9obiBidXlzIHRoYW5rIHlvdSBjYXJkcy4gIEhlIGRlY2lkZXMgdG8gYnV5IHRoZW0gZm9yIHBlb3BsZSB3aG8gZ290IGhpbSBDaHJpc3RtYXMgYW5kIGJpcnRoZGF5IHByZXNlbnRzLiAgSGUgc2VudCAyMCBmb3IgQ2hyaXN0bWFzIGdpZnRzIGFuZCAxNSBmb3IgYmlydGhkYXkgZ2lmdHMuICBJZiBlYWNoIGNhcmQgY29zdCAkMiBob3cgbXVjaCBkaWQgaGUgc3BlbmQgb24gY2FyZHM/ | null | train | 1 | openai_gsm8k | 0.7 | 0.000094 | 97 | 0.000084 | 839 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a field where there are 200 animals, there are 40 cows, 56 sheep and goats. How many goats are there? Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start|>assist... | [
{
"input_cost_usd_once": 0.000007499999999999999,
"input_tokens": 75,
"output_cost_usd": 0.000022400000000000002,
"output_tokens": 224,
"rollout_cost_usd": 0.000022400000000000002,
"score": 0,
"text": "To determine the number of goats in the field, we need to follow these steps:\n\n1. Id... | 104 | 0.000007 | 5 | 56 | 0 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 0 | In a field where there are 200 animals, there are 40 cows, 56 sheep and goats. How many goats are there? | SW4gYSBmaWVsZCB3aGVyZSB0aGVyZSBhcmUgMjAwIGFuaW1hbHMsIHRoZXJlIGFyZSA0MCBjb3dzLCA1NiBzaGVlcCBhbmQgZ29hdHMuIEhvdyBtYW55IGdvYXRzIGFyZSB0aGVyZT8= | null | train | 0 | openai_gsm8k | 0.7 | 0.000168 | 75 | 0.000161 | 1,605 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Paul is working at a university. He is part of a big project, which involves 70 scientists in total. Half of them are from Europe and one-fifth are from Canada. The rest are from the USA. How many scient... | [
{
"input_cost_usd_once": 0.0000099,
"input_tokens": 99,
"output_cost_usd": 0.000025500000000000003,
"output_tokens": 255,
"rollout_cost_usd": 0.000025500000000000003,
"score": 1,
"text": "To determine how many scientists in the project are from the USA, we need to follow these steps:\n\n... | 21 | 0.00001 | 5 | 21 | 1 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 1 | Paul is working at a university. He is part of a big project, which involves 70 scientists in total. Half of them are from Europe and one-fifth are from Canada. The rest are from the USA. How many scientists in this project are from the USA? | UGF1bCBpcyB3b3JraW5nIGF0IGEgdW5pdmVyc2l0eS4gSGUgaXMgcGFydCBvZiBhIGJpZyBwcm9qZWN0LCB3aGljaCBpbnZvbHZlcyA3MCBzY2llbnRpc3RzIGluIHRvdGFsLiBIYWxmIG9mIHRoZW0gYXJlIGZyb20gRXVyb3BlIGFuZCBvbmUtZmlmdGggYXJlIGZyb20gQ2FuYWRhLiBUaGUgcmVzdCBhcmUgZnJvbSB0aGUgVVNBLiBIb3cgbWFueSBzY2llbnRpc3RzIGluIHRoaXMgcHJvamVjdCBhcmUgZnJvbSB0aGUgVVNB... | null | train | 1 | openai_gsm8k | 0.7 | 0.000135 | 99 | 0.000125 | 1,251 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Mark is reading books, for 2 hours each day. He decided to increase his time spent on reading books weekly, by 4 hours. How much time does Mark want to spend during one week on reading books? Let's think... | [
{
"input_cost_usd_once": 0.0000087,
"input_tokens": 87,
"output_cost_usd": 0.000024100000000000003,
"output_tokens": 241,
"rollout_cost_usd": 0.000024100000000000003,
"score": 1,
"text": "To determine how much time Mark wants to spend during one week on reading books, we need to follow t... | 18 | 0.000009 | 5 | 18 | 1 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 1 | Mark is reading books, for 2 hours each day. He decided to increase his time spent on reading books weekly, by 4 hours. How much time does Mark want to spend during one week on reading books? | TWFyayBpcyByZWFkaW5nIGJvb2tzLCBmb3IgMiBob3VycyBlYWNoIGRheS4gSGUgZGVjaWRlZCB0byBpbmNyZWFzZSBoaXMgdGltZSBzcGVudCBvbiByZWFkaW5nIGJvb2tzIHdlZWtseSwgYnkgNCBob3Vycy4gSG93IG11Y2ggdGltZSBkb2VzIE1hcmsgd2FudCB0byBzcGVuZCBkdXJpbmcgb25lIHdlZWsgb24gcmVhZGluZyBib29rcz8= | null | train | 1 | openai_gsm8k | 0.7 | 0.000128 | 87 | 0.00012 | 1,197 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A survey conducted by the school showed that only 20% of the 800 parents agree to a tuition fee increase. How many parents disagree with the tuition fee increase? Let's think step by step and output the ... | [
{
"input_cost_usd_once": 0.000008000000000000001,
"input_tokens": 80,
"output_cost_usd": 0.0000247,
"output_tokens": 247,
"rollout_cost_usd": 0.0000247,
"score": 1,
"text": "To determine how many parents disagree with the tuition fee increase, we need to follow these steps:\n\n1. Calcula... | 640 | 0.000008 | 5 | 640 | 1 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 1 | A survey conducted by the school showed that only 20% of the 800 parents agree to a tuition fee increase. How many parents disagree with the tuition fee increase? | QSBzdXJ2ZXkgY29uZHVjdGVkIGJ5IHRoZSBzY2hvb2wgc2hvd2VkIHRoYXQgb25seSAyMCUgb2YgdGhlIDgwMCBwYXJlbnRzIGFncmVlIHRvIGEgdHVpdGlvbiBmZWUgaW5jcmVhc2UuIEhvdyBtYW55IHBhcmVudHMgZGlzYWdyZWUgd2l0aCB0aGUgdHVpdGlvbiBmZWUgaW5jcmVhc2U/ | null | train | 1 | openai_gsm8k | 0.7 | 0.000118 | 80 | 0.00011 | 1,101 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
In a shop, there is a sale of clothes. Every shirt costs $5, every hat $4, and a pair of jeans $10. How much do you need to pay for three shirts, two pairs of jeans, and four hats? Let's think step by st... | [
{
"input_cost_usd_once": 0.0000094,
"input_tokens": 94,
"output_cost_usd": 0.000027099999999999998,
"output_tokens": 271,
"rollout_cost_usd": 0.000027099999999999998,
"score": 1,
"text": "To determine the total cost of the items, we need to calculate the cost of each type of item separat... | 51 | 0.000009 | 5 | 51 | 1 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 1 | In a shop, there is a sale of clothes. Every shirt costs $5, every hat $4, and a pair of jeans $10. How much do you need to pay for three shirts, two pairs of jeans, and four hats? | SW4gYSBzaG9wLCB0aGVyZSBpcyBhIHNhbGUgb2YgY2xvdGhlcy4gRXZlcnkgc2hpcnQgY29zdHMgJDUsIGV2ZXJ5IGhhdCAkNCwgYW5kIGEgcGFpciBvZiBqZWFucyAkMTAuIEhvdyBtdWNoIGRvIHlvdSBuZWVkIHRvIHBheSBmb3IgdGhyZWUgc2hpcnRzLCB0d28gcGFpcnMgb2YgamVhbnMsIGFuZCBmb3VyIGhhdHM/ | null | train | 1 | openai_gsm8k | 0.7 | 0.000138 | 94 | 0.000128 | 1,284 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Titan's father has an onion farm ready for harvest. He borrows Mr. Clay's pickup and transports the harvest to their store, carrying ten bags per trip, prepared for sale. If the onions are in 50 kgs bags... | [
{
"input_cost_usd_once": 0.000011400000000000001,
"input_tokens": 114,
"output_cost_usd": 0.0000218,
"output_tokens": 218,
"rollout_cost_usd": 0.0000218,
"score": 1,
"text": "To determine the total weight of onions harvested by Titan's father, we need to follow these steps:\n\n1. Calcula... | 10000 | 0.000011 | 5 | 10000 | 1 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 1 | Titan's father has an onion farm ready for harvest. He borrows Mr. Clay's pickup and transports the harvest to their store, carrying ten bags per trip, prepared for sale. If the onions are in 50 kgs bags, and the pickup makes 20 trips, what's the total weight of onions harvested by Titan's father? | VGl0YW4ncyBmYXRoZXIgaGFzIGFuIG9uaW9uIGZhcm0gcmVhZHkgZm9yIGhhcnZlc3QuIEhlIGJvcnJvd3MgTXIuIENsYXkncyBwaWNrdXAgYW5kIHRyYW5zcG9ydHMgdGhlIGhhcnZlc3QgdG8gdGhlaXIgc3RvcmUsIGNhcnJ5aW5nIHRlbiBiYWdzIHBlciB0cmlwLCBwcmVwYXJlZCBmb3Igc2FsZS4gSWYgdGhlIG9uaW9ucyBhcmUgaW4gNTAga2dzIGJhZ3MsIGFuZCB0aGUgcGlja3VwIG1ha2VzIDIwIHRyaXBzLCB3aGF0... | null | train | 1 | openai_gsm8k | 0.7 | 0.000119 | 114 | 0.000108 | 1,076 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
New York is two-thirds as populated as all of New England. If New England has 2100000 people, calculate the combined population of both states. Let's think step by step and output the final answer within... | [
{
"input_cost_usd_once": 0.0000078,
"input_tokens": 78,
"output_cost_usd": 0.0000348,
"output_tokens": 348,
"rollout_cost_usd": 0.0000348,
"score": 1,
"text": "To determine the combined population of New York and New England, we need to follow these steps:\n\n1. Calculate the population ... | 3500000 | 0.000008 | 5 | 3500000 | 1 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 1 | New York is two-thirds as populated as all of New England. If New England has 2100000 people, calculate the combined population of both states. | TmV3IFlvcmsgaXMgdHdvLXRoaXJkcyBhcyBwb3B1bGF0ZWQgYXMgYWxsIG9mIE5ldyBFbmdsYW5kLiBJZiBOZXcgRW5nbGFuZCBoYXMgMjEwMDAwMCBwZW9wbGUsIGNhbGN1bGF0ZSB0aGUgY29tYmluZWQgcG9wdWxhdGlvbiBvZiBib3RoIHN0YXRlcy4= | null | train | 1 | openai_gsm8k | 0.7 | 0.000183 | 78 | 0.000175 | 1,751 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Miriam currently has 30 marbles, but she used to have more. Miriam gave her brother 60 marbles, gave her sister twice that amount and gave her friend Savanna three times the amount she currently has. How... | [
{
"input_cost_usd_once": 0.000010100000000000002,
"input_tokens": 101,
"output_cost_usd": 0.0000276,
"output_tokens": 276,
"rollout_cost_usd": 0.0000276,
"score": 1,
"text": "To determine how many marbles Miriam started with, we need to account for all the marbles she gave away and the m... | 300 | 0.00001 | 5 | 300 | 1 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 1 | Miriam currently has 30 marbles, but she used to have more. Miriam gave her brother 60 marbles, gave her sister twice that amount and gave her friend Savanna three times the amount she currently has. How many marbles did Miriam start with? | TWlyaWFtIGN1cnJlbnRseSBoYXMgMzAgbWFyYmxlcywgYnV0IHNoZSB1c2VkIHRvIGhhdmUgbW9yZS4gTWlyaWFtIGdhdmUgaGVyIGJyb3RoZXIgNjAgbWFyYmxlcywgZ2F2ZSBoZXIgc2lzdGVyIHR3aWNlIHRoYXQgYW1vdW50IGFuZCBnYXZlIGhlciBmcmllbmQgU2F2YW5uYSB0aHJlZSB0aW1lcyB0aGUgYW1vdW50IHNoZSBjdXJyZW50bHkgaGFzLiBIb3cgbWFueSBtYXJibGVzIGRpZCBNaXJpYW0gc3RhcnQgd2l0aD8= | null | train | 1 | openai_gsm8k | 0.7 | 0.000148 | 101 | 0.000138 | 1,382 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Lisa is making a pizza. She uses 30 pieces of pepperoni for a pizza, twice as many pieces of ham, and 12 more pieces of sausage than pepperoni. If there are 6 slices of pizza, and everything was distribu... | [
{
"input_cost_usd_once": 0.000010700000000000001,
"input_tokens": 107,
"output_cost_usd": 0.0000332,
"output_tokens": 332,
"rollout_cost_usd": 0.0000332,
"score": 1,
"text": "To determine how many pieces of meat are on each slice of pizza, we need to follow these steps:\n\n1. Calculate t... | 22 | 0.000011 | 5 | 22 | 1 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 1 | Lisa is making a pizza. She uses 30 pieces of pepperoni for a pizza, twice as many pieces of ham, and 12 more pieces of sausage than pepperoni. If there are 6 slices of pizza, and everything was distributed evenly, how many pieces of meat altogether are on each slice? | TGlzYSBpcyBtYWtpbmcgYSBwaXp6YS4gU2hlIHVzZXMgMzAgcGllY2VzIG9mIHBlcHBlcm9uaSBmb3IgYSBwaXp6YSwgdHdpY2UgYXMgbWFueSBwaWVjZXMgb2YgaGFtLCBhbmQgMTIgbW9yZSBwaWVjZXMgb2Ygc2F1c2FnZSB0aGFuIHBlcHBlcm9uaS4gSWYgdGhlcmUgYXJlIDYgc2xpY2VzIG9mIHBpenphLCBhbmQgZXZlcnl0aGluZyB3YXMgZGlzdHJpYnV0ZWQgZXZlbmx5LCBob3cgbWFueSBwaWVjZXMgb2YgbWVhdCBh... | null | train | 1 | openai_gsm8k | 0.7 | 0.000165 | 107 | 0.000154 | 1,542 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Markus is twice the age of his son, and Markus's son is twice the age of Markus's grandson. If the sum of the ages of Markus, his son, and his grandson is 140 years, then how many years old is Markus's ... | [
{
"input_cost_usd_once": 0.0000099,
"input_tokens": 99,
"output_cost_usd": 0.000023100000000000002,
"output_tokens": 231,
"rollout_cost_usd": 0.000023100000000000002,
"score": 1,
"text": "To determine the age of Markus's grandson, we start by defining the variables for the ages of Markus... | 20 | 0.00001 | 5 | 20 | 1 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 1 | Markus is twice the age of his son, and Markus's son is twice the age of Markus's grandson. If the sum of the ages of Markus, his son, and his grandson is 140 years, then how many years old is Markus's grandson? | TWFya3VzIGlzIHR3aWNlIHRoZSBhZ2Ugb2YgaGlzIHNvbiwgYW5kIE1hcmt1cydzIHNvbiBpcyB0d2ljZSB0aGUgYWdlIG9mIE1hcmt1cydzIGdyYW5kc29uLiAgSWYgdGhlIHN1bSBvZiB0aGUgYWdlcyBvZiBNYXJrdXMsIGhpcyBzb24sIGFuZCBoaXMgZ3JhbmRzb24gaXMgMTQwIHllYXJzLCB0aGVuIGhvdyBtYW55IHllYXJzIG9sZCBpcyBNYXJrdXMncyBncmFuZHNvbj8= | null | train | 1 | openai_gsm8k | 0.7 | 0.00014 | 99 | 0.00013 | 1,300 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
When Betty makes cheesecake, she sweetens it with a ratio of one part sugar to four parts cream cheese, and she flavors it with one teaspoon of vanilla for every two cups of cream cheese. For every one t... | [
{
"input_cost_usd_once": 0.000011400000000000001,
"input_tokens": 114,
"output_cost_usd": 0.0000316,
"output_tokens": 316,
"rollout_cost_usd": 0.0000316,
"score": 1,
"text": "To determine how many eggs Betty used, we need to follow the given ratios step by step.\n\n1. **Determine the amo... | 8 | 0.000011 | 5 | 8 | 1 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 1 | When Betty makes cheesecake, she sweetens it with a ratio of one part sugar to four parts cream cheese, and she flavors it with one teaspoon of vanilla for every two cups of cream cheese. For every one teaspoon of vanilla, she uses two eggs. She used two cups of sugar in her latest cheesecake. How many eggs did she use... | V2hlbiBCZXR0eSBtYWtlcyBjaGVlc2VjYWtlLCBzaGUgc3dlZXRlbnMgaXQgd2l0aCBhIHJhdGlvIG9mIG9uZSBwYXJ0IHN1Z2FyIHRvIGZvdXIgcGFydHMgY3JlYW0gY2hlZXNlLCBhbmQgc2hlIGZsYXZvcnMgaXQgd2l0aCBvbmUgdGVhc3Bvb24gb2YgdmFuaWxsYSBmb3IgZXZlcnkgdHdvIGN1cHMgb2YgY3JlYW0gY2hlZXNlLiBGb3IgZXZlcnkgb25lIHRlYXNwb29uIG9mIHZhbmlsbGEsIHNoZSB1c2VzIHR3byBlZ2dz... | null | train | 1 | openai_gsm8k | 0.7 | 0.000152 | 114 | 0.000141 | 1,407 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
A florist offers for sale 75 narcissus flowers and 90 chrysanthemums. Using all the flowers, how many bouquets containing 5 flowers each can he make? Let's think step by step and output the final answer ... | [
{
"input_cost_usd_once": 0.0000083,
"input_tokens": 83,
"output_cost_usd": 0.0000204,
"output_tokens": 204,
"rollout_cost_usd": 0.0000204,
"score": 1,
"text": "To determine how many bouquets the florist can make, we need to follow these steps:\n\n1. **Calculate the total number of flower... | 33 | 0.000008 | 5 | 33 | 1 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 1 | A florist offers for sale 75 narcissus flowers and 90 chrysanthemums. Using all the flowers, how many bouquets containing 5 flowers each can he make? | QSBmbG9yaXN0IG9mZmVycyBmb3Igc2FsZSA3NSBuYXJjaXNzdXMgZmxvd2VycyBhbmQgOTAgY2hyeXNhbnRoZW11bXMuIFVzaW5nIGFsbCB0aGUgZmxvd2VycywgaG93IG1hbnkgYm91cXVldHMgY29udGFpbmluZyA1IGZsb3dlcnMgZWFjaCBjYW4gaGUgbWFrZT8= | null | train | 1 | openai_gsm8k | 0.7 | 0.000103 | 83 | 0.000094 | 944 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Every week of last month Paul tried out a new cake recipe. The first week, he followed a cake recipe that called for 24 cups of sugar. Each week after that, he reduced the amount of sugar by half. How m... | [
{
"input_cost_usd_once": 0.0000104,
"input_tokens": 104,
"output_cost_usd": 0.0000184,
"output_tokens": 184,
"rollout_cost_usd": 0.0000184,
"score": 1,
"text": "To determine how much sugar Paul used for the cake on the fourth week, we need to follow the pattern of reducing the amount of ... | 3 | 0.00001 | 5 | 3 | 1 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 1 | Every week of last month Paul tried out a new cake recipe. The first week, he followed a cake recipe that called for 24 cups of sugar. Each week after that, he reduced the amount of sugar by half. How much sugar did he use for the cake on the fourth week? | RXZlcnkgd2VlayBvZiBsYXN0IG1vbnRoIFBhdWwgdHJpZWQgb3V0IGEgbmV3IGNha2UgcmVjaXBlLiAgVGhlIGZpcnN0IHdlZWssIGhlIGZvbGxvd2VkIGEgY2FrZSByZWNpcGUgdGhhdCBjYWxsZWQgZm9yIDI0IGN1cHMgb2Ygc3VnYXIuIEVhY2ggd2VlayBhZnRlciB0aGF0LCBoZSByZWR1Y2VkIHRoZSBhbW91bnQgb2Ygc3VnYXIgYnkgaGFsZi4gSG93IG11Y2ggc3VnYXIgZGlkIGhlIHVzZSBmb3IgdGhlIGNha2Ugb24g... | null | train | 1 | openai_gsm8k | 0.7 | 0.000108 | 104 | 0.000098 | 976 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
When Diane turns 30, she will be half the age of Alex and twice as old as Allison. Diane is 16 years old now. What is the sum of the ages of Alex and Allison now? Let's think step by step and output the ... | [
{
"input_cost_usd_once": 0.0000087,
"input_tokens": 87,
"output_cost_usd": 0.000034699999999999996,
"output_tokens": 347,
"rollout_cost_usd": 0.000034699999999999996,
"score": 1,
"text": "To solve the problem, we need to determine the current ages of Alex and Allison based on the informa... | 47 | 0.000009 | 5 | 47 | 1 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 1 | When Diane turns 30, she will be half the age of Alex and twice as old as Allison. Diane is 16 years old now. What is the sum of the ages of Alex and Allison now? | V2hlbiBEaWFuZSB0dXJucyAzMCwgc2hlIHdpbGwgYmUgaGFsZiB0aGUgYWdlIG9mIEFsZXggYW5kIHR3aWNlIGFzIG9sZCBhcyBBbGxpc29uLiBEaWFuZSBpcyAxNiB5ZWFycyBvbGQgbm93LiBXaGF0IGlzIHRoZSBzdW0gb2YgdGhlIGFnZXMgb2YgQWxleCBhbmQgQWxsaXNvbiBub3c/ | null | train | 0.8 | openai_gsm8k | 0.7 | 0.000206 | 87 | 0.000197 | 1,972 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Adam teaches 50 students a year. How many students will Adam teach in 10 years if in the first year he only teaches 40 students? Let's think step by step and output the final answer within \boxed{}.<|im_... | [
{
"input_cost_usd_once": 0.000007600000000000001,
"input_tokens": 76,
"output_cost_usd": 0.000021000000000000002,
"output_tokens": 210,
"rollout_cost_usd": 0.000021000000000000002,
"score": 1,
"text": "To determine how many students Adam will teach in 10 years, we need to consider that i... | 490 | 0.000008 | 5 | 490 | 1 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 1 | Adam teaches 50 students a year. How many students will Adam teach in 10 years if in the first year he only teaches 40 students? | QWRhbSB0ZWFjaGVzIDUwIHN0dWRlbnRzIGEgeWVhci4gSG93IG1hbnkgc3R1ZGVudHMgd2lsbCBBZGFtIHRlYWNoIGluIDEwIHllYXJzIGlmIGluIHRoZSBmaXJzdCB5ZWFyIGhlIG9ubHkgdGVhY2hlcyA0MCBzdHVkZW50cz8= | null | train | 1 | openai_gsm8k | 0.7 | 0.000118 | 76 | 0.00011 | 1,103 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Olaf collects colorful toy cars. At first, his collection consisted of 150 cars. His family, knowing his hobby, decided to give him some toy cars. Grandpa gave Olaf twice as many toy cars as the uncle. D... | [
{
"input_cost_usd_once": 0.000014200000000000001,
"input_tokens": 142,
"output_cost_usd": 0.000047100000000000006,
"output_tokens": 471,
"rollout_cost_usd": 0.000047100000000000006,
"score": 1,
"text": "To determine the total number of toy cars Olaf has after receiving gifts from his fam... | 196 | 0.000014 | 5 | 196 | 1 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 1 | Olaf collects colorful toy cars. At first, his collection consisted of 150 cars. His family, knowing his hobby, decided to give him some toy cars. Grandpa gave Olaf twice as many toy cars as the uncle. Dad gave Olaf 10 toy cars, 5 less than Mum. Auntie gave Olaf 6 toy cars, 1 more than the uncle. How many toy cars does... | T2xhZiBjb2xsZWN0cyBjb2xvcmZ1bCB0b3kgY2Fycy4gQXQgZmlyc3QsIGhpcyBjb2xsZWN0aW9uIGNvbnNpc3RlZCBvZiAxNTAgY2Fycy4gSGlzIGZhbWlseSwga25vd2luZyBoaXMgaG9iYnksIGRlY2lkZWQgdG8gZ2l2ZSBoaW0gc29tZSB0b3kgY2Fycy4gR3JhbmRwYSBnYXZlIE9sYWYgdHdpY2UgYXMgbWFueSB0b3kgY2FycyBhcyB0aGUgdW5jbGUuIERhZCBnYXZlIE9sYWYgMTAgdG95IGNhcnMsIDUgbGVzcyB0aGFu... | null | train | 0.8 | openai_gsm8k | 0.7 | 0.000222 | 142 | 0.000208 | 2,080 |
<|im_start|>system
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>user
Marcy is a makeup artist and has agreed to do some makeup for her friend's wedding. The only makeup she has limited stock of is lip gloss so she counts how many tubes she needs. Each tube of lip gloss wi... | [
{
"input_cost_usd_once": 0.0000147,
"input_tokens": 147,
"output_cost_usd": 0.000023000000000000003,
"output_tokens": 230,
"rollout_cost_usd": 0.000023000000000000003,
"score": 1,
"text": "To determine how many people Marcy is doing makeup for, we need to follow these steps:\n\n1. Calcul... | 36 | 0.000015 | 5 | 36 | 1 | 3,000 | Qwen/Qwen2.5-Math-1.5B-Instruct | 1 | Marcy is a makeup artist and has agreed to do some makeup for her friend's wedding. The only makeup she has limited stock of is lip gloss so she counts how many tubes she needs. Each tube of lip gloss will hold enough lip gloss for 3 people's makeup. Marcy decides to bring 6 tubs of lip gloss, each of which holds 2 tub... | TWFyY3kgaXMgYSBtYWtldXAgYXJ0aXN0IGFuZCBoYXMgYWdyZWVkIHRvIGRvIHNvbWUgbWFrZXVwIGZvciBoZXIgZnJpZW5kJ3Mgd2VkZGluZy4gVGhlIG9ubHkgbWFrZXVwIHNoZSBoYXMgbGltaXRlZCBzdG9jayBvZiBpcyBsaXAgZ2xvc3Mgc28gc2hlIGNvdW50cyBob3cgbWFueSB0dWJlcyBzaGUgbmVlZHMuIEVhY2ggdHViZSBvZiBsaXAgZ2xvc3Mgd2lsbCBob2xkIGVub3VnaCBsaXAgZ2xvc3MgZm9yIDMgcGVvcGxl... | null | train | 1 | openai_gsm8k | 0.7 | 0.000127 | 147 | 0.000112 | 1,121 |
End of preview. Expand in Data Studio
Generations Dataset: gsm8k
LLM-generated solutions across train/validation/test splits for multiple models.
Columns
| Column | Type | Description |
|---|---|---|
problem |
str | Problem statement |
generated_solutions |
list | Generated solutions with scores |
success_rate |
float | Fraction of correct generations |
majority_vote_is_correct |
int (0/1) | Whether majority vote is correct |
k |
int | Number of samples generated |
temperature |
float | Sampling temperature |
max_len |
int | Maximum generation length |
model_name |
str | Model used for generation |
Usage
from datasets import load_dataset
dataset = load_dataset("CoffeeGitta/difficulty-gsm8k-generations", name="<org--model>")
train = dataset["train"]
Citation
@article{lugoloobi_llms_2026,
title = {LLMs Encode Their Failures: Predicting Success from Pre-Generation Activations},
url = {http://arxiv.org/abs/2602.09924},
author = {Lugoloobi, William and Foster, Thomas and Bankes, William and Russell, Chris},
year = {2026},
}
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