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[ { "from": "user", "value": "Return your final response within \\boxed{}. Find [the decimal form of] the largest prime divisor of $100111011_6$.\n" }, { "from": "assistant", "value": "<think>\nOkay, so I need to find the largest prime divisor of the number 100111011 in base 6, converted to decima...
Find [the decimal form of] the largest prime divisor of $100111011_6$.
null
null
[ { "content": "You like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer.", "role": "system" }, { "content": "Return your final response with...
181
{ "api_url": "http://10.32.36.236:9080/v1", "backend": "litellm", "chat_template_applied": true, "generation_params": { "chat_template_applied": true, "max_tokens": 4096, "n": 2, "repetition_penalty": 1.1, "temperature": 0.7, "top_k": 20, "top_p": 0.8 }, "model_name": "hosted_vll...
openthoughts
openthoughts
[ "To find the largest prime divisor of \\( 100111011_6 \\), we need to first convert this number from base-6 to base-10.\n\nThe number \\( 100111011_6 \\) can be expanded as follows:\n\\[\n1 \\cdot 6^8 + 0 \\cdot 6^7 + 0 \\cdot 6^6 + 1 \\cdot 6^5 + 1 \\cdot 6^4 + 1 \\cdot 6^3 + 0 \\cdot 6^2 + 1 \\cdot 6^1 + 1 \\cdot...
[ false ]
[ "337781" ]
original
[ { "content": "You think step by step and reflect on the given answer for the question reasoning about if the answer was correct or incorrect. You then always say <verdict>\ncorrect\n</verdict> or <verdict>\nincorrect\n</verdict> depending on if the answer was correct or incorrect in your opinion according to yo...
[ "" ]
[ false ]
[ "" ]
{ "api_url": "http://10.32.36.196:9080/v1", "backend": "litellm", "chat_template_applied": true, "generation_params": { "chat_template_applied": true, "max_tokens": 512, "n": 1, "repetition_penalty": 1.1, "temperature": 0.7, "top_k": 20, "top_p": 0.8 }, "model_name": "hosted_vllm...
{ "backend": "litellm", "model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct", "n_responses": 1 }
[ { "from": "user", "value": "Return your final response within \\boxed{}. Find [the decimal form of] the largest prime divisor of $100111011_6$.\n" }, { "from": "assistant", "value": "<think>\nOkay, so I need to find the largest prime divisor of the number 100111011 in base 6, converted to decima...
Find [the decimal form of] the largest prime divisor of $100111011_6$.
null
null
[ { "content": "You like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer.", "role": "system" }, { "content": "Return your final response with...
181
{ "api_url": "http://10.32.36.236:9080/v1", "backend": "litellm", "chat_template_applied": true, "generation_params": { "chat_template_applied": true, "max_tokens": 4096, "n": 2, "repetition_penalty": 1.1, "temperature": 0.7, "top_k": 20, "top_p": 0.8 }, "model_name": "hosted_vll...
openthoughts
openthoughts
[ "To find the decimal form of the largest prime divisor of \\( 100111011_6 \\), we first need to convert this base-6 number into a decimal (base-10) number.\n\nThe base-6 number \\( 100111011_6 \\) can be expanded as follows:\n\\[ 1 \\cdot 6^8 + 0 \\cdot 6^7 + 0 \\cdot 6^6 + 1 \\cdot 6^5 + 1 \\cdot 6^4 + 1 \\cdot 6^...
[ false ]
[ "99353" ]
original
[ { "content": "You think step by step and reflect on the given answer for the question reasoning about if the answer was correct or incorrect. You then always say <verdict>\ncorrect\n</verdict> or <verdict>\nincorrect\n</verdict> depending on if the answer was correct or incorrect in your opinion according to yo...
[ "" ]
[ false ]
[ "" ]
{ "api_url": "http://10.32.36.196:9080/v1", "backend": "litellm", "chat_template_applied": true, "generation_params": { "chat_template_applied": true, "max_tokens": 512, "n": 1, "repetition_penalty": 1.1, "temperature": 0.7, "top_k": 20, "top_p": 0.8 }, "model_name": "hosted_vllm...
{ "backend": "litellm", "model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct", "n_responses": 1 }
[ { "from": "user", "value": "Return your final response within \\boxed{}. Find [the decimal form of] the largest prime divisor of $100111011_6$.\n" }, { "from": "assistant", "value": "<think>\nOkay, so I need to find the largest prime divisor of the number 100111011 in base 6, converted to decima...
Find [the decimal form of] the largest prime divisor of $100111011_6$.
null
null
[ { "content": "You like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer.", "role": "system" }, { "content": "Return your final response with...
181
{ "api_url": "http://10.32.36.236:9080/v1", "backend": "litellm", "chat_template_applied": true, "generation_params": { "chat_template_applied": true, "max_tokens": 4096, "n": 2, "repetition_penalty": 1.1, "temperature": 0.7, "top_k": 20, "top_p": 0.8 }, "model_name": "hosted_vll...
openthoughts
openthoughts
[ "First, I'll try to understand the problem better by writing out a plan and go really deep into detail about how I should solve this.\n1. Convert the base-6 number \\(100111011_6\\) to its decimal (base-10) equivalent because it's easier to work with large numbers in base-10 for factorization.\n2. Once converted to...
[ false ]
[ "2993" ]
plan_and_execute
[ { "content": "You think step by step and reflect on the given answer for the question reasoning about if the answer was correct or incorrect. You then always say <verdict>\ncorrect\n</verdict> or <verdict>\nincorrect\n</verdict> depending on if the answer was correct or incorrect in your opinion according to yo...
[ "" ]
[ false ]
[ "" ]
{ "api_url": "http://10.32.36.196:9080/v1", "backend": "litellm", "chat_template_applied": true, "generation_params": { "chat_template_applied": true, "max_tokens": 512, "n": 1, "repetition_penalty": 1.1, "temperature": 0.7, "top_k": 20, "top_p": 0.8 }, "model_name": "hosted_vllm...
{ "backend": "litellm", "model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct", "n_responses": 1 }
[{"from":"user","value":"Return your final response within \\boxed{}. Find [the decimal form of] the(...TRUNCATED)
Find [the decimal form of] the largest prime divisor of $100111011_6$.
null
null
[{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED)
181
{"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED)
openthoughts
openthoughts
["First, I'll try to understand the problem better by writing out a plan and go really deep into det(...TRUNCATED)
[ false ]
[ "337781" ]
plan_and_execute
[{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED)
[ "" ]
[ false ]
[ "" ]
{"api_url":"http://10.32.36.196:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED)
{ "backend": "litellm", "model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct", "n_responses": 1 }
[{"from":"user","value":"Return your final response within \\boxed{}. Find [the decimal form of] the(...TRUNCATED)
Find [the decimal form of] the largest prime divisor of $100111011_6$.
null
null
[{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED)
181
{"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED)
openthoughts
openthoughts
["Rewritten Question: Find the decimal form of the largest prime divisor of \\(100111011_6\\).\n\nSt(...TRUNCATED)
[ false ]
[ "239" ]
rephrase
[{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED)
[ "" ]
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{"api_url":"http://10.32.36.196:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED)
{ "backend": "litellm", "model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct", "n_responses": 1 }
[{"from":"user","value":"Return your final response within \\boxed{}. Find [the decimal form of] the(...TRUNCATED)
Find [the decimal form of] the largest prime divisor of $100111011_6$.
null
null
[{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED)
181
{"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED)
openthoughts
openthoughts
["Rewritten Question: Find the decimal form of the largest prime divisor of \\(100111011_6\\).\n\nSt(...TRUNCATED)
[ false ]
[ "6379" ]
rephrase
[{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED)
[ "" ]
[ false ]
[ "" ]
{"api_url":"http://10.32.36.196:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED)
{ "backend": "litellm", "model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct", "n_responses": 1 }
[{"from":"user","value":"Return your final response within \\boxed{}. Find [the decimal form of] the(...TRUNCATED)
Find [the decimal form of] the largest prime divisor of $100111011_6$.
null
null
[{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED)
181
{"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED)
openthoughts
openthoughts
["First, let's convert \\( 100111011_6 \\) from base-6 to base-10.\n\n\\[ \n100111011_6 = 1 \\cdot 6(...TRUNCATED)
[ false ]
[ "2447" ]
alternative
[{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED)
[ "" ]
[ false ]
[ "" ]
{"api_url":"http://10.32.36.196:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED)
{ "backend": "litellm", "model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct", "n_responses": 1 }
[{"from":"user","value":"Return your final response within \\boxed{}. Find [the decimal form of] the(...TRUNCATED)
Find [the decimal form of] the largest prime divisor of $100111011_6$.
null
null
[{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED)
181
{"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED)
openthoughts
openthoughts
["First, we need to convert the base-6 number \\(100111011_6\\) to its decimal (base-10) equivalent.(...TRUNCATED)
[ false ]
[ "593" ]
alternative
[{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED)
[ "" ]
[ false ]
[ "" ]
{"api_url":"http://10.32.36.196:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED)
{ "backend": "litellm", "model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct", "n_responses": 1 }
[{"from":"user","value":"The maximum value of the function $f(x)=\\frac{4}{{x-3}}+x(x<3)$ is ( ).\(...TRUNCATED)
"The maximum value of the function $f(x)=\\frac{4}{{x-3}}+x(x<3)$ is ( ).\n\nA: $-4$\n\nB: $1$\n\n(...TRUNCATED)
null
null
[{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED)
D
{"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED)
openthoughts
openthoughts
["To find the maximum value of the function \\( f(x) = \\frac{4}{x-3} + x \\) for \\( x < 3 \\), we (...TRUNCATED)
[ false ]
[ "-1" ]
original
[{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED)
["Let us verify this answer. The model correctly identified the function \\( f(x) = \\frac{4}{x-3} +(...TRUNCATED)
[ false ]
[ "" ]
{"api_url":"http://10.32.36.196:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED)
{ "backend": "litellm", "model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct", "n_responses": 1 }
[{"from":"user","value":"The maximum value of the function $f(x)=\\frac{4}{{x-3}}+x(x<3)$ is ( ).\(...TRUNCATED)
"The maximum value of the function $f(x)=\\frac{4}{{x-3}}+x(x<3)$ is ( ).\n\nA: $-4$\n\nB: $1$\n\n(...TRUNCATED)
null
null
[{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED)
D
{"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED)
openthoughts
openthoughts
["To find the maximum value of the function \\( f(x) = \\frac{4}{x-3} + x \\) for \\( x < 3 \\), we (...TRUNCATED)
[ false ]
[ "-1" ]
original
[{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED)
["Let us verify this answer. The model correctly identified the critical point at \\( x = 1 \\) thro(...TRUNCATED)
[ false ]
[ "" ]
{"api_url":"http://10.32.36.196:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED)
{ "backend": "litellm", "model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct", "n_responses": 1 }
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