problem_id large_string | problem large_string | perturbation_type large_string | model_is_robust int64 | model_hf_id string |
|---|---|---|---|---|
349493 | We call a sequence a_1,a_2,... of non-negative integers delightful if there exists N such that for all n>N a_n=0 and for all i>=1 a_i counts the number of multiples of i in a_1,...,a_N. How many delightful sequences exist? | distract | 1 | Qwen/Qwen3.5-397B-A17B-FP8 |
71beb6 | For a positive integer n let S(n) be the sum of digits in base 10. Compute S(S(1)+S(2)+...+S(N)) with N=10^100−2. | rename | 1 | Qwen/Qwen3.5-397B-A17B-FP8 |
71beb6 | For a positive integer n let S(n) be the sum of digits in base 10. Compute S(S(1)+S(2)+...+S(N)) with N=10^100−2. | rephrase | 1 | moonshotai/Kimi-K2.6 |
057f8a | Three airline companies depart every 100, 120 and 150 days respectively from Dodola island. What is the greatest positive integer d such that there will be d consecutive days without a flight regardless of departure times? | rephrase | 1 | Qwen/Qwen3.5-397B-A17B-FP8 |
71beb6 | For a positive integer n let S(n) be the sum of digits in base 10. Compute S(S(1)+S(2)+...+S(N)) with N=10^100−2. | expert-rephrase | 1 | openai/gpt-oss-120b |
bbd91e | Alice writes integers 1 to n (n>=11). Bob erases ten numbers. The mean of remaining numbers is 3000/37. Let erased sum be S. Find remainder of n*S mod 997. | no_solution | 1 | Qwen/Qwen3.5-397B-A17B-FP8 |
a1d40b | Count prime factors (with multiplicity) of N where N counts n<10^101 such that n^2+(n+1)^2 divisible by 5 but F_{n-1}^2+F_n^2 not divisible by 5. | no_solution | 1 | openai/gpt-oss-120b |
a1d40b | Count prime factors (with multiplicity) of N where N counts n<10^101 such that n^2+(n+1)^2 divisible by 5 but F_{n-1}^2+F_n^2 not divisible by 5. | no_solution | 1 | Qwen/Qwen3.5-397B-A17B-FP8 |
1acac0 | Triangle ABC has AB=120 and circumradius 100. Let D be foot from C to AB. What is the maximum possible CD? | no_solution | 0 | Qwen/Qwen3.5-397B-A17B-FP8 |
1fce4b | Find the three-digit integer n such that repeating any other three-digit number 10^2024 and 10^2024+2 times gives numbers divisible by n. | no_solution | 0 | openai/gpt-oss-120b |
1fce4b | Find the three-digit integer n such that repeating any other three-digit number 10^2024 and 10^2024+2 times gives numbers divisible by n. | distract | 0 | Qwen/Qwen3.5-397B-A17B-FP8 |
480182 | Triangle ABC has BC=108 CA=126 AB=39. With angle bisector BX and circumcircle constructions as defined, compute m+n if BE=m/n. | rephrase | 0 | Qwen/Qwen3.5-397B-A17B-FP8 |
a1d40b | Count prime factors (with multiplicity) of N where N counts n<10^101 such that n^2+(n+1)^2 divisible by 5 but F_{n-1}^2+F_n^2 not divisible by 5. | rephrase | 0 | moonshotai/Kimi-K2.6 |
1acac0 | Triangle ABC has AB=120 and circumradius 100. Let D be foot from C to AB. What is the maximum possible CD? | distract | 0 | moonshotai/Kimi-K2.6 |
a1d40b | Count prime factors (with multiplicity) of N where N counts n<10^101 such that n^2+(n+1)^2 divisible by 5 but F_{n-1}^2+F_n^2 not divisible by 5. | domain | 0 | lukealonso/GLM-5.1-NVFP4 |
bbd91e | Alice writes integers 1 to n (n>=11). Bob erases ten numbers. The mean of remaining numbers is 3000/37. Let erased sum be S. Find remainder of n*S mod 997. | rephrase | 0 | lukealonso/GLM-5.1-NVFP4 |
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