MathDB
2023 Spring LMT Team #3

Source:

August 10, 2023
number theory

Problem Statement

Beter Pai wants to tell you his fastest 4040-line clear time in Tetris, but since he does not want Qep to realize she is better at Tetris than he is, he does not tell you the time directly. Instead, he gives you the following requirements, given that the correct time is t seconds: ∙\bullet t<100t < 100. ∙\bullet tt is prime. ∙\bullet t−1t -1 has 5 proper factors. ∙\bullet all prime factors of t+1t +1 are single digits. ∙\bullet t−2t -2 is a multiple of 33. ∙\bullet t+2t +2 has 22 factors. Find t.
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