MathDB

3

Part of 2023 LMT Spring

Problems(2)

2023 Spring LMT Team #3

Source:

8/10/2023
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.
number theory
2023 LMT Spring Accuracy Problem 3

Source:

9/29/2023
Phoenix is counting positive integers starting from 11. When he counts a perfect square greater than 11, he restarts at 11, skipping that square the next time. For example, the first 1010 numbers Phoenix counts are 11, 22, 33, 44, 11, 22, 33, 55, 66, 77, ...... How many numbers will Phoenix have counted after counting 10000 for the first time?
number theory