Search problems

2 problems match “lower bounds”. Clear

Visitors search a sample. Sign in for free to search every problem. Sign in

1. Minimum operations to clear 2021 piles ●●●○○ 50 ptsThere are 2021 piles of stones, with the number of stones in each pile being $1, 2, \ldots, 2021$ respectively. In one operation you select any number of piles and remove the same number of stones from each selected pile. What is the minimum number of operations required to remove all the stones?
2. Least number of factors giving 51/2010 ●●●●○ 100 ptsFind the least positive integer $n$ for which there exists a set $\{s_1, s_2, \ldots, s_n\}$ consisting of $n$ distinct positive integers such that $$\left(1-\frac{1}{s_1}\right)\left(1-\frac{1}{s_2}\right)\cdots\left(1-\frac{1}{s_n}\right)=\frac{51}{2010}.$$