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2 problems match “binary number system”. Clear

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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. Reachable values on a blackboard ●●●●○ 100 ptsSvitlana writes the number 147 on a blackboard. Then, at any point, if the number on the blackboard is $n$, she can perform one of the following three operations: if $n$ is even, she can replace $n$ with $\frac{n}{2}$; if $n$ is odd, she can replace $n$ with $\frac{n+255}{2}$; and if $n \geq 64$, she can replace $n$ with $n-64$. Compute the number of possible values that Svitlana can obtain by doing zero or more operations.