Question 97
Bob has the collection of $n$ coins. Each of them weights an integer number of grams, and their total weight is equal to $300$ grams. Let $k, l, m$ be positive integers such that $k + l + m = 300$.
Find the smallest possible number of $n$ for which Bob always (independently of coin's weights and for all possible $k, l, m$) can partition his collection into three groups so that the total weight of the coins in the first, second, and third groups is equal to $k, l$, and $m$ grams, respectively.
Find the smallest possible number of $n$ for which Bob always (independently of coin's weights and for all possible $k, l, m$) can partition his collection into three groups so that the total weight of the coins in the first, second, and third groups is equal to $k, l$, and $m$ grams, respectively.