Fede chooses $50$ distinct integers from the set $\{1, 2, 3, \ldots, 100\}$ such that their sum equals $2900$. Determine the minimum number of even numbers that can be among the $50$ numbers chosen by Fede.
Source: 2020 Argentina L2 P1
Tags: combinatorics
Fede chooses $50$ distinct integers from the set $\{1, 2, 3, \ldots, 100\}$ such that their sum equals $2900$. Determine the minimum number of even numbers that can be among the $50$ numbers chosen by Fede.