Fifty Numbers Summing to 2025

★ 6/10combinatorics number theory Modular Arithmetic Estimation

Problem

A set $A = \{a_1, a_2, \ldots, a_{50}\}$ consists of $50$ distinct positive integers. Let $S(A)$ be the sum of all elements of $A$ and $E(A)$ the number of even elements. If $S(A) = 2025$ , find the minimum possible value of $E(A)$ .

Answer

Solution

Difficulty	6/10
Topics	combinatorics, number theory, Modular Arithmetic, Estimation

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