Problem

Source: Iran Team selection test 2024 - P11

Tags: combinatorics



Let $n<k$ be two natural numbers and suppose that Sepehr has $n$ chemical elements , $2k$ grams from each , divided arbitrarily in $2k$ cups.Find the smallest number $b$ such that there is always possible for Sepehr to choose $b$ cups , containing at least $2$ grams from each element in total. Proposed by Josef Tkadlec & Morteza Saghafian