MathDB

C2

Part of 2018 Romanian Master of Mathematics Shortlist

Problems(1)

Least number of integer valued coins

Source: 2018 RMM Shortlist C2

2/21/2019
Fix integers n≥k≥2n\ge k\ge 2. We call a collection of integral valued coins n−diversen-diverse if no value occurs in it more than nn times. Given such a collection, a number SS is n−reachablen-reachable if that collection contains nn coins whose sum of values equals SS. Find the least positive integer DD such that for any nn-diverse collection of DD coins there are at least kk numbers that are nn-reachable.
[I]Proposed by Alexandar Ivanov, Bulgaria.
combinatorics