MathDB
Least number of integer valued coins

Source: 2018 RMM Shortlist C2

February 21, 2019
combinatorics

Problem Statement

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.
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