IMO 2013 Shortlist C1

Let n be a positive integer. Find the smallest integer k with the following property: Given any real numbers a1,...,ad s...

imomathematicsolympiadshortlistcombinatorics

IMO 2013 Shortlist C1

Category: Combinatorics

Problem

Let n be a positive integer. Find the smallest integer k with the following property: Given any real numbers a1,...,ad such that a1 a2 ¨¨¨ ` ad “ n and 0 ď ai ď 1 for i “ 1,2,...,d, it is possible to partition these numbers into k groups (some of which may be empty) such that the sum of the numbers in each group is at most 1. (Poland)