IMO Shortlist 2013 problem C1

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Dodao/la: arhiva
21. rujna 2014.
Let n be a positive integer. Find the smallest integer k with the following property: Given any real numbers a_1, \ldots, a_d such that a_1 + a_2 + \cdots + a_d = n and 0 \leq a_i \leq 1 for i = 1, 2, \ldots, 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.
Izvor: Poland