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1010 numbers in each rearrangement of the 2006 integer numbers

Source: Argentina 2006 OMA L3 p4

May 12, 2024
combinatoricsnumber theory

Problem Statement

Find the greatest number MM with the following property: in each rearrangement of the 20062006 integer numbers 1,2,...20061,2,...2006 there are 10101010 numbers located consecutively in that rearrangement whose sum is greater than or equal to MM.