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Breaking sticks

Source: St Petersburg Olympiad 2012, Grade 9, P7

September 29, 2017
combinatoricsnumber theory

Problem Statement

We have 20122012 sticks with integer length, and sum of length is nn. We need to have sticks with lengths 1,2,....,20121,2,....,2012. For it we can break some sticks ( for example from stick with length 66 we can get 11 and 44). For what minimal nn it is always possible?
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