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rearrange numbers 1 - 60 - All-Russian MO 2002 Regional (R4) 9.5

Source:

September 17, 2024
number theorycombinatorics

Problem Statement

Is it possible to arrange the numbers 1,2,...,601, 2, . . . , 60 in that order, so that the sum of any two numbers between which there is one number, divisible by 22, the sum of any two numbers between which there are two numbers divisible by 33, . . . , the sum of any two numbers between which there is are there six numbers, divisible by 77?