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placing numbers 1,2,3...., 18 so that 3 / sum on three concurrent segments

Source: CRMO 2014 region 4 p6

September 29, 2018
combinatoricsnumber theoryDivisibility

Problem Statement

In the adjacent fi gure, can the numbers 1,2,3,4,...,181,2,3, 4,..., 18 be placed, one on each line segment, such that the sum of the numbers on the three line segments meeting at each point is divisible by 33?
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