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TOT 078 1984 Autumn S3 +1 on vertices and diag.inter. on regular decagon

Source:

August 24, 2019
combinatorial geometrycombinatoricsDecagon

Problem Statement

We are given a regular decagon with all diagonals drawn. The number "+1+ 1 " is attached to each vertex and to each point where diagonals intersect (we consider only internal points of intersection). We can decide at any time to simultaneously change the sign of all such numbers along a given side or a given diagonal . Is it possible after a certain number of such operations to have changed all the signs to negative?