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In the diagram below we have pentagon ABCDE with 5 edges and 5 diagonals. These 10 line segments are currently all colored black. The diagram contains several triangles but for this puzzle we are...
#1: Initial revision
by
will.octagon.gibson
·
2026-08-01T16:42:42Z (about 2 months ago)
Can you avoid monochromatic triangles?
In the diagram below we have pentagon **ABCDE** with 5 edges and 5 diagonals. These 10 line segments are currently all colored black. The diagram contains several triangles but for this puzzle we are only interested in the 10 triangles where all three of its vertices are vertices of pentagon **ABCDE**. A triangle is considered monochromatic if all three of its edges are the same color. Currently all 10 triangles are monochromatic black. Is it possible to recolor some of the 10 line segments red, leaving the other line segments black, so that none of the 10 triangles are monochromatic? If yes, provide a diagram showing the recoloring. If no, prove it is impossible. 