Subcontests
(6)a - d = e - b = c - f in equiangular hexagon
Show that if equiangular hexagon has sides a,b,c,d,e,f in order then a−d=e−b=c−f. a - b= one of the numbers m, n, m - n, m + n when coloring integers in 4 colors
Suppose that every integer is colored using one of 4 colors. Let m,n be distinct odd integers such that m+n=0. Prove that there exist integers a, b of the same color such that a−b equals one of the numbers m, n, m−n, m+n.