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tiling n triangular tiles to create convex equiangular hexagon

Source: Singapore Junior Math Olympiad 2006 2nd Round p5 SMO

March 25, 2020

combinatoricsTilinghexagontiles

Problem Statement

You have a large number of congruent equilateral triangular tiles on a table and you want to fit

n

of them together to make a convex equiangular hexagon (i.e. one whose interior angles are

120^o

) . Obviously,

n

cannot be any positive integer. The first three feasible

n

are

6, 10

and

13

. Show that

12

is not feasible but

14

is.