Problem of the Week 1158

A Cute Triangle Problem

It is easy to divide an equilateral triangle into strictly isosceles triangles: use the three angle bisectors. Show how to divide an equilateral triangle into acute, strictly isosceles triangles. That is, the smaller triangles must be isosceles, have only acute angles, and must not be equilateral.

One wants a small number of isosceles triangles, but the exact minimum here is an unsolved problem.

Source: Suggested by Ed Pegg. Original problem due to Elliot Line (author of a couple of puzzle books: Very Clever Puzzle Compendium, and Shadowbox, both available on Amazon). More info on the problem is at

© Copyright 2012 Stan Wagon. Reproduced with permission.

30 October 2012