# 20 right isosceles triangles into a square

Five graded difficulty isosceles right triangle into square tilings

Two difficult "Seventeen right isosceles triangles into a square" tilings

The challenge is to fit the smallest $20$ integer-sided scaled right isosceles triangles into a square with diagonal $46$

For convenience, I list the areas of the triangles:

$1, 2, 4, 8, 9, 16, 18, 25, 32, 36, 49, 50, 64, 72, 81, 98, 100, 121, 128, 144$

There are four ways of doing it (not two as originally posted). A brave person it would be who tackled this by hand.

By way of illustration/clarification, here are the right isosceles triangles of area

$1, 2, 4, 9, 16, 18, 50$

arranged into a $10\times 10$ square: