# Unlucky tiling: Arrange thirteen right isosceles triangles into a square

Link to next puzzle in this series:Five graded difficulty isosceles right triangle into square tilings

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

V.hard problem, 20 right isosceles triangles into a square

This problem has only one solution, and will be challenging by hand, but probably more satisfying. Computers allowed, probably challenging too. Not for the computer, but for the programmer.

The challenge is to arrange thirteen right isosceles triangles of the following areas into a $36\times 36$ square with no gaps or overlaps.

$2, 4, 8, 18, 32, 64, 72, 98, 128, 144, 196, 242, 288$

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:

If you can solve this with scalene right triangles of the correct area... I'll accept that too.

• Do the triangles have to be isosceles? – NL628 Apr 21 '18 at 0:48
• Yep... I'll add that. Possibly it could be done with non-isosceles right triangles... much harder though. I'll accept an answer with non-isosceles right triangles! – theonetruepath Apr 21 '18 at 3:20
• It's my puzzle. I found it with my tiling program, there's only one solution, the proof is "brute force". – theonetruepath Apr 21 '18 at 7:57