This is a variation of Pythagorean quilts.

I will make it short, this time.

Pythagoras's theorem also works for triangles. This leads to the following variation:

Dissect the triangles of size 5 and 12 and use the pieces to recompose a triangle of size 13.

enter image description here

You are allowed to cut only along triangle boundaries, i.e. the gray lines. Straight cuts are not required, you can cut any twisted path you like. The resulting pieces must be connex by sharing full sides, not only by touching corners.

Unlike for the pythagoran quilts, you are allowed to rotate or flip the pieces. In fact, the count of "up" and "down" triangles doesn't match on both sides so a flip or a rotation will be necessary.

As usual, you have to minimize the number of pieces.


  • $\begingroup$ rot13(Whfg cybc gur 12 fvqrq gevnatyr va gurer, gura phg gur 5 gevnatyr fb vg svgf gur erznvavat fcnpr.) $\endgroup$
    – Stevo
    Commented Sep 17, 2021 at 23:03
  • $\begingroup$ @Stevo Are you sure that's the minimal number of pieces? $\endgroup$
    – Gareth McCaughan
    Commented Sep 17, 2021 at 23:35
  • $\begingroup$ no. but if we put the 5 sided triangle on the corner... i have a feeling its 4. $\endgroup$
    – Stevo
    Commented Sep 17, 2021 at 23:37

1 Answer 1


Eureka! I've got it in four pieces!

enter image description here

  • $\begingroup$ Very good! It is the same solution as I had. $\endgroup$
    – Florian F
    Commented Sep 18, 2021 at 7:56

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