In an old book (*) I found an advert with a puzzle I had never seen before.

Original copy

Unfortunately the book is very rare and it is hard to make out in the scanned photocopy above. I have redrawn it:

Goldman's transformation puzzle

It looks a bit like the classic Tangram puzzle, but it consists of three identical trapezoid/trapezium shapes and three triangles of different sizes.

With these pieces you have to form a square, and then transform it into a triangle by moving only two pieces.

*) The book was The Arithmachinist by Henry Goldman, from 1898. It was a self-published book promoting the mechanical calculator that he invented. A pdf file of the book can be found on this page. I have not been able to find a patent, and assume that the patent application was rejected.

  • $\begingroup$ Do we have to start with this particular square ? $\endgroup$ Commented Apr 11, 2020 at 15:05
  • $\begingroup$ @classicalMpk: I didn't think so, but El-Guest's answer shows it can be done with that square too. $\endgroup$ Commented Apr 11, 2020 at 15:48

2 Answers 2


It looks like you should be able to do this as follows:

enter image description here

Edit: it works! Before picture:

enter image description here

And after picture:

enter image description here

Please excuse my lack of scissors. The pieces to be moved are therefore

5 and 6 as per my diagram.

  • $\begingroup$ Very good! I hadn't found a solution that started with the original square arrangement, only one with a different square, and I then moved two trapezoids. That's why I phrased my question so as to leave the starting square arrangement undetermined. $\endgroup$ Commented Apr 11, 2020 at 15:31
  • $\begingroup$ Thank you! I was thinking about using a different square to start but I wasn’t clever enough to find that at first. $\endgroup$
    – El-Guest
    Commented Apr 11, 2020 at 15:34

Square I have in mind.

Possible Solution!

I hope this would be of some help. The question clearly says we have independence of forming our own square 😁


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