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Supposing you have a rectangle (with different weight and heigh), how can you obtain the sizes of a square that, in grid order, fits perfectly within the rectangle size?

Example of a wrong square size:

Example of a perfect fit:

The images above are of a 215.9 mm x 279.4 mm (US Letter 8.5 in x 11.0 in)

DATALOT
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    If you have squares 12.7mm on each side, then the letter will be a 17 by 22 grid of these squares. Any squares larger will not fill the letter exactly, since 17 and 22 are coprime. I used $\gcd(2159, 2794)$ and divided by 10. – 79037662 Sep 24 '19 at 20:32
  • You have enough reputation to answer this question. Please do it because I want to mark you as accepted. I have been using your formula all this time (almost a year) and is really helpful – DATALOT Jul 01 '20 at 18:08
  • I just can add that if you extract all the divisors of that number you will get more square sizes to make perfect-fit grids. – DATALOT Jul 01 '20 at 18:08
  • Honestly I had forgotten about this question, happy to hear it's still helpful 9 months later. – 79037662 Jul 01 '20 at 20:26

1 Answers1

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If you have squares $12.7$mm on each side, then the letter will be a $17$ by $22$ grid of these squares. Any squares larger will not fill the letter exactly, since $17$ and $22$ are coprime. I used $\gcd(2159,2794)$ and divided by $10$.

79037662
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