(related to Problem: How To Make Cisterns)

Here is a general formula for solving this problem. Call the two sides of the rectangle a and b. Then

$$\frac{a + b\; - \sqrt{a^2 + b^2\; - ab}}6$$

equals the side of the little square pieces to cut away. The measurements given were $8$ ft. by $3$ ft., and the above rule gives $8$ in. as the side of the square pieces that have to be cut away. Of course it will not always come out exact, as in this case (on account of that square root), but you can get as near as you like with decimals.

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Project Gutenberg

  1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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