(related to Problem: Stealing The Bell-ropes)

Whenever we have one side $a$ of a right-angled triangle, and know the difference between the second side and the hypotenuse (which difference we will call $b$), then the length of the hypotenuse will be

$$\frac{a^2}{2b} + \frac b2.$$

In the case of our puzzle, this will be

$$\left(\frac{48 \times 48}6 + 1 \frac 12\right)\text{ in. } = 32 \text{ ft. } 1\frac 12 \text{ in. },$$

which is the length of the rope.

Thank you to the contributors under CC BY-SA 4.0!



Project Gutenberg

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

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