(related to Problem: The Three Villages)

Calling the three villages by their initial letters, it is clear that the three roads form a triangle, $A,$ $B,$ $C,$ with a perpendicular, measuring twelve miles, dropped from $C$ to the base $A, B.$ This divides our triangle into two right-angled triangles with a twelve-mile side in common. It is then found that the distance from $A$ to $C$ is $15$ miles, from $C$ to $B$ $20$ miles, and from $A$ to $B$ $25$ (that is $9$ and $16$) miles. These figures are easily proved, for the square of $12$ added to the square of $9$ equals the square of $15,$ and the square of $12$ added to the square of $16$ equals the square of $20.$

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



Project Gutenberg

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

This eBook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this edition or online at If you are not located in the United States, you'll have to check the laws of the country where you are located before using this ebook.