Another beautiful puzzle from one of the Martin Gardner collections – this one is from “Mathematical Circus” in a chapter titled “Eccentric Chess and Other Problems”. I am reproducing this verbatim from his collection.
This cryptarithm (or alphametic, as some puzzlists prefer to call them) is an old one of unknown origin, surely one of the best and, I hope, unfamiliar to most readers:
The same letters stand for the same digits, zero included. The fraction EVE/DID has been reduced to its lowest terms. Its decimal form has a repeating period of four digits. The solution is unique. To solve this, recall that the standard way to obtain the simplest fraction equivalent to a decmal of n repeating digits is to put the repeating digit over n 9’s and reduce the fraction to its lowest terms.
As always, please send your answers as comments within the blog (preferred), or send an e-mail to email@example.com. Please do share the puzzle with others if you like, and please also send puzzles that you have come across that you think I can share in this blog.