Wednesday, 11 December 2013

Alphametics (a.k.a. Cryptarithms)

This addition sum

  SEND
  MORE
MONEY

was first published by Henry Dudeney in 1924. The conventions for verbal arithmetic, as it is known, are that

  • each letter stands for a different digit and 
  • none of the numbers involved start with a zero. 


It is a bonus if

  • there is a unique solution, and
  • the words make up a meaningful phrase,
Here are two more

  WRONG
  WRONG
  R I GHT

and  MAKE + THIS = ADDUP.

A nice variation on the idea has been used by Susan Denham*, author of some of the more elegant Enigma puzzles in the New Scientist, a British science weekly. Here are two of her examples:

  1. EIGHT is a cube, PRIME is a prime, and NINE  is divisible by 9.
  2. NINETY is divisible by 9, TEN is one more than a perfect square, which is also divisible by 9, and there are SIX perfect squares between TEN and NINETY. 
Readers are invited to send in their solutions for a prize, so the second one ended with the question "What number should be SENT?"

*This name is a pseudonym, which is an approximate homophone for Sue Denham.

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