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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