Enigma 1195: Damn love
2 November 2015
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From New Scientist #2351, 13th July 2002 [link]
You are probably familiar with the word-chain game where you have to get from one word
to another by changing one letter at a time, making a proper word at each stage.
For example one shortest chain for changing DAMN to LOVE is:
DAMN – DAME – DOME – DOVE – LOVE.
Your task today is to find a shortest chain from MALE to DIRT. But your chain has to have a further property. You have to consistently replace each letter by a non-zero digit throughout the chain, different digits being used for different letters. For example, one such substitution in the above chain yields:
1863 – 1869 – 1769 – 1749 – 5749.
In that chain some of the four-figure numbers are prime and some are not. But in your substitution for a shortest MALE to DIRT chain all the four-figure numbers must be primes less than 2500.
What is the number for MALE?