# Sunday Times Teaser 2824 – New Extension

*by Danny Roth*

#### Published: 6 November 2016 (link)

George has just moved departments and he has a new four-figure telephone extension number. He shows it to Martha and proudly points out that, if you delete any two of the digits of the extension number, then the remaining two-figure number is prime. Martha then lists the resulting six different primes and comments delightedly that more than one of them divides exactly into the extension number.

What is George’s new extension number?

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A fairly direct Python interpretation runs in 215ms.

Using the general alphametic solver from the

enigma.pylibrary gives a solution in 82ms.We can use analysis to limit the digits that can be assigned to each letter (e.g. C and D both appear as the units digit of two different primes, so cannot be even, etc.), but I’m not sure it’s worth it for a programmatic solution.