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Programming Enigma Puzzles

30 January 2017

Posted by on **From New Scientist #2286, 14th April 2001** [link]

To practise my long multiplication I have taken two three-figure numbers (using six different digits between them) and multiplied the first by the second. Then, as a check, I multiplied the second by the first. The results are shown with dashes for all non-zero digits:

What were the two three figure numbers?

[enigma1130]

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The intermediate multiplications in the sums are given in the opposite order (from top to bottom) than I would normally write them, and also I would normally use blanks to pad the right hand side, rather then zeros. But the form of the sum is clear.

I used the general Alphametic solver (

SubstitutedExpression()) from theenigma.pylibrary to consider the multiplications (ABC × DEF) and (DEF × ABC). The digits ABCDEF are used for the two three-figure numbers and are all different, I use the lower-case lettersabcdefghijklmnopqrstuvwto stand for the remaining non-zero digits, withZstanding for zero.This is the run file, which executes in 94.6ms.

Solution:The three-figure numbers are 534 and 216.Here are the two multiplications in full: