**From New Scientist #2848, 21st January 2011** [link]

My niece, Angela, has two younger twin siblings, Ann and Ian. To celebrate the twins’ birthday, she asked me to compose a puzzle in which their names feature. Here it is:

With different letters denoting different digits consistently throughout, and with no leading zeros appearing, the number denoted by GEMINI is exactly divisible by the numbers corresponding to ANN and IAN. These two three-digit numbers have no common factor. The number denoted by ANGIE has digits which increase from left to right.

What number corresponds to ENIGMA?

[enigma1681]

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The following Python program runs in 31ms.

Solution:ENIGMA = 836502.This problem can be solved using the command line Alphametic solver (

SubstitutedExpression) in theenigma.pylibrary, without the need to write a program. The command runs in 74ms.