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Programming Enigma Puzzles

29 July 2019

Posted by on **From New Scientist #1662, 29th April 1989** [link]

Professor Puzzleothers has privately decided to allow his ex-wife a resettlement of precisely one third his current annual salary, but only if she can work out exactly how much she is to get.

He instructs his solicitor to tell her lawyers that he will agree to alimony calculated according to the following formula.

She has to find two numbers A and B which between them contain each of the digits from 1 to 9 exactly once and contain no 0 digit, such that B = 2A, A is divisible by 3, and the quotient when A is divided by 3 is a number which contains all the digits from 1 to 4. Then £A will be the annual settlement.

What does Puzzleothers currently earn?

[enigma510]

%d bloggers like this:

The two numbers

aandb, contain all the digits from 1-9 exactly once and are such thatb = 2a.So

amust consist of 4 digits andbmust consist of 5 digitsSo we can consider this as an alphametic problem where

a =andABCDb =.EFGHIWe can then use the [[

SubstitutedExpression()]] solver from theenigma.pylibrary to solve the puzzle.The following run file executes in 147ms.

Run:[ @repl.it ]Solution:The professor’s salary is £21,879.So we have: