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Programming Enigma Puzzles

25 November 2016

Posted by on **From New Scientist #1521, 14th August 1986** [link]

In this division sum, each letter stands for a different digit.

Rewrite the sum with letters replaced by digits.

[enigma372]

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We can solve this puzzle using the

SubstitutedDivision()solver in theenigma.pylibrary. Here’s the run file:Or we can use the

SubstitutedExpressionsolver (also in theenigma.bylibrary). Here’s the run file for that:Either way we get the same answer in about the same time (96ms for

SubstitutedDivision, 92ms forSubstitutedExpression).Solution:The sum with numbers substituted for letters is 50078 ÷ 343 = 146:Once again I’m moved to say how little imagination is shown by those who set such puzzles with a random jumble of letters. My favourite in this case is MUM × GIN = BOOZY. Anyone who finds that sexist or otherwise offensive is welcome to suggest an alternative.

My complaint about this, Hugh, is not that it is sexist but that it’s not alphametic (good try though!).

Oh, I wonder what went wrong there! Perhaps my division was faulty.

Does this work? Last two lines TOBY, top line JUG ?

I am not sure of the change you want to make here, Hugh. I just noticed that mapping MUM x GIN = BOOZY onto 343 x 146 = 50078 makes both U and I equal to 4, which means it is not a (normal) alphametic. I haven’t looked for meaningful words that make this sum correct.

I’m evidently not very good at expressing myself. Divide MUM into BOOZY to get the quotient JUG. G × MUM = TOBY, subtracted in the last step to give no remainder.

For equality, no doubt something could be found to fit DAD as divisor.

I now see where the GIN came from. My pen sputtered when I copied down the puzzle, so that aeg came out as acg. My word-matching program then did its best, and I didn’t check the arithmetic. Sorry sorry.

The middle letters of MUM and GIN would have to be the same, so “MUM × GUN = BOOZY” which isn’t as satisfying. Maybe “PIP × GIN = BOOZY”.