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Programming Enigma Puzzles

3 December 2018

Posted by on **From New Scientist #1628, 1st September 1988** [link]

In the following long multiplication I’ve replaced digits with letters in some places and left gaps in the rest. Where letters are used, different letters are used for different digits.

That’s all you actually need, but to avoid hours of work I can also tell you that GAP is divisible by 9.

What is the value of IMPINGE?

[enigma477]

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We can use the [[

SubstitutedExpression()]] solver from theenigma.pylibrary to tackle this puzzle. I’ve used lower case letters for the dashes.The following run file executes in 156ms.

Run:[ @repl.it ]Solution:IMPINGE = 5285061.And A=4.

The multiplication sum is: 163 × 648 = 105624.

Although it is not necessary to solve the puzzle, the extra [[

"GAP % 9 = 0"]] expression saves about 25ms of CPU time.Am I alone in thinking that one normally writes the intermediate lines in the reverse order?

I know it makes no difference to the sum, but the way the puzzle is arranged looks odd.

Yes. The intermediate totals are in the opposite to order to what I would expect too. Although the positioning in the columns makes it clear which is which, and in some ways presenting the multiples of G, A, P in that order makes sense.