**From New Scientist #1555, 9th April 1987** [link]

It is true, of course, that there are rather a lot of letters in this puzzle, but despite that I though that for once Uncle Bungle was going to write it out correctly. In fact there was no mistake until the answer but in that, I’m afraid, one of the letters was incorrect.

This is another addition sum with letters substituted for digits. Each letter stands for the same digit whenever it appears, and different letters stand for different digits. Or at least they should, and they do, but for the mistake in the last line across.

Which letter is wrong?

Write out the correct addition sum.

**Note:** This is a corrected version of **Enigma 401**.

[enigma405]

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This puzzle is a corrected version of

Enigma 401. In the original puzzle the result of the addition sum was given incorrectly.As noted in my comment on

Enigma 1113I have used several methods in the past to solve this kind of problem.Here is a Python program that uses the [[

`SubstitutedSum()`

]] solver from theenigma.pylibrary. It runs in 503ms.And here is Python program that uses the

minizinc.pywrapper to generate a MiniZinc model to find the solution. It runs in 233ms.Solution:The 9th (penultimate) letter of the result is wrong. (The T should be an H). The correct sum should be: 695513243 + 673596633 = 1369109876.So, the puzzle that Uncle Bungle should have submitted is:

Which can be solved directly using the [[

`SubstitutedSum()`

]] solver from theenigma.pylibrary in 120ms:Or, using the [[

`bungled_sum()`

]] solver (seePuzzle 56):