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The following Python program runs in 38ms.

Solution:661580022 ÷ 29 = 22813104 remainder 6.The following program takes a different approach, based on the form of the answer of the division. It runs in 134ms, and is shorter (although about half of it is checking all the intermediate sums once the answer is found).

Using the [[

`SubstitutedDivision()`

]] solver from theenigma.pylibrary solves the problem in 66ms.Jim, sorry to be a nuisance! I have just tackled Enigma 41 and couldn’t solve it. When I applied your published solution it indicated a misprint in the division. The last line three-digit line should be t t s, not t s s.

Thanks for pointing this out. A bit of an embarrassing mistake to make in a puzzle called “Division Bungle”. I’ve corrected the diagram now.