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Programming Enigma Puzzles

10 July 2013

Posted by on **From New Scientist #2925, 13th July 2013** [link]

I have written a list of five different three-figure numbers, each of which is a power of a single digit. The first number is odd, and thereafter each number has the same hundreds digit or the same tens digit or the same units digit as its predecessor.

What, in order, are the five numbers?

This puzzle was republished as **Enigma 1770**.

[enigma1757]

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This is straightforward to solve. This Python program runs in 31ms.

Solution:The five numbers are 343, 243, 256, 216 and 512.Pretty similar in structure to Jim’s version

Without writing a computer program, here is my list:

343, 243, 256 216 512

The only discrepency I have with this solution is that the enigma specifies that proceeding numbers can have the same hundreth _or_ the same tens _or_ the same units.

E.g. 343 couldn’t be followed by 243 (since the tens match _and_ the units match)

By sticking to this stringently the puzzle is unsolvable though…

I agree that the puzzle could have been clearer on whether the “or” was “exclusive” or “inclusive”. But having studied logic and programming I was perfectly happy to use the standard inclusive meaning. And, as you point out, there are no solutions if you assume the exclusive meaning.