**From New Scientist #2938, 12th October 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 (apart from a comma) is exactly the same as **Enigma 1757**.

**New Scientist** has stated that the puzzle was republished in error.

[enigma1770]

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I’m guessing that the difference between this puzzle and

Enigma 1757is supposed to be that instead of saying “The first number is odd”, this puzzle is supposed to say “The first number is even”. If so, a simple change to the code forEnigma 1757gives a solution to this problem too (although the numbers are just the same as the solution toEnigma 1757, but presented in the reverse order, so it’s not really much of a variation). This Python code runs in 34ms.Here is the solution to the suggested variation on

Enigma 1757(although it’s just the same solution as that forEnigma 1757with the list reversed).Solution:The five numbers are 512, 216, 256, 243 and 343.The summer weather had started when 1757 was published, so I didn’t have a chance to do it as I had started my walking holidays.

I hope NS aren’t going to repeat all the summer’s puzzles, but as there is another opportunity, here is my solution to 1757 and Jim’s suggested variation that might be 1770.

It’s not the first time the same puzzle has been published twice – back in the early days

Enigma 9later re-appeared asEnigma 83(and I never found any acknowledgement of the fact in the New Scientist archives). And more recently we’ve had variations on a theme, withEnigma 1740&Enigma 1755, and alsoEnigma 1748&Enigma 1762. The fact that this week’s puzzle is titled “Power point 2” makes me thinkEnigma 1770is meant to be one of these variations on a theme.The latest comment from

New Scientistis:So there probably won’t be a revision to Enigma 1770.

In the meantime there are 520 other Enigma puzzles on this site to have a go at, and I shall continue adding puzzles from the archive.