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Thanks, Spanner, for the suggestion. In fact, D was OK, but I'd made the mistake of assuming that all the letters were powers of prime numbers, whereas it seems that S is the cube of a composite number. This possibility of using composite numbers gives many more options for the squares than I'm comfortable with, so I think I'll just watch the rugby now, then Endeavour! Thanks again for help offered.

Since the values for N = 0 are all trivial I think N = 0 can be excluded, and since there is room for doubt I don't think starting with zero or omitting zero will be marked wrong.

Is this startling property widely known in mathematical trivia circles? I've not come across it before.

I’m no mathematician, but I am curious as to why the preamble didn’t say “The property holds for a series of consecutive positive integer values of N” just to avoid ambiguity.

Surely the fact that it doesn't means that the required answer is N = 0 - ?

That’s certainly my view, crosswhit99, but anyone unaware of the peculiarity of the power of zero might feel hard done by if they were marked incorrect

In general mathematicians wouldn't omit mention of 'trivial' cases in the statements of their results.

Slightly stretching the topic but, for weekends when the Listener goes numerical, what's the best, similar, alternative? Preferably available in a Saturday newspaper. Thanks.

Hi Granama. The Inquisitor crossword (also known as the IQ) in the i newspaper on Saturday is akin to the Listener

… or on a Sunday, Enigmatic Variations in The Telegraph

Thanks! I'll give IQ and EV a go ready for the next numeric.