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dylan, 18ac does end in one of those digits

Thanks, Bananabean, but how then does a cube+8th power end in one of those digits- I can't make it work!

A cube can end in any digit.

Any number to the power zero equals one. I bet Elap didn't think of that!

I'll take that bet!

That occurred to me yesterday after doing all the endgame maths. I can't believe Elap didn't think of it.

I think I must be missing something here. I’ve filled the grid, got the message, and done the subtraction, yet I cannot see any relationship with the results, and don’t, therefore, understand what to do next. Can anyone advise, bearing in mind that I’m no mathematician?

So, presumably that is the first of the integer values (zero is considered an integer, isn't it?)

xij,

Raise each of the six numbers in a set to a certain power, and then sum the results.
If you do that for all nine sets, the sum is the same.

Then work out what powers this applies to.

Dylan, I had the same problem, so in case you did the same as me: the number I had initially assigned to D was a 7th power not an 8th power (having not spotted that the list didn't include any 7th powers).