I thought that would give them pause for thought, because they wouldn’t be able to *just* do a computer search, because how would they know it had found the largest? (Ok, so they could have stopped when they reached numbers too big to plausibly be my age, but that’s clearly not in the spirit of the challenge ðŸ™‚

My strategy was to prove inductively that all can be written as such a sum, provided we can find an integer suitable to be the base case of the induction. We don’t know what actually is at this point â€“ but if we write down the inductive step of the proof anyway and see what conditions it demands of , we can then finish off with a computer search that quickly finds a workable value of and a list of all the cases below it that don’t work.

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