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Bob Greenwade wrote on Tue, Sep 5, 2023 02:12 PM UTC:

50. Root-N25 Leaper. This piece isn't really meant for actual use; and even though I have it filed under "Mostly for Laughs," it's not really a joke piece either. It works as either of those (it does have some potential for a game; and there are humorous aspects, as we'll soon see), but really it's a thought experiment that serves as a mathematical exercise and illustration.

We have a Root-25 leaper (0,5)(3,4) and a Root-50 leaper (1,7)(5,5); and there are many other numbers that, especially on larger boards, could also be used. So, what if a piece could make any jump as long as it's a multiple of 25?

On an 8x8 square board, this is very basic; it's a compound of the Root-25 and Root-50 leapers (ZDXFXXGY).

On a 10x10 board, only one more move is added, a (6,8) from a Root-100 (ZDXFXXGYDYYY).

On a 12x12 board, there are several more moves, from Root-100 (0,10), Root-125 (2,11)(5,10), and Root-200 (10,10) (ZDXFXXGYDYYYWXXXAXXXCXYYAYYY).

On a 16x16 board, we add (0,15) from Root-225, (2,14) from Root-200, (9,12) from Root-225, (9,13) from Root-250, (10,15) from Root-325, and (15,15) from Root-450 (ZDXFXXGYDYYYWXXXAXXXCXYYAYYYHXXXXAXXXXGXYYYFXYYYYDXYYYYYGYYYYYY).

And we can all be thankful that there rarely are boards larger than 16x16. I mean, do you really want to know what the Betza code is for a Root-N25 Leaper on a 24x24 board?

I keep thinking that maybe this needs a better physical piece... but then again, maybe it doesn't.

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