[seqfan] Re: Stepping Stones: Very nice new versions of the puzzle.

hv at crypt.org hv at crypt.org
Tue Feb 1 19:28:42 CET 2022

Neil Sloane <njasloane at gmail.com> wrote:
:Dear Seqfans, My old friend Rudolfo Kurchan just wrote to me saying that he
:and his friends have been studying some new versions of the Stepping Stones
:Problem (A337663, which is also described in the Youtube/Numberphile video
:Stones on an Infinite Chessboard,
:https://www.youtube.com/watch?v=m4Uth-EaTZ8 )

Very nice. Just for interest, another variant I considered is a 2-player
version of the original puzzle, where the objective is to leave the other
player without a move.

As in the original puzzle, the players can place 1s anywhere on the board
until one chooses to make a break for it by placing a 2. For that move,
and subsequent moves (which must place 3, 4 etc in turn), the non-empty
cells in the Moore neighbourhood of the placement must sum to the number
being placed.

I don't see anything obviously a sequence here, but interesting questions
are who wins on an N x N board, and on the infinite board (for which I
assume best play will be an infinite series of carefully placed 1s) what
losing moves look like.


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