# [seqfan] Re: Elimination game in a square of integers

Allan Wechsler acwacw at gmail.com
Fri May 1 20:29:29 CEST 2020

I was able to follow Ali Sada's explanation perfectly. Perhaps it would
clarify things to say: the board is initialized with n^2 chess kings,
numbered in raster order. The kings retain their labels after they move.
They take turns moving; after king "n^2" moves, king 1 gets to move again.
If a king has already been captured, or has no captures available to it, it
passes its turn. On each turn, a king captures the highest-labeled king
available. Play continues until no remaining king can capture; the "winner"
is the highest-numbered king remaining.

For the 1x1 board, the winner is 1.

For the 2x2 board, the winner is 1 (ends on cell 3).

For the 3x3 board, the winner is 3 (ends on cell 8).

For the 4x4 board, I believe the winner is 2; king 2 ends on cell 8, and
king 1 is still on the board at cell 15, but they cannot attack each other.

On Fri, May 1, 2020 at 1:29 PM Nacin, David <NACIND at wpunj.edu> wrote:

> Meant to include a
>
> 7 takes out 4
>
> in there as well before I couldn't proceed.
>
> -David
> ________________________________
> From: Nacin, David <NACIND at wpunj.edu>
> Sent: Friday, May 1, 2020 1:12 PM
> To: Sequence Fanatics Discussion List <seqfan at list.seqfan.eu>
> Cc: Ali Sada <pemd70 at yahoo.com>
> Subject: Re: [seqfan] Elimination game in a square of integers
>
> Are we having the king jump over removed squares?  Otherwise I can only
>
> 1 takes out 5
> 2 takes out 6
> 3 takes out 2
> 4 takes out 8
>
> and then we have a 1,3,7 and 9 which aren't adjacent to each other.
>
> Best,
>
> -David
> ________________________________
> From: SeqFan <seqfan-bounces at list.seqfan.eu> on behalf of Ali Sada via
> SeqFan <seqfan at list.seqfan.eu>
> Sent: Friday, May 1, 2020 12:22 PM
> To: Sequence Fanatics Discussion List <seqfan at list.seqfan.eu>
> Cc: Ali Sada <pemd70 at yahoo.com>
> Subject: [seqfan] Elimination game in a square of integers
>
> Hi Everyone,
> We take the numbers from 1 to n^2 and put them in a square. Starting with
> 1, and moving as a chess king, each number in its tern takes out the
> largest number it can get.
> a(n) is the largest remaining number.
>
> For example, in a 3 by 3 square we have the following moves:
> 1 takes out 5
> 2 takes out 6
> 3 takes out 2
> 4 takes out 8
> 7 takes out 4
> 9 takes out 7
> 1 takes out 9
> and 3 takes out 1.
> a(3) = 3
>
>
> I usually make mistakes when I calculate the terms, so I would really
> appreciate it if you could help me with this. I would love to know if there
> is a pattern here. Also, I want to check if this is a suitable sequence for
> the OEIS.
>
> Best,
>
> Ali
>
>
>
>
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