# [seqfan] Re: « King-walking » integers in a square box

Dmitry Kamenetsky dmitry.kamenetsky at rsise.anu.edu.au
Sat Jul 24 03:24:36 CEST 2010

```Hi Eric,

What an interesting problem, thank you! This problem seems perfect for our
competitions: http://www.v-sonline.com/index.pl
I will propose the problem and if it gets accepted then we will probably
explore all NxN squares with N from 3 to 32.

Cheers,
Dmitry

----------------original message-----------------
From: "Eric Angelini" Eric.Angelini at kntv.be
To: "Sequence Fanatics Discussion list" seqfan at list.seqfan.eu
Date: Fri, 23 Jul 2010 16:50:20 +0200
-------------------------------------------------

>
> Hello SeqFans,
> In this 4x5 box one can read all
> consecutive integers from 0 to 158
> (included):
> 5 8 0 7 3
> 9 6 5 1 8
> 1 3 2 4 2
> 4 0 9 7 6
> (grid submitted by James Dow Allen
> on rec.puzzles two days ago)
>
> The rules are:
> - an integer is there if it's digits
> can be walked on by a chess King
> (one step in 8 directions:
> 4 straightly, 4 diagonally)
> - two identical digits (or more) can
> follow each other (as if the King
> was jumping on the same square).
>
> Example:
> - the integers 58073, 13997 and 13887
> are visible below,
> - the integer 159 is not:
> 5 8 0 7 3
> 9 6 5 1 8
> 1 3 2 4 2
> 4 0 9 7 6
> It seems impossible to find such a
> 4x5 box showing all consecutive in-
> tegers from 0 to 'n' with 'n' > 158.
>
> Here is Giovanni Resta's 158 solution
> for the same box:
> 0 3 6 4 2
> 1 7 5 1 3
> 4 0 2 8 9
> 8 9 6 5 7
> (published on rec.puzzles yesterday)
>
> Question:
> Using the same rules, what would be
> the highest reachable integer in the
> successive square boxes 1x1, 2x2, 3x3,
> 4x4, 5x5, ...
> This might constitute a seq S for Neil.
> [S starts 0, 3, 8, ...]
> Best,
> É.
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

```