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

Dmitry Kamenetsky dmitry.kamenetsky at rsise.anu.edu.au
Sat Aug 14 14:29:53 CEST 2010

```Hello all,

It gives me great pleasure to announce that our King Walking contest has
started. Everyone is welcome. Enjoy!

http://www.v-sonline.com/index.pl?C6

Sincerely,
Dmitry Kamenetsky

----------------original message-----------------
From: "Dmitry Kamenetsky" dmitry.kamenetsky at rsise.anu.edu.au
To: "Sequence Fanatics Discussion list" seqfan at list.seqfan.eu, "Eric
Angelini" Eric.Angelini at kntv.be
Date: Sat, 24 Jul 2010 11:24:42 +1000
-------------------------------------------------

> 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/
>>
>

```