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

[Dmitry Kamenetsky]

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.
>> 
>> 
>> 
>> _______________________________________________
>> 
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>> 
>