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

Eric Angelini Eric.Angelini at kntv.be
Fri Jul 23 16:50:20 CEST 2010

```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.

```