G'morning Aleksej, 

 ARS> Hmm, reminds me of "Japanese crosswords". And there are
 ARS> programs who solve them. ;)
 ARS> I don't dare to solve this on paper, or even in text editor
 ARS> - just tried and failed ;-) I think there are programs for
 ARS> them, just like for J.cs? To make an initially-null value
 ARS> gray, and to highlight errors... Hm, would it be fair?

Japanese `crosswords' ?  With numbers instead of words ?

I got systematic and made me up a paper sheet with 9 x 9 squares 
like this...

123 123 123  123 123 123  123 123 123
456 456 456  456 456 456  456 456 456
789 789 789  789 789 789  789 789 789

123 123 123  123 123 123  123 123 123
456 456 456  456 456 456  456 456 456
789 789 789  789 789 789  789 789 789

123 123 123  123 123 123  123 123 123
456 456 456  456 456 456  456 456 456
789 789 789  789 789 789  789 789 789


123 123 123  123 123 123  123 123 123
456 456 456  456 456 456  456 456 456
789 789 789  789 789 789  789 789 789

etc...

Then I cracked the puzzle I sent you by writing in a big `5' over 
the top left square - crossing out all the other 5's horizontally. 
vertically and then in the top left set of nine.

When I'd written in all the numbers,  there were one or two 
squares which only had 1 digit clear - and I scored them off 
across, down and in their square.

This led to the solution I sent you - all very time-consuming, 
finickity and boring....  but obviously easily programmed for.

It took my mind back to playing n-dimensional tic-tac-toe over 
Fidonet years ago,  using i,j,k notation.

For example,  in 2 dimensions the game would proceed like this

0 - 1,3     =   - - -
                - - -
                0 - -

X - 2,2     =   - - -
                - X -
                0 - -

0 - 3,1     =   - - 0
                - X -
                0 - -

X - 3,3     =   - - 0
                - X -
                0 - X

0 - 1,1     =   0 - 0
                - X -
                0 - X

X - 1,2     =   0 - 0
                X X -
                0 - X

0 - 2,1     =   0 0 0 !
                X X -
                0 - X

We'd only send the moves as

0> 1,3 -,-

X> 1,3 2,2
X> -,-

0> 1,3 2,2
0> 3,1 - -

X> 1,3 2,2
X> 3,1 3,3
X> -,-

0> 1,3 2,2
0> 3,1 3,3
0> 1,1 -,-

X> 1,3 2,2
X> 3,1 3,3
X> 1,1 1,2
X> -,-

O> 1,3 2,2
O> 3,1 3,3
O> 1,1 1,2
0> 2,1 !!!

And this allowed us to move into N dimensions - the center square 
in 5 dimensions was 2,2,2,2,2 for example,  and was a winning move 
if you already had 2,1,2,2,2 and 2,2,2,3,2 !

You could why when you lined up your moves thus...

2.1.2.2.2
2,2,2,2,2
2,2,2,3,2

The 1,2,3 line meant a win and you never had to try and draw a 7 
dimensional playing area....

It could be very confusing for others, however....

:-)
 
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