Question: We are interested in getting 7 digit phone number by watching a chess piece (rook) traverse a board with numbers on each board position.

Given a 3 by 3 board that looks like this.

1 2 3
4 5 6
7 8 9

And assuming that a rook starts on position 4, write a function which provides all of the combinations of 7 digit numbers which start with 4.

For example:

456-3214 would be generated when the rook moves
{ right one, right one, up one, left one, left one, down one }

464-6464 would be generated when the rook moves
{right two, left two, right two, left two, right two, left two }

I couldnt come up with a solution. Any ideas ?