Puzzle (5 pi)

I have a calculator that can display ten digits. How many different ten-digit numbers can I type using just the 0-9 keys once each, and moving from one keypress to the next using the knight’s move in chess? (In chess, the knight move in an L-shape – one square up and two across, two squares down and one across, two squares up and one across, and other like combinations)

Are we to assume the numbers 1 to 9 form a 3 x 3 grid, with the zero underneath the center digit of the bottom row?

Also, can numbers begin with zero?

Depends on where to '0' is...

If the zero is in the bottom left, there are 4 solutions:

5034927618

5038167294

8167294305

4927618305

If the zero is in the bottom middle, you can't get the 5, so no solutions.

I forgot to specify, the 0 is in the bottom left. That is correct, and you get 5 pi.