Anyone can give me an idea how I approach calculating the following problem. How many possible valid numbers, where a valid number is any number between 0-9, length of 10 digits, excluding # or *, a piece of Chess can trace while travelling across a telephone keypad. Here say I have a King, it can move only as in a real game, in any direction but only a single cell at a time.
So the keypad looks like this:
1 2 3 4 5 6 7 8 9 * 0 #
So the piece makes 10 moves each time and each unique number created by it is a valid number. A piece starts its journey from an initial starting position.
The pieces can move or stay in one place (where moving or staying will both count as a move) as well as revisit the cells (as long as its allowed within their respective moving rights). So for example if a King moves from position 1 a three valid 10-move paths to create a valid number number could be 1236547890 or 1111111111 or 1212121212
All help much appreciated.