Problem

The following diagram is of a standard telephone keypad. It consists of a 4x3 grid of buttons. Using the valid moves of a piece from the game of chess, varying combinations of 7-digit phone numbers can be derived. For example, starting in the upper-right corner (the "3" key) using a rook (which moves any number of spaces horizontally or vertically), one valid number, after pressing the initial "3" key, is: 3145289

1	2	3
4	5	6
7	8	9
*	0	#

Write a program that will count the number of valid 7-digit phone numbers that can be traced out on the keypad for every given chess piece. The following rules define a valid phone number:

• Seven digits in length
• Cannot start with 0 or 1
• Cannot contain a * or #

Remember

• It is possible that some pieces may not have any valid phone numbers
• You must provide the correct answers for each individual chess piece.
• Your solution should be maintainable by someone who has not seen it.
• Object-oriented design concepts should be used where-ever they make sense.
• It should be easy to extend the program for new requirements:
  • New keyboard layouts
  • Different rules
  • New types of chess pieces