Every day when Frank goes to work, he needs to enter a keycode with six different digits to get into the building. The front door has one keypad style and the back door has a different keypad style. One day, Frank realized that each digit in his keycode was horizontally, vertically or diagonally adjacent to the next digit on both keypads.

If the first digit of Frank's keycode is larger than the last, can you determine his keycode?

    Front               Back
+---+---+---+   +---+---+---+---+---+
| 1 | 2 | 3 |   | 1 | 2 | 3 | 4 | 5 |
+---+---+---+   +---+---+---+---+---+
| 4 | 5 | 6 |   | 6 | 7 | 8 | 9 | 0 |
+---+---+---+   +---+---+---+---+---+
| 7 | 8 | 9 |
+---+---+---+
    | 0 |
    +---+

Example: 2,6 is a possible part of the keycode but 3,6 and 1,6 are not since those are adjacent on only one keypad.

(In reply to Solution by K Sengupta)

Your table is of common adjacent digits?
  In the "phonepad" layout for '0' it has only '9' as a neighour.

Reflect.  That may alter some of what you intended to report.

Posted by brianjn on 2007-09-07 05:53:18