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.

Depending on whether or not you consider the zero as the largest or smallest number the solution is as follows -

Zero as smallest: 784590

Zero as largest: 095487

Posted by elisha on 2007-09-12 17:24:01