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 re: Solution -- mis read? by brianjn)

right, if 0 were allowed to be connected to 5, you could have 784509 in addition to 784590. Also 789054. See the diagrams on my comment, and connect the 5 to the 0 with a line.

BTW the "phonepad" does connect the zero to 7 and 8--just the rectangle rules these out.

Edited on September 7, 2007, 9:03 am

Posted by Charlie on 2007-09-07 08:50:56