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(2): Solution -- mis read? by Charlie)

Sometimes I seem to be too hasty in "opening my keyboard".

I refer to http://perplexus.info/show.php?pid=5745&cid=38415
just a few coments back.

I realised that KS had the solution by valid reasoning although his table was matching his criteria.

Charlie, thanks for that.  Maybe KS might add a note re this issue and maybe correct his table. 

In light of this maybe just a footnote at that locale and a later comment noting attention to this matter?  This is not a big issue.

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