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)
The table as posted earlier was indeed erroneous, since the digits incorporated in the same stemmed from a misunderstanding of the fundamental tenets corresponding to the problem.
Accordingly, I confirm having amended the said table.
Edited on September 7, 2007, 9:41 am
re: Solution
