Draw only one continuous line into the 8x8 diagram below, which begins in the left cell above (with a “01”) and ends in the right bottom cell (with a “33”). The line must pass through all the numbers from 01 to 33 (through the center of each cell), once and only once through each one, and can run only horizontally or vertically (not diagonally). Besides, the line may not cross itself.

Far from being a trial and error problem, this can be solved logically.

     +-----+-----+-----+-----+-----+-----+-----+-----+
     | 01  | 16  | 05  | 20  | 25  | 09  | 21  | 01  |
     +-----+-----+-----+-----+-----+-----+-----+-----+
     | 18  | 10  | 27  | 26  | 11  | 17  | 12  | 32  |
     +-----+-----+-----+-----+-----+-----+-----+-----+
     | 32  | 11  | 15  | 19  | 08  | 06  | 27  | 20  |
     +-----+-----+-----+-----+-----+-----+-----+-----+
     | 17  | 04  | 13  | 24  | 30  | 28  | 31  | 02  |
     +-----+-----+-----+-----+-----+-----+-----+-----+
     | 25  | 10  | 02  | 26  | 04  | 28  | 22  | 13  |
     +-----+-----+-----+-----+-----+-----+-----+-----+
     | 05  | 14  | 30  | 08  | 15  | 31  | 19  | 06  |
     +-----+-----+-----+-----+-----+-----+-----+-----+
     | 23  | 07  | 24  | 16  | 29  | 22  | 18  | 19  |
     +-----+-----+-----+-----+-----+-----+-----+-----+
     | 03  | 12  | 09  | 03  | 07  | 14  | 23  | 33  |
     +-----+-----+-----+-----+-----+-----+-----+-----+

+-----+-----+-----+-----+-----+-----+-----+-----+
| 01  |     | 05 ---20 ---25 ---09 ---21  |     |
+- | -+-----+- | -+-----+-----+-----+- | -+-----+
| 18  | 10 ---27  |     |     | 17 ---12  |     |
+- | -+- | -+-----+-----+-----+- | -+-----+-----+
| 32 ---11  |     | 19 ---08  | 06  |     |     |
+-----+-----+-----+- | -+- | -+- | -+-----+-----+
|     |     | 13 ---24  | 30 ---28  |     |     |
+-----+-----+- | -+-----+-----+-----+-----+-----+
|     |     | 02 ---26 ---04  |     |     |     |
+-----+-----+-----+-----+- | -+-----+-----+-----+
|     |     |     |     | 15 ---31  |     |     |
+-----+-----+-----+-----+-----+- | -+-----+-----+
|     |     |     | 16 ---29 ---22  |     |     |
+-----+-----+-----+- | -+-----+-----+-----+-----+
|     |     |     | 03 ---07 ---14 ---23 ---33  |
+-----+-----+-----+-----+-----+-----+-----+-----+

Posted by Dej Mar on 2008-09-23 13:35:47