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  |
     +-----+-----+-----+-----+-----+-----+-----+-----+

I see that Dej Mar had almost the same solution as I, but used the other "15".  Leming had exactly the same selection of cells as I, but used a slightly different path in the center cells. I regret I do not have familiarity with the tools to present the neat diagrams they presented.  Did either or both of you get all the way from start to finish without ANY "trial and error"?  I found the inferences were easiest with the perimeter cells, but less productive in the center where my procedure was to try to build segments and then join them by trials and errors.

Did pcbouhid believe there was a unique solution, or have a method in mind for the full construction?

Posted by ed bottemiller on 2008-09-23 18:19:25