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

(In reply to Analytical solutions (hopefully all of them) by Gamer)

The solution I have, logically obtained, is the second presented by Gamer.

Analyzing "my solution", at a certain step, it´s said:"Thus the other 19 belongs to the line", refering to the 19 at (6, 7), though in the drawing still had a 19 at (3, 4).

When the problem was in the queue, Brian asked me if the matrix was right with only one 29 and three 19´s. And I checked it, answering "yes" to him.

But, with all those solutions found so far, it seems to me that the "19" at (3, 4) is a typo.    

Posted by pcbouhid on 2008-09-24 09:01:21