SudokuSolver Forum

I'm talking about wrap-around not only in the locations of the GT and LT symbols (i.e. on the edges of the puzzle), but also wrap-around in the digits themselves. 1,2,3,4,5,6,7,8,9,1,2,3, etc.

Imagine the digits 1-9 as being placed around a circle, going clockwise. Define x<y in case you get from x to y faster by going around the circle clockwise than by going counterclockwise.

Examples:

5 is less than 6,7,8,9 but greater than 1,2,3,4.

2 is less than 3,4,5,6 but greater than 7,8,9,1.

9 is less than 1,2,3,4 but greater than 5,6,7,8.

With this definition, the technique of starting with 1's and 9's, then 2's and 8's, etc, is foiled, because all digits have essentially the same properties.

Hatman, or anybody, would you care to come up with some nifty examples?

Any such puzzle with one solution would, of course, automatically have nine solutions, because you could just add x to (or subtract 9-x from) each cell, where x is any number 0 through 8. So you'd have to consider a "unique" solution to be any set of nine solutions. (Or you could adopt the convention that the center cell r5c5 must contain a 5, or something.)

Bill Smythe

Bill

Standard GTLT does not need any givens, but as you say this will need at least one given. The given will need to link to a < or > to avoid the puzzle being Ruudiculous.

Cheers

Maurice