Text: Show
Solution: Show
Well done. My impression is that these will get easier as you solve more, so that your eyes will automatically look at the grid as a toroid or your brain will memorize the kNight's move for each cell. My next puzzle may be too excessive as it is a Toroidal Anti Root 50 Sudoku [ (7,1) & (5,5)]Smythe Dakota wrote:After a few hours, I finally got your last one. Whew! Why do you call these "easy"?
I just read about them. I liked the Projective plane which should be on the to do list. I'll stick mostly to Anti-King after the next one unless somebody insists on an Eye coordination challenge. The Cylinder, Mobius Strip & Klein bottle are also possible but not as symmetricalSmythe Dakota wrote:Have you considered the same idea, but on a projective plane or Klein bottle instead of a torus?
tarek wrote: .... My next puzzle may be .... a Toroidal Anti Root 50 Sudoku [ (7,1) & (5,5) ] ....
tarek wrote:I'm not sure if the projective plane will work well with anti chess. I know it will definitely not work with anti-king (r1c1 is a king's move away from r1c1)
simon_blow_snow wrote:because the only way to construct the 2 orthogonal steps is r1c1-r9c9-r1c1, which in the (imaginary space of) projective plane still form a "straight line".
simon_blow_snow wrote: .... r1c1 does not qualify as a target [ of r1c1 ] because the only way to construct the 2 orthogonal steps is r1c1-r9c9-r1c1, which in the (imaginary space of) projective plane still form a "straight line".
Leaper (x,y) Example
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Anti-King (1,0) and (1,1) r1c1
Anti-Fers (1,1) r1c1
Anti-Tripper (3,3) r2c2
Anti-Camel (1,3) r1c2
Anti-Ostrich (1,5) r1c3
Anti-Root50 (1,7) and (5,5) r1c4
Hilarious as it may sound ... The solver can be programmed to handle it.Smythe Dakota wrote:It would be hilarious if you could come up with a Klein bottle that has exactly one vertical and one horizontal solution, with the two solutions different.
Or, one that has multiple solutions, both vertical and horizontal, but only one which works both ways.