The puzzle does have a single solution, but it's a tough one to find. I couldn't see anyway to begin to solve it, and so exported it to
www.sudokuwiki.org. If you step through the solution at that site, you will see it solved by applying about a dozen strategies. The first step I have drawn out below:
- Extreme50 puzzle.png (34.1 KiB) Viewed 694 times
Assuming that 4 is the solution at row 7 col 2, a chain of implications shows that it cannot be a solution since it would imply that the 4 in the cell above would also be one. Therefore 4 at (7,2) can be removed:
+4(7,2) -7(7,2) +7(1,2) -7(2,3 & 3,3) +7(4,3) +7(4,3) -4(4,3) +4(6,2)
What makes this chain work is that although there are three 7's in column 3, there is a strong link between two of them and the third one below the two. This is true because when there are n possibles in a unit, and n-1 of them are the same color, then the one with the single color must be the solution.
Most of the other strategies used in this puzzle are digit, or cell, or unit forcing strategies. I am still looking at them.