by **champagne** » Thu Sep 05, 2019 8:04 am

Unique Loop type 4

The cells R1C5,R1C6,R4C6,R6C4,R7C4,R7C7,R2C7,R2C9,R6C9,R4C8,R9C8,R9C3,R8C3,R8C5 form a Unique Loop with the values 3 and 1. There are exactly two ways of placing the values 3 and 1 in the cells of the Unique Loop, forming two possible configurations. In both configurations, each row, column or block touched by the Unique Loop contains each of the two values 3 and 1 exactly once. As a result, if one of these two configurations were part of the solution, it could then be replaced by the other one to get a second valid solution.

Because a valid sudoku cannot have more than one solution, none of the two configurations of the Unique Loop can be valid. Note that the two cells R9C3 and R8C3 are the only possible positions of the value 3 in the column, thus, one of these two cells will contain the value 3. Therefore, the only possible way to avoid the two configurations is if neither R9C3 nor R8C3 contains the value 1.