With this solving technique, we will prove the two following assertions:
Each assertion is proved by a chain of simple assertions. The chains are Nishio (Binary) chains, which means that they only involve two contradictory consequences of a single value assumption. The chains may be dynamic, which means that the conclusions of multiple sub-chains are combined.
The details of each chain are given below. Use the view selector below the grid to switch between the two graphical illustrations of the chains.
Chain 1: If A3 contains the value 5, then C8 must contain the value 5 (View 1):
(1) If A3 contains the value 5 then E3 cannot contain the value 5 (the value can occur only once in the row)
(2) If E3 does not contain the value 5 then F1 must contain the value 5 (only remaining position in the box)
(3) If F1 contains the value 5 then F8 cannot contain the value 5 (the value can occur only once in the col)
(4) If A3 contains the value 5 (initial assumption) then A8 cannot contain the value 5 (the value can occur only once in the col)
(5) If A8 does not contain the value 5 and F8 does not contain the value 5 (3) then C8 must contain the value 5 (only remaining position in the row)
Chain 2: If A3 contains the value 5, then C8 cannot contain the value 5 (View 2):
(1) If A3 contains the value 5 then C2 cannot contain the value 5 (the value can occur only once in the box)
(2) If A3 contains the value 5 (initial assumption) then A2 cannot contain the value 5 (the value can occur only once in the box)
(3) If A2 does not contain the value 5 and C2 does not contain the value 5 (misplaced towel) then G2 must contain the value 5 (only remaining position in the row)
(4) If G2 contains the value 5 then G5 cannot contain the value 5 (the value can occur only once in the col)
(5) If A3 contains the value 5 (initial assumption) then A5 cannot contain the value 5 (the value can occur only once in the col)
(6) If A5 does not contain the value 5 and G5 does not contain the value 5 (4) then C5 must contain the value 5 (only remaining position in the row)
(7) If C5 contains the value 5 then C8 cannot contain the value 5 (the value can occur only once in the col)