Dynamic Region Forcing Chain

With this solving technique, we will prove the following assertions:

Because the value 9 cannot be placed elsewhere in row 6, and the results are the same, we can conclude that E6 cannot contain the value 8.

Each assertion is proved by a different chain of simple rules. 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 graphical illustrations of the different chains.

Chain 1: If A6 contains the value 9 then E6 cannot contain the value 8 (View 1):
(1) If A6 contains the value 9 then A6 cannot contain the value 3 (the cell can contain only one value)
(2) If A6 does not contain the value 3 then E6 must contain the value 3 (only remaining position in the row)
(3) If E6 contains the value 3 then E6 cannot contain the value 8 (the cell can contain only one value)

Chain 2: If B6 contains the value 9 then E6 cannot contain the value 8 (View 2):
(1) If B6 contains the value 9 then B4 cannot contain the value 9 (the value can occur only once in the box)
(2) If B6 contains the value 9 (initial assumption) then A4 cannot contain the value 9 (the value can occur only once in the box)
(3) If A4 does not contain the value 9 and B4 does not contain the value 9 (misplaced towel) then E4 must contain the value 9 (only remaining position in the row)
(4) If E4 contains the value 9 then E4 cannot contain the value 1 (the cell can contain only one value)
(5) If E4 does not contain the value 1 then D5 must contain the value 1 (only remaining position in the box)
(6) If D5 contains the value 1 then D2 cannot contain the value 1 (the value can occur only once in the col)
(7) If B6 contains the value 9 (initial assumption) then A6 cannot contain the value 9 (the value can occur only once in the box)
(8) If A4 does not contain the value 9 (2) and A6 does not contain the value 9 then A2 must contain the value 9 (only remaining position in the column)
(9) If A2 contains the value 9 then D2 cannot contain the value 9 (the value can occur only once in the row)
(10) If D2 does not contain the value 9 and D2 does not contain the value 1 (6) then D2 must contain the value 4 (only remaining potential value in the cell)
(11) If D2 contains the value 4 then D6 cannot contain the value 4 (the value can occur only once in the col)
(12) If B6 contains the value 9 (initial assumption) then D6 cannot contain the value 9 (the value can occur only once in the row)
(13) If D6 does not contain the value 9 and D6 does not contain the value 4 (11) then D6 must contain the value 8 (only remaining potential value in the cell)
(14) If D6 contains the value 8 then E6 cannot contain the value 8 (the value can occur only once in the box)

Chain 3: If D6 contains the value 9 then E6 cannot contain the value 8 (View 3):
(1) If D6 contains the value 9 then E6 cannot contain the value 9 (the value can occur only once in the box)
(2) If D6 contains the value 9 (initial assumption) then E4 cannot contain the value 9 (the value can occur only once in the box)
(3) If E4 does not contain the value 9 and E6 does not contain the value 9 (misplaced towel) then E1 must contain the value 9 (only remaining position in the column)
(4) If E1 contains the value 9 then E1 cannot contain the value 3 (the cell can contain only one value)
(5) If E1 does not contain the value 3 then E6 must contain the value 3 (only remaining position in the column)
(6) If E6 contains the value 3 then E6 cannot contain the value 8 (the cell can contain only one value)

Chain 4: If E6 contains the value 9 then E6 cannot contain the value 8 (View 4):
(1) If E6 contains the value 9 then E6 cannot contain the value 8 (the cell can contain only one value)