Dynamic Cell Reduction Forcing Chain

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

Because the cell D2 cannot contain other values, and the results are the same, we can conclude that D6 cannot contain the value 5.

Each assertion is proved by a different chain of simple steps. The chains can be dynamic, which means that the conclusions of multiple sub-chains are combined in some cases.

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 D2 contains the value 2 then D6 cannot contain the value 5 (View 1):
(1) If D2 contains the value 2 then E1 cannot contain the value 2 (the value can occur only once in the box)
(2) If E1 does not contain the value 2 then E1 must contain the value 6 (only remaining potential value in the cell)
(3) If E1 contains the value 6 then C1 cannot contain the value 6 (the value can occur only once in the row)
(4) If C1 does not contain the value 6 then C2 must contain the value 6 (only remaining position in the box)
(5) If C2 contains the value 6 then I2 cannot contain the value 6 (the value can occur only once in the row)
(6) If E1 contains the value 6 (2) then I1 cannot contain the value 6 (the value can occur only once in the row)
(7) If I1 does not contain the value 6 and I2 does not contain the value 6 (5) then I5 must contain the value 6 (only remaining position in the column)
(8) If I5 contains the value 6 then I5 cannot contain the value 3 (the cell can contain only one value)
(9) If C2 contains the value 6 (4) then G2 cannot contain the value 6 (the value can occur only once in the row)
(10) If D2 contains the value 2 (initial assumption) then G2 cannot contain the value 2 (the value can occur only once in the row)
(11) If G2 does not contain the value 2 and G2 does not contain the value 6 (9) then G2 must contain the value 3 (only remaining potential value in the cell)
(12) If G2 contains the value 3 then I1 cannot contain the value 3 (the value can occur only once in the box)
(13) If G2 contains the value 3 (11) then I2 cannot contain the value 3 (the value can occur only once in the box)
(14) If I2 does not contain the value 3, I1 does not contain the value 3 (12) and I5 does not contain the value 3 (8) then I8 must contain the value 3 (only remaining position in the column)
(15) If I8 contains the value 3 then F8 cannot contain the value 3 (the value can occur only once in the row)
(16) If D2 contains the value 2 (initial assumption) then D2 cannot contain the value 5 (the cell can contain only one value)
(17) If D2 does not contain the value 5 then F2 must contain the value 5 (only remaining position in the box)
(18) If F2 contains the value 5 then F2 cannot contain the value 3 (the cell can contain only one value)
(19) If F2 does not contain the value 3 and F8 does not contain the value 3 (15) then F1 must contain the value 3 (only remaining position in the column)
(20) If F1 contains the value 3 then C1 cannot contain the value 3 (the value can occur only once in the row)
(21) If C2 contains the value 6 (4) then C2 cannot contain the value 3 (the cell can contain only one value)
(22) If C2 does not contain the value 3 and C1 does not contain the value 3 (20) then C5 must contain the value 3 (only remaining position in the column)
(23) If C5 contains the value 3 then C5 cannot contain the value 9 (the cell can contain only one value)
(24) If E1 does not contain the value 2 (misplaced towel) then E6 must contain the value 2 (only remaining position in the column)
(25) If E6 contains the value 2 then G6 cannot contain the value 2 (the value can occur only once in the row)
(26) If G2 does not contain the value 2 (10) and G6 does not contain the value 2 then G8 must contain the value 2 (only remaining position in the column)
(27) If G8 contains the value 2 then A8 cannot contain the value 2 (the value can occur only once in the row)
(28) If E6 contains the value 2 (24) then A6 cannot contain the value 2 (the value can occur only once in the row)
(29) If A6 does not contain the value 2 and A8 does not contain the value 2 (27) then A5 must contain the value 2 (only remaining position in the column)
(30) If A5 contains the value 2 then A5 cannot contain the value 9 (the cell can contain only one value)
(31) If A5 contains the value 2 (29) then A5 cannot contain the value 8 (the cell can contain only one value)
(32) If A5 does not contain the value 8 then D5 must contain the value 8 (only remaining position in the row)
(33) If D5 contains the value 8 then D5 cannot contain the value 9 (the cell can contain only one value)
(34) If A5 contains the value 2 (29) then A5 cannot contain the value 1 (the cell can contain only one value)
(35) If A5 does not contain the value 1 then G5 must contain the value 1 (only remaining position in the row)
(36) If G5 contains the value 1 then G5 cannot contain the value 9 (the cell can contain only one value)
(37) If I5 contains the value 6 (7) then I5 cannot contain the value 9 (the cell can contain only one value)
(38) If I5 does not contain the value 9, G5 does not contain the value 9 (36), D5 does not contain the value 9 (33), A5 does not contain the value 9 (30) and C5 does not contain the value 9 (23) then H5 must contain the value 9 (only remaining position in the row)
(39) If H5 contains the value 9 then G6 cannot contain the value 9 (the value can occur only once in the box)
(40) If G5 contains the value 1 (35) then G6 cannot contain the value 1 (the value can occur only once in the box)
(41) If G2 contains the value 3 (11) then G6 cannot contain the value 3 (the value can occur only once in the col)
(42) If G6 does not contain the value 3, G6 does not contain the value 2 (25), G6 does not contain the value 1 (40) and G6 does not contain the value 9 (39) then G6 must contain the value 5 (only remaining potential value in the cell)
(43) If G6 contains the value 5 then D6 cannot contain the value 5 (the value can occur only once in the row)

Chain 2: If D2 contains the value 5 then D6 cannot contain the value 5 (View 2):
(1) If D2 contains the value 5 then D6 cannot contain the value 5 (the value can occur only once in the col)

Chain 3: If D2 contains the value 8 then D6 cannot contain the value 5 (View 3):
(1) If D2 contains the value 8 then D3 cannot contain the value 8 (the value can occur only once in the box)
(2) If D3 does not contain the value 8 then D3 must contain the value 7 (only remaining potential value in the cell)
(3) If D3 contains the value 7 then F1 cannot contain the value 7 (the value can occur only once in the box)
(4) If D2 contains the value 8 (initial assumption) then D2 cannot contain the value 5 (the cell can contain only one value)
(5) If D2 does not contain the value 5 then F2 must contain the value 5 (only remaining position in the box)
(6) If F2 contains the value 5 then F2 cannot contain the value 7 (the cell can contain only one value)
(7) If F2 does not contain the value 7 and F1 does not contain the value 7 (3) then F8 must contain the value 7 (only remaining position in the column)
(8) If F8 contains the value 7 then F8 cannot contain the value 3 (the cell can contain only one value)
(9) If F2 contains the value 5 (5) then F2 cannot contain the value 3 (the cell can contain only one value)
(10) If F2 does not contain the value 3 and F8 does not contain the value 3 (8) then F1 must contain the value 3 (only remaining position in the column)
(11) If F1 contains the value 3 then F1 cannot contain the value 6 (the cell can contain only one value)
(12) If D2 contains the value 8 (initial assumption) then D2 cannot contain the value 2 (the cell can contain only one value)
(13) If D2 does not contain the value 2 then E1 must contain the value 2 (only remaining position in the box)
(14) If E1 contains the value 2 then E1 cannot contain the value 6 (the cell can contain only one value)
(15) If F2 contains the value 5 (5) then F2 cannot contain the value 6 (the cell can contain only one value)
(16) If F2 does not contain the value 6, E1 does not contain the value 6 (14) and F1 does not contain the value 6 (11) then E3 must contain the value 6 (only remaining position in the box)
(17) If E3 contains the value 6 then E6 cannot contain the value 6 (the value can occur only once in the col)
(18) If E1 contains the value 2 (13) then E6 cannot contain the value 2 (the value can occur only once in the col)
(19) If E6 does not contain the value 2 and E6 does not contain the value 6 (17) then E6 must contain the value 5 (only remaining potential value in the cell)
(20) If E6 contains the value 5 then D6 cannot contain the value 5 (the value can occur only once in the box)