Dynamic Plus Region Forcing Chain

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

Because the value 5 cannot be placed elsewhere in box 2, and the results are the same, we can conclude that C5 must contain the value 9.

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.

Plus means that the standard Sudoku solving techniques: (Point & Claim, Naked Pairs, Hidden Pairs, and Swampfish) are applied (only when no other chain-step is found).

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 D1 contains the value 5 then C5 must contain the value 9 (View 1):
(1) If D1 contains the value 5 then H1 cannot contain the value 5 (the value can occur only once in the row)
(2) If D1 contains the value 5 (initial assumption) then I1 cannot contain the value 5 (the value can occur only once in the row)
(3) If I1 does not contain the value 5 and H1 does not contain the value 5 (misplaced towel) then I2 cannot contain the value 7 (Hidden Pair: H2, I2: 5, 8 in box 3)
(4) If I1 does not contain the value 5 (2) and H1 does not contain the value 5 (misplaced towel) then H2 cannot contain the value 7 (Hidden Pair: H2, I2: 5, 8 in box 3)
(5) If H2 does not contain the value 7 and I2 does not contain the value 7 (3) then G2 must contain the value 7 (only remaining position in the box)
(6) If G2 contains the value 7 then G2 cannot contain the value 6 (the cell can contain only one value)
(7) If G2 does not contain the value 6 then G9 cannot contain the value 2 (Hidden Pair: G3, G9: 6, 9 in col G)
(8) If G2 does not contain the value 6 (6) then G3 cannot contain the value 2 (Hidden Pair: G3, G9: 6, 9 in col G)
(9) If G3 does not contain the value 2 and G9 does not contain the value 2 (7) then G7 must contain the value 2 (only remaining position in the column)
(10) If G7 contains the value 2 then A7 cannot contain the value 2 (the value can occur only once in the row)
(11) If G2 contains the value 7 (5) then G4 cannot contain the value 7 (the value can occur only once in the col)
(12) If G2 contains the value 7 (5) then G6 cannot contain the value 7 (the value can occur only once in the col)
(13) If G6 does not contain the value 7 and G4 does not contain the value 7 (11) then B5 cannot contain the value 7 (Pointing: box 6 and row 5 on 7)
(14) If B5 does not contain the value 7 then B9 cannot contain the value 8 (Hidden Pair: B6, B9: 5, 7 in col B)
(15) If B5 does not contain the value 7 (13) then B6 cannot contain the value 8 (Hidden Pair: B6, B9: 5, 7 in col B)
(16) If B6 does not contain the value 8 and B9 does not contain the value 8 (14) then B8 must contain the value 8 (only remaining position in the column)
(17) If B8 contains the value 8 then A7 cannot contain the value 8 (the value can occur only once in the box)
(18) If A7 does not contain the value 8 and A7 does not contain the value 2 (10) then A7 must contain the value 1 (only remaining potential value in the cell)
(19) If A7 contains the value 1 then E7 cannot contain the value 1 (the value can occur only once in the row)
(20) If G7 contains the value 2 (9) then E7 cannot contain the value 2 (the value can occur only once in the row)
(21) If E7 does not contain the value 2 and E7 does not contain the value 1 (19) then E7 must contain the value 5 (only remaining potential value in the cell)
(22) If E7 contains the value 5 then E4 cannot contain the value 5 (the value can occur only once in the col)
(23) If E4 does not contain the value 5 then E4 must contain the value 9 (only remaining potential value in the cell)
(24) If E4 contains the value 9 then F5 cannot contain the value 9 (the value can occur only once in the box)
(25) If E4 contains the value 9 (23) then D5 cannot contain the value 9 (the value can occur only once in the box)
(26) If D5 does not contain the value 9 and F5 does not contain the value 9 (24) then C5 must contain the value 9 (only remaining position in the row)

Chain 2: If E1 contains the value 5 then C5 must contain the value 9 (View 2):
(1) If E1 contains the value 5 then E4 cannot contain the value 5 (the value can occur only once in the col)
(2) If E4 does not contain the value 5 then E4 must contain the value 9 (only remaining potential value in the cell)
(3) If E4 contains the value 9 then F5 cannot contain the value 9 (the value can occur only once in the box)
(4) If E4 contains the value 9 (2) then D5 cannot contain the value 9 (the value can occur only once in the box)
(5) If D5 does not contain the value 9 and F5 does not contain the value 9 (3) then C5 must contain the value 9 (only remaining position in the row)

Chain 3: If F1 contains the value 5 then C5 must contain the value 9 (View 3):
(1) If F1 contains the value 5 then H1 cannot contain the value 5 (the value can occur only once in the row)
(2) If F1 contains the value 5 (initial assumption) then I1 cannot contain the value 5 (the value can occur only once in the row)
(3) If I1 does not contain the value 5 and H1 does not contain the value 5 (misplaced towel) then I2 cannot contain the value 7 (Hidden Pair: H2, I2: 5, 8 in box 3)
(4) If I1 does not contain the value 5 (2) and H1 does not contain the value 5 (misplaced towel) then H2 cannot contain the value 7 (Hidden Pair: H2, I2: 5, 8 in box 3)
(5) If H2 does not contain the value 7 and I2 does not contain the value 7 (3) then G2 must contain the value 7 (only remaining position in the box)
(6) If G2 contains the value 7 then G2 cannot contain the value 6 (the cell can contain only one value)
(7) If G2 does not contain the value 6 then G9 cannot contain the value 2 (Hidden Pair: G3, G9: 6, 9 in col G)
(8) If G2 does not contain the value 6 (6) then G3 cannot contain the value 2 (Hidden Pair: G3, G9: 6, 9 in col G)
(9) If G3 does not contain the value 2 and G9 does not contain the value 2 (7) then G7 must contain the value 2 (only remaining position in the column)
(10) If G7 contains the value 2 then A7 cannot contain the value 2 (the value can occur only once in the row)
(11) If G2 contains the value 7 (5) then G4 cannot contain the value 7 (the value can occur only once in the col)
(12) If G2 contains the value 7 (5) then G6 cannot contain the value 7 (the value can occur only once in the col)
(13) If G6 does not contain the value 7 and G4 does not contain the value 7 (11) then B5 cannot contain the value 7 (Pointing: box 6 and row 5 on 7)
(14) If B5 does not contain the value 7 then B9 cannot contain the value 8 (Hidden Pair: B6, B9: 5, 7 in col B)
(15) If B5 does not contain the value 7 (13) then B6 cannot contain the value 8 (Hidden Pair: B6, B9: 5, 7 in col B)
(16) If B6 does not contain the value 8 and B9 does not contain the value 8 (14) then B8 must contain the value 8 (only remaining position in the column)
(17) If B8 contains the value 8 then A7 cannot contain the value 8 (the value can occur only once in the box)
(18) If A7 does not contain the value 8 and A7 does not contain the value 2 (10) then A7 must contain the value 1 (only remaining potential value in the cell)
(19) If A7 contains the value 1 then E7 cannot contain the value 1 (the value can occur only once in the row)
(20) If G7 contains the value 2 (9) then E7 cannot contain the value 2 (the value can occur only once in the row)
(21) If E7 does not contain the value 2 and E7 does not contain the value 1 (19) then E7 must contain the value 5 (only remaining potential value in the cell)
(22) If E7 contains the value 5 then E4 cannot contain the value 5 (the value can occur only once in the col)
(23) If E4 does not contain the value 5 then E4 must contain the value 9 (only remaining potential value in the cell)
(24) If E4 contains the value 9 then F5 cannot contain the value 9 (the value can occur only once in the box)
(25) If E4 contains the value 9 (23) then D5 cannot contain the value 9 (the value can occur only once in the box)
(26) If D5 does not contain the value 9 and F5 does not contain the value 9 (24) then C5 must contain the value 9 (only remaining position in the row)

Chain 4: If E2 contains the value 5 then C5 must contain the value 9 (View 4):
(1) If E2 contains the value 5 then E4 cannot contain the value 5 (the value can occur only once in the col)
(2) If E4 does not contain the value 5 then E4 must contain the value 9 (only remaining potential value in the cell)
(3) If E4 contains the value 9 then F5 cannot contain the value 9 (the value can occur only once in the box)
(4) If E4 contains the value 9 (2) then D5 cannot contain the value 9 (the value can occur only once in the box)
(5) If D5 does not contain the value 9 and F5 does not contain the value 9 (3) then C5 must contain the value 9 (only remaining position in the row)