With this solving technique, we will prove the following assertions:
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 B8 must contain the value 8 (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 G4 cannot contain the value 7 (the value can occur only once in the col)
(7) If G2 contains the value 7 (5) then G6 cannot contain the value 7 (the value can occur only once in the col)
(8) If G6 does not contain the value 7 and G4 does not contain the value 7 (6) then B5 cannot contain the value 7 (Pointing: box 6 and row 5 on 7)
(9) If B5 does not contain the value 7 then B9 cannot contain the value 8 (Hidden Pair: B6, B9: 5, 7 in col B)
(10) If B5 does not contain the value 7 (8) then B6 cannot contain the value 8 (Hidden Pair: B6, B9: 5, 7 in col B)
(11) If B6 does not contain the value 8 and B9 does not contain the value 8 (9) then B8 must contain the value 8 (only remaining position in the column)
Chain 2: If E1 contains the value 5 then B8 must contain the value 8 (View 2):
(1) If E1 contains the value 5 then H1 cannot contain the value 5 (the value can occur only once in the row)
(2) If E1 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 G4 cannot contain the value 7 (the value can occur only once in the col)
(7) If E1 contains the value 5 (initial assumption) then E4 cannot contain the value 5 (the value can occur only once in the col)
(8) If E1 contains the value 5 (initial assumption) then E6 cannot contain the value 5 (the value can occur only once in the col)
(9) If E6 does not contain the value 5 and E4 does not contain the value 5 (7) then D4 cannot contain the value 7 (Hidden Pair: D4, F4: 3, 5 in box 5)
(10) If E6 does not contain the value 5 (8) and E4 does not contain the value 5 (7) then F4 cannot contain the value 7 (Hidden Pair: D4, F4: 3, 5 in box 5)
(11) If F4 does not contain the value 7, D4 does not contain the value 7 (9) and G4 does not contain the value 7 (6) then C4 must contain the value 7 (only remaining position in the row)
(12) If C4 contains the value 7 then B6 cannot contain the value 7 (the value can occur only once in the box)
(13) If E4 does not contain the value 5 (7) then E4 must contain the value 9 (only remaining potential value in the cell)
(14) If E4 contains the value 9 then F5 cannot contain the value 9 (the value can occur only once in the box)
(15) If E4 contains the value 9 (13) then D5 cannot contain the value 9 (the value can occur only once in the box)
(16) If D5 does not contain the value 9 and F5 does not contain the value 9 (14) then C5 must contain the value 9 (only remaining position in the row)
(17) If C5 contains the value 9 then C5 cannot contain the value 2 (the cell can contain only one value)
(18) If C5 contains the value 9 (16) then C5 cannot contain the value 6 (the cell can contain only one value)
(19) If C5 does not contain the value 6 and C5 does not contain the value 2 (17) then B5 cannot contain the value 7 (Hidden Pair: B5, F5: 2, 6 in row 5)
(20) If B5 does not contain the value 7 and B6 does not contain the value 7 (12) then B9 must contain the value 7 (only remaining position in the column)
(21) If B9 contains the value 7 then B9 cannot contain the value 5 (the cell can contain only one value)
(22) If B9 does not contain the value 5 then B6 must contain the value 5 (only remaining position in the column)
(23) If B6 contains the value 5 then B6 cannot contain the value 8 (the cell can contain only one value)
(24) If B9 contains the value 7 (20) then B9 cannot contain the value 8 (the cell can contain only one value)
(25) If B9 does not contain the value 8 and B6 does not contain the value 8 (23) then B8 must contain the value 8 (only remaining position in the column)
Chain 3: If F1 contains the value 5 then B8 must contain the value 8 (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 G4 cannot contain the value 7 (the value can occur only once in the col)
(7) If G2 contains the value 7 (5) then G6 cannot contain the value 7 (the value can occur only once in the col)
(8) If G6 does not contain the value 7 and G4 does not contain the value 7 (6) then B5 cannot contain the value 7 (Pointing: box 6 and row 5 on 7)
(9) If B5 does not contain the value 7 then B9 cannot contain the value 8 (Hidden Pair: B6, B9: 5, 7 in col B)
(10) If B5 does not contain the value 7 (8) then B6 cannot contain the value 8 (Hidden Pair: B6, B9: 5, 7 in col B)
(11) If B6 does not contain the value 8 and B9 does not contain the value 8 (9) then B8 must contain the value 8 (only remaining position in the column)
Chain 4: If E2 contains the value 5 then B8 must contain the value 8 (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)
(6) If C5 contains the value 9 then C5 cannot contain the value 2 (the cell can contain only one value)
(7) If C5 contains the value 9 (5) then C5 cannot contain the value 6 (the cell can contain only one value)
(8) If C5 does not contain the value 6 and C5 does not contain the value 2 (6) then B5 cannot contain the value 7 (Hidden Pair: B5, F5: 2, 6 in row 5)
(9) If B5 does not contain the value 7 then B9 cannot contain the value 8 (Hidden Pair: B6, B9: 5, 7 in col B)
(10) If B5 does not contain the value 7 (8) then B6 cannot contain the value 8 (Hidden Pair: B6, B9: 5, 7 in col B)
(11) If B6 does not contain the value 8 and B9 does not contain the value 8 (9) then B8 must contain the value 8 (only remaining position in the column)