With this solving technique, we will prove the following assertions:
Each assertion is proved by a different chain of simple rules. The chain is static, which means that each step in the chain relies only on what we see the grid, not on the results of previous assertions (ie "Dynamic Chaining").
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 F1 contains the value 5 then B9 cannot contain the value 7 (View 1):
(1) If F1 contains the value 5 then E3 cannot contain the value 5 (the value can occur only once in the box)
(2) If E3 does not contain the value 5 then B3 must contain the value 5 (only remaining position in the row)
(3) If B3 contains the value 5 then B3 cannot contain the value 4 (the cell can contain only one value)
(4) If B3 does not contain the value 4 then B9 must contain the value 4 (only remaining position in the column)
(5) If B9 contains the value 4 then B9 cannot contain the value 7 (the cell can contain only one value)
Chain 2: If F7 contains the value 5 then B9 cannot contain the value 7 (View 2):
(1) If F7 contains the value 5 then F7 cannot contain the value 2 (the cell can contain only one value)
(2) If F7 does not contain the value 2 then F8 must contain the value 2 (only remaining position in the box)
(3) If F8 contains the value 2 then F8 cannot contain the value 9 (the cell can contain only one value)
(4) If F8 does not contain the value 9 then D8 must contain the value 9 (only remaining position in the box)
(5) If D8 contains the value 9 then D8 cannot contain the value 7 (the cell can contain only one value)
(6) If D8 does not contain the value 7 then D9 must contain the value 7 (only remaining position in the box)
(7) If D9 contains the value 7 then B9 cannot contain the value 7 (the value can occur only once in the row)
Chain 3: If F8 contains the value 5 then B9 cannot contain the value 7 (View 3):
(1) If F8 contains the value 5 then F8 cannot contain the value 9 (the cell can contain only one value)
(2) If F8 does not contain the value 9 then D8 must contain the value 9 (only remaining position in the box)
(3) If D8 contains the value 9 then D8 cannot contain the value 7 (the cell can contain only one value)
(4) If D8 does not contain the value 7 then D9 must contain the value 7 (only remaining position in the box)
(5) If D9 contains the value 7 then B9 cannot contain the value 7 (the value can occur only once in the row)