Duncan's SuDoku Solver

This is a version 10.0 screenshot

Rows and Columns (Double):

Occurances of a particular Possible occur just twice in their Rows and are also aligned in Columns (or appear just twice in their Columns and are also aligned in Rows).

In this example, the 9's (coloured purple) occur just twice in their Columns and are also aligned in Rows.

Because of this, for each of the Columns 2 and 5, there are only two Squares where a 9 can be a Solution - namely those in Rows A and J.

If the 9 for Column 2 is in Row A, then there is only one Square left for the remaining Column - that for Row J.

Because there is now a 9 in place for Rows A and J, there cannot be any other 9's in those Rows.

The 9's in A1, A6 and J4 (outlined in orange) are impossible solutions and may be removed.

This logic works whatever order you choose the Rows and Columns.

This is a version 10.1 screenshot

Rows and Columns (Double) - FINNED:

In this variant, the 3's (coloured purple) almost form the perfect Rows and Columns pattern apart from an extra 'fin' in B6.

Despite this, the logic still allows for the removal of an impossible solution (outlined in orange) in A4 as follows:

If D4 IS a 3, then clearly A4 cannot be a 3. But if D4 is NOT a 3, then D8 must be a 3, in which case B8 cannot be a 3, so the only places left for a 3 in Row B are B4 or B6 - either way A4 cannot be a 3. So A4 cannot be a 3 irrespective of the value of D4 and can be removed.

The logic works so long as the 'fins' are contained within the same Box.

This variant of the Rows and Columns analysis requires version 10.1 or later.

This is a version 10.1 screenshot

Rows and Columns (Double) - FINNED:

In this variant of the finned arrangement (aka 'Sushimi Finned X-Wing'), one of the corners of the basic arrangement (A5) is missing, but there are two 'fins' (on A4 and A6).

The logic is as follows:

If J5 IS a 4, then clearly B5 cannot be a 4. But if J5 is NOT a 4, then J7 must be a 4, in which case A7 cannot be a 4, so the only places left for a 4 in Row A are A4 or A6 - either way B5 cannot be a 4. So B5 cannot be a 4 irrespective of the value of J5 and can be removed.

The logic works so long as the 'fins' are contained within the same Box.

This variant of the Rows and Columns analysis requires version 10.1 or later.

This is a version 10.1 screenshot

Rows and Columns (Double) - FINNED:

In this second example of the 'Sushimi Finned X-Wing', the missing corner of the basic arrangement is J8, with an extra 'fin' (on J7).

The logic is as follows:

If A8 IS a 3, then clearly G8 and H8 cannot be a 3. But if A8 is NOT a 3, then A4 must be a 3, in which case J4 cannot be a 3, so J7 must be a 3. and G8/H8 cannot be a 3. So G8/H8 cannot be a 3 irrespective of the value of A8 and can be removed.

The logic works so long as any 'fins' are contained within the same Box.

This variant of the Rows and Columns analysis requires version 10.1 or later.

© Duncan Nightingale 2024