In/Out rule for Jigsaw Sudoku
Jigsaw Sudoku looks complicated because of the shape of its grids. Now we will look at a solving technique/ strategy for Jigsaw Sudoku, aka, Chaos sudoku, Irregular sudoku. Attached below is a unsolved Jigsaw sudoku. For better understanding, I have colored each nonet.
Let us draw a vertical line between the Column5 and Column 6. This divides the grid into 2 parts, say left part and right part. Now when we look at the grid we see that 2 cells from the left part ( R6C6 and R7C6 ) protrude (Go Out ) into the right part and simultaneously 2 cells from the right part ( R1C5 and R8C5 ) protrude (Come In) to the left side. For this to be a normal solvable sudoku, contents of the 2 cells going out ( R6C6 and R7C6 ) have to be the same as the contents of the 2 cells ( R1C5 and R8C5 ) coming in.
now we have 2 possibilities for R6C6 and R7C6, viz, 5,8. Since 5 and 8 are the only options for R6C6 and R7C7, we can safely remove other possibilities from R1C5 and R8C5 and have only 5 and 8 there. once pencil marks updated we see that for Column 5, we have a hidden single 3 for R9C5. In Column 5, there is no place for number 3 except in R9C5.
Swordfish
Now I could have simply borrowed and copy pasted the explanation but believe me it would hav gone over our heads... So like before I will attempt to explain it using examples. Basically, Sqordfish is an extension of the X-Wing.
In X-Wing, we had only 2 row and columns for a particular given number. In Swordfish, This extends to more than 2 rows or columns. Let us take number 6 in this example. For Column 2, Column 5 and Column 9, the 6 can only appear in Row 3, Row 4 and Row 9. (circled cells) . Hence for these 3 rows, the number can only be in Column, 2, 5, and 9 and no where else. This leads to elimination of the number 6 in the highlighted yellow cells.
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