### 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.