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Twin Line-swapping Sudoku

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2
By Henry Kwok

Twin A Twin B
Twin A Twin B

Here is a Word document with the Twin Sudoku that you can download.

Rules of Twin Line-swapping Sudoku

This Sudoku variant consists of a pair of linked standard Sudoku puzzles each with some starting digits.

As usual, the object of this Sudoku variant is to fill in the whole of each 9x9 grid with digits 1 through 9 so that each row, each column and each block contain all the digits 1 through 9.

Twin B is related to twin A in the following ways:
Given that twin A is the original puzzle, twin B is obtained by swapping the rows/columns within a chute/band of blocks. By such transformation, twin A and twin B are essentially the same Sudoku puzzle.

For example, figure 2 is obtained from figure 1 below by: swapping row 1 and row 3 within the top horizontal chute/band of blocks, swapping row 5 and row 6 within the middle horizontal chute/band of blocks, swapping row 7 and row 8 within the bottom horizontal chute/band of blocks.
figure 1 figure 2 figure 3
figure 1 figure 2 figure 3

Similarly an equivalent puzzle (figure 3) can be obtained from figure 1 by: swapping column 1 and column 3 within the left vertical chute/band of blocks, swapping column 5 and column 6 within the middle vertical chute/band of blocks, swapping column 7 and column 8 within the right vertical chute/band of blocks.

The three puzzles are equivalent to one another. Equivalent puzzles can also be created from figure 2 and figure 3 by similar transformations.