Twin Equivalent Sudoku

'Twin Equivalent Sudoku' printed from https://nrich.maths.org/

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By Henry Kwok

Twin A	Twin B

Here is a Word document with the two Sudoko grids that you can download for printing.

Rules of Twin Equivalent Sudoku

This Sudoku consists of a pair of linked standard Sudoku puzzles each with some starting digits. As usual, the object of this Sudoku 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:

1. Given that twin A is the original puzzle, we can create an equivalent puzzle from twin A by swapping a horizontal/vertical chute or band of 3 blocks with another horizontal/vertical chute or band of 3 blocks.

For example, an equivalent puzzle (fig 2) is created from fig 1 by swapping the left vertical chute of 3 blocks with the middle vertical chute of 3 blocks.

Similarly an equivalent puzzle (fig 3) can be created from fig 1 by swapping the top horizontal chute of 3 blocks with the middle horizontal chute of 3 blocks.

2. After swapping the chutes, we can create a third equivalent puzzle (twin B) by renaming all the elements of second equivalent puzzle.

For example, we create an equivalent puzzle (fig 4) by renaming the elements of fig 3 in the following way:

fig 3 $\rightarrow $ fig 4

$1 \rightarrow7 $

$ 2 \rightarrow 6 $

$ 3\rightarrow 1 $

$4 \rightarrow 9 $

$ 5 \rightarrow 3 $

$6 \rightarrow 2 $

$7 \rightarrow 8 $

$8 \rightarrow 5 $

$9 \rightarrow 4$

The four puzzles (fig 1 to fig 4) are equivalent to one another. Equivalent puzzles can also be created from fig 1 and fig 2 by renaming the elements in the respective grids. Instead of calling fig 1 and fig 4 by the clumsy name of 'twin element-renaming chute-swapping sudoku', we can simply call them 'twin equivalent sudoku'.