Twin Equivalent Sudoku

This Sudoku problem consists of a pair of linked standard Suduko puzzles each with some starting digits
Age
16 to 18
Challenge level
filled star empty star empty star
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



By Henry Kwok

Twin A Twin B
Twin Equivalent Sudoku
Twin Equivalent Sudoku
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.
Twin Equivalent Sudoku
Twin Equivalent Sudoku
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.
Twin Equivalent Sudoku


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 $


$9 \rightarrow 4$
Twin Equivalent Sudoku
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'.