# Twin chute-swapping Sudoku

A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?

## Problem

By Henry Kwok

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:

Given that twin A is the original puzzle, twin B is obtained by swapping a horizontal/vertical chute or band of blocks with another horizontal/vertical chute or band of blocks. By such transformation, twin A and twin B are essentially the same or equivalent Sudoku puzzle.

For example, fig 2 is created from fig 1 by shifting the first chute of 3 blocks sideways to the right and the second chute of 3 blocks sideways to the left.

Similarly an equivalent puzzle (fig 3) can be created from fig 1 by shifting the first chute of 3 blocks downwards and the second chute of 3 blocks upwards.

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

### Twin A

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### Twin B

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#### Rules of Twin Chute-Swapping Sudokus

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:

Given that twin A is the original puzzle, twin B is obtained by swapping a horizontal/vertical chute or band of blocks with another horizontal/vertical chute or band of blocks. By such transformation, twin A and twin B are essentially the same or equivalent Sudoku puzzle.

For example, fig 2 is created from fig 1 by shifting the first chute of 3 blocks sideways to the right and the second chute of 3 blocks sideways to the left.

Image

Image

Similarly an equivalent puzzle (fig 3) can be created from fig 1 by shifting the first chute of 3 blocks downwards and the second chute of 3 blocks upwards.

Image

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

## Student Solutions

Twin A solution

Twin B solution

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Twin B solution

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