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Introducing the Cuboku

Can you solve our 3D Sudoku puzzles?

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Here at Chalkdust HQ, we love inventing ways to make Sudoku-style puzzles more interesting. This week, I will be sharing some 3D puzzles, which I call Cuboku.

To build a Cuboku, start with a small Sudoku made of four 2×2 squares as opposed to nine 3×3 squares. To make the visualisation in 3D easier, I will be using four different colours (red, green, blue, yellow) instead of numbers. The usual rules apply: you cannot put the same colour twice in any of the vertical or the horizontal lines or in any of the four 2×2 squares. A completed Sudoku may look like this:

First Layer Cuboku

Now, you only have to pile up four of these Sudoku to obtain a cube — except that the slices along each axis also have to satisfy the rules of Sudoku! So you now have to solve 12 (4×3) Sudoku! A completed Cuboku may look like this:
CubokuBanner

12 Sudoku are formed (the transparent cube has been added to demonstrate how the different slices relate to each other):

Four seen from the front,...

Four seen from the front,…

Lateral Cuboku

…four from the side…

Vertical Cuboku

…and four from the top.

Now for the puzzles:

The First Puzzle

Now that we are all set up with the rules and how to play this fabulous game, let’s start with
the first puzzle: complete the rest of the Cuboku.

CubokuPuzzle

The Second Puzzle

Fill the rest of this cuboku.

SecondPuzzle

Now that you have a little practice solving Cuboku, here’s two more challenging puzzles:

It’s All About the Corners!

If the vertices of the cube are coloured as below, how many ways are there to complete the rest of the Cuboku?
CubokuCorners

Cuboku Counts!

If you begin with the following cubes, how many ways are there to complete the Cuboku?
CubokuCounts

Rafael Prieto Curiel is the Editorial Director of Chalkdust. He is doing a PhD in Mathematics and Crime and he is interested in mathematical modelling of any social issues, such as road accidents, migration, crime, fear and gossips.
Twitter  @rafaelprietoc   Website  rafaelprietocuriel.wordpress.com    + More articles by Rafael

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