# Introducing the Cuboku

Can you solve our 3D Sudoku puzzles?

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:

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:

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 from the side…

…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.

### The Second Puzzle

Fill the rest of this cuboku.

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?

### Cuboku Counts!

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

Rafael Prieto Curiel is doing a PhD in mathematics and crime. He is interested in mathematical modelling of any social issues, such as road accidents, migration, crime, fear and gossip.

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