The 9 colour Ball Sudoku Cube puzzle was already mentioned by Juanan in the marketplace section.

Since it can be considered to be a new puzzle (or at least a puzzle with new features), I am presenting some more background information about the puzzle here.

The Ball Sudoku Cube puzzle consists of 26 balls in 9 colours.

Attachment:

9 colour Ball Sudoku Cube.JPG [ 742.69 KiB | Viewed 2795 times ]
Given a situation of having maximum 3 balls of the same colour, there is a unique arrangement regarding the distribution of the colours over the centers, edges and corners of a 3x3x3 cube.

This unique arrangement is a follows:

- Colour number 1 has 2 corner balls

- Colour numbers 2-7 have 1 corner ball, 1 edge ball and 1 center ball

- Colour numbers 8 and 9 have 3 edge balls.

The reason for this unique arrangement can be explained as follows:

- There are 26 balls. Since each colour appears at maximum 3 times, there is 1 colour with 2 balls [colour number 1] and 8 colours with 3 balls

- Colour number 1 has to appear at 2 corners in diametrical positions since otherwise the 2 balls cannot cover all 6 planes

- The remaining corners have to be coloured differently [colours 2-7] since otherwise it would not be possible to position a 3rd ball of this colour

- Remaining then are 12 edge positions and 6 center positions for which we have 6 sets of 2 balls [colours 2-7] and 2 sets of 3 balls [colours 8-9]

- The colours 8 and 9 have to be at the edges since otherwise these 3 balls cannot cover 6 planes

- Colours 2-7 each occupy a corner (each covering 3 faces). So, per colour 3 faces still need to be covered which can only be realised by combinations of a center + an edge.

So, with maximum 3 balls per colour there is only one unique arrangement possible of distributing the colours over the centers, edges and corners.

Randomly trying to solve a 9 colour Ball Sudoku puzzle is probably difficult, but it becomes easier when considering the distribution of the colours over the corner, edge end center positions.

Basically, every ‘middle’ layer consists of 4 fixed center balls + the following 4 balls/colours:

- one of each of the 2 balls of the colours 8 and 9 (the colours that appear as sets of 3 edge balls)

- the colour that also appears in the center of the bottom layer

- the colour that also appears in the center of the top layer.

Assuming that the bottom layer is solved, a logical sequence of solving the edge balls in the middle layer is:

- positioning the edge ball having the same colour as the center ball of the top layer [only 1 position possible]

- positioning each of the 2 edge balls out of the 2 sets of 3 edge balls [colours 8 and 9, each time only 1 or 2 positions possible]

- positioning the edge ball having the same colour as the center ball of the bottom layer [remaining position].

This can all be achieved easily by using known sequences of e.g. the layer by layer method of solving a regular Rubik’s Cube.

The same goes for correctly positioning the remaining balls in the top layer.

There are some additional restrictions, meaning that the procedure above will not always lead to a solution.

On the other hand, there are several solutions possible.

One of the solutions, shown schematically below, is nicely symmetrical.

The colours 1-7 are listed, the colours 8 and 9 easily fit in the remaining open spaces.

Attachment:

9 colour Ball Sudoku Cube puzzle with symmetrical solution.jpg [ 27.72 KiB | Viewed 2795 times ]
The symmetry becomes visible when holding the two corner balls of the same colour [colour number 1] as north pole and south pole.

Between both poles 5 rings/levels can be observed:

Level 1: 3 edge balls

Level 2: 6 balls: 3 corner balls and 3 center balls

Level 3: 6 edge balls

Level 4: 6 balls: 3 corner balls and 3 center balls

Level 5: 3 edge balls

In this symmetrical solution level 1 and level 4 contain the same balls and the same goes for levels 2 and 5.

The balls in level 2 and 4 form a kind of circle around the poles.

Level 3 contains the 2 sets of 3 edge balls, forming a kind of equator with 2 alternating colours.

The puzzle is available for pre-order via Meffert’s and the Jade Club.

The final colours might deviate a bit from the initial sample shown.

Geert