The very quick solution that Sarah found satisfied her a lot. She used some bits of coloured papers, and used the four doubles across the top to start off.

She noticed how each of the four corner arrangements of four contained one of each colour for both the cups and the saucers. She also had managed to achieve differences throughout the diagonals as well, although that was not asked for.

This led me to look more closely:-

Here I copied Sarahs top left hand corner four, but I slightly changed the top right hand four saucers so that the clockwise order of saucers [ white, blue, red & green] should remain the same, and the arrangement was just a rotation of 180'. The bottom left hand four then turned out to be a flip [along the y axis] from the top left hand four. The bottom right hand then came from either rotating the bottom left hand four OR flipping the top right hand four . These were the saucers sorted out and the cups worked in a similar way but with the transformations swopped over, as shown in the diagramme.

Many youngsters have produced a result like this :-

Here the diagonals are of one saucer colour each. It is a good solution to look at as it has some interesting patterns in it.

When I want to create a solution and I may have forgotten one then I work on it in the following way:-

I place the four "doubles" in a square to be the middle [diag 1]. East and west of the top two must be red/blue and blue/red so I have a 50% chance of being correct [diag 2]. East and west of the lower pair must be white/green and green/white, [diag 3]. I then do the northand south of the left two of the original square and these must be blue/green and green/blue, [diag 4]. Similarly [diag 5] for the right hand side. This leaves just the four corners and that's very easy [diag 6].

Many youngsters have gone on to have a look at different numbers of cups and saucers.

Some new patterns can be seen when you look at these arrangements that have an odd number of sets of coloured cups and saucers.