Answer: 48 paving slabs make up the path
The winner is Peter Smith of Cropston, Leicester, UK. There were 80 entries.
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Worked answer
It is first necessary to determine the number of unique patterns of 3 colours (which we will call 1, 2 and 3).
A large number of patterns can be eliminated by listing the 鈥渃olours鈥� in numerical order.
As the list progresses, it becomes reasonably obvious if a pattern is being repeated (see diagram, top-right)
In designing his path, Joe made 24 cards with the colour patterns listed above. He then placed them in a rectangle so that where cards touched the colours matched.
There are several rectangles that can be made with the 24 cards, and there are many ways the complete rectangle can be produced.
Joe then overlapped the cards to produce the final arrangement of 48 paving slabs.