BMAT 2009 · Question 29 · Spatial
SaveA particular company manufactures square floor tiles whose patterns consist of 16 smaller squares of equal size. Two of the smaller square on each tile are black, whilst the rest are white. When I opened a packet of 12 of these tiles this morning and laid them out as shown below, I thought that they were all different.

On closer inspection, however, I realised that rotation of the relevant tiles would reveal that some are identical to at least one of the others. How many different patterns are there in my packet of 12 tiles?