25. For Beatrix's latest art installation, she has fixed a $2 \times 2$ square sheet of steel to a wall. She has two $1 \times 2$ magnetic tiles, both of which she attaches to the steel sheet, in any orientation, so that none of the sheet is visible and the line separating the two tiles cannot be seen. As shown alongside, one tile has one black cell and one grey cell; the other tile has one black cell and one spotted cell.
How many different looking $2 \times 2$ installations can Beatrix obtain?

A 4
B 8
C 12
D 14
E 24
Solution: $\mathbf{C}$
In the $2 \times 2$ square sheet, there are 4 positions in which Beatrix could place the spotted cell. For each position of the spotted cell, there remain 3 positions where she could place the grey cell. Once she has placed these, she has no choice for the two black cells. Hence there are $4 \times 3=12$ possible installations. It can be checked that Beatrix can make each of these installations by positioning the two tiles appropriately. [She can create each of the installations in which the black squares occupy the diagonal positions in two ways, and all the other installations in just one way.] So Beatrix can create 12 differently looking installations.