25. The diagram shows a trapezium made from three equilateral triangles. Three copies of the trapezium are placed together, without gaps or overlaps and so that complete edges coincide, to form a polygon with $N$ sides.
How many different values of $N$ are possible?

A 4
B 5
C 6
D 7
E 8
Solution: $\mathbf{C}$
The three trapeziums have 12 edges in total. Whenever two of them are joined together, the total number of edges is reduced by at least 2 . So the maximum possible value of $N$ is $12-2 \times 2=8$. The minimum number of sides for a polygon is 3 . So there are just 6 values for $N$, namely 3,4 , $5,6,7$ and 8 , that could possibly occur. The diagrams below show that they all can be achieved.