17. Some beavers and some kangaroos are standing in a circle. There are three beavers in total and no beaver is standing next to another beaver. Exactly three kangaroos stand next to another kangaroo. What is the number of kangaroos in the circle?
A 4
B 5
C 6
D 7
E 8
Solution
Any two beavers are separated by one or more kangaroos. If there were two, or more, separate groups of two, or more, kangaroos standing next to another kangaroo, there would be four, or more, kangaroos standing next to each other. Since the question tells us that there are exactly three kangaroos who stand next to another kangaroo, they are in a group of three and there are no more kangaroos standing next to another kangaroo.

Therefore, since there are three beavers in the circle and none of the beavers is next to another beaver, the arrangement of animals round the circle, starting with one of the beavers, is В К В К В ККК and hence there are exactly five kangaroos in the circle.