8. A mob of 2015 kangaroos contains only red and grey kangaroos. One grey kangaroo is taller than exactly one red kangaroo, one grey kangaroo is taller than exactly three red kangaroos, one grey kangaroo is taller than exactly five red kangaroos and so on with each successive grey kangaroo being taller than exactly two more red kangaroos than the previous grey kangaroo. The final grey kangaroo is taller than all the red kangaroos. How many grey kangaroos are in the mob?
8. 672 The first grey kangaroo has only one red kangaroo smaller than itself. Apart from that, each grey kangaroo can be grouped with two red kangaroos whose heights lie between its height and that of the previous grey kangaroo. The number of such groups is $(2015-2) / 3=671$. Hence there are 672 grey kangaroos in the mob.