16. A caterpillar starts from its hole and moves across the ground, turning $90^{\circ}$ either left or right after each hour. It moves $2 \mathrm{~m}$ in the first hour, followed by $3 \mathrm{~m}$ in the second hour and $4 \mathrm{~m}$ in the third hour and so on. What is the greatest distance it can be from its hole after seven hours?
A $35 \mathrm{~m}$
B $30 \mathrm{~m}$
C $25 \mathrm{~m}$
D $20 \mathrm{~m}$
E $15 \mathrm{~m}$
16. C The caterpillar will be as far away as possible from its hole if, at each turn, it always heads away from the hole. Hence its maximum distance will occur when it has travelled $(2+4+6+8)$ metres $=20$ metres in one direction and $(3+5+7)$ metres $=15$ metres in a perpendicular direction. Using Pythagoras' Theorem, the maximum distance in metres is then $\sqrt{20^{2}+15^{2}}=\sqrt{625}=25$.