3. Nico is learning to drive. He knows how to turn right but has not yet learned how to turn left. What is the smallest number of right turns he could make to travel from $\mathrm{P}$ to $\mathrm{Q}$, moving first in the direction shown?
A 3
B 4
C 6
D 8
E 10
Solution
B

Since Nico can only turn right, he cannot approach $\mathrm{Q}$ from the right as to do so would require a left turn. Therefore he must approach $\mathrm{Q}$ from below on the diagram. Hence he will be facing in the same direction as he originally faced. As he can only turn right, he must make a minimum of four right turns to end up facing in the same direction as he started. The route indicated on the diagram below shows that he can reach Q making four right turns. Hence the smallest number of right turns he could make is four.