PK 2018 Q9
9. Monika plans to travel across the network in the diagram from point \(P\) to point \(Q\), travelling only in the direction of the arrows. How many different routes are possible?
- A 20
- B 16
- C 12
- D 9
- E 6
Pink Kangaroo 2018, Question 9. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 16
Label the vertices \(R\), \(S\), \(T\) as shown. There are four ways to get from \(P\) to \(T\): \(PT\), \(PRT\), \(PST\) and \(PSRT\). Similarly there are four ways to get from \(T\) to \(Q\), so \(4 \times 4 = 16\) ways to get from \(P\) to \(Q\).
Solution © UK Mathematics Trust, from the PK 2018 solutions.