GK 2017 Q18
18. Ten kangaroos stood in a line as shown in the diagram.
At a particular moment, two kangaroos standing nose-to-nose exchanged places by jumping past each other. Each of the two kangaroos involved in an exchange continued to face the same way as it did before the exchange. This was repeated until no further exchanges were possible. How many exchanges were made?
- A 15
- B 16
- C 18
- D 20
- E 21
Grey Kangaroo 2017, Question 18. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 18
Label the kangaroos facing right as K1, K2, K3, K4, K5 and K6 as shown in the diagram.
No further exchanges will be possible only when the kangaroos facing right have moved past all the kangaroos facing left. Kangaroos K1, K2 and K3 each have four left-facing kangaroos to move past while kangaroos K4, K5 and K6 each have two left-facing kangaroos to move past. Hence there will be (3 × 4 + 3 × 2) = 18 exchanges made before no further exchanges are possible.
Solution © UK Mathematics Trust, from the GK 2017 solutions.