Library / UKMT Grey Kangaroo /104 of 242

UKMT Grey Kangaroo, 2017

Combinatorics Difficulty 2.0 Junior Find the answer United Kingdom

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) $21$

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