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UKMT Junior Kangaroo, 2016

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

The diagram shows part of a river which has two islands in it. There are six bridges linking the islands and the two banks as shown. Leonhard goes for a walk every day in which he walks over each bridge exactly once. He always starts at point $A$ , goes first over bridge 1 and always finishes at point $B$ . What is the maximum number of days that he can walk without repeating the order in which he crosses the bridges?

(A) $2$ (B) $4$ (C) $5$ (D) $6$ (E) More than $6$

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