Official Guide Explanation:
Problem Solving #135




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Solution and Metadata

Question: 135
Page: 171
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Counting Methods > Permutations
Category 2: Word Problems > Geometry Problems >

Explanation: This is a complicated problem with a simple solution. There are three different places in which the mouse must make a decision. At the second point to the right of X, the mouse can take the higher or lower path, giving it two options. At the second decision point (the beginning of the middle quadrilateral), the mouse again has two options. At the third decision point (the left side of the quadrilateral with the line through it), the mouse can take any of three paths. From this point, it's a permutation problem. To find the total number of possible routes, multiply the number of options at each point: 2 * 2 * 3 = 12, choice (C).

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