2019 AMC 12B Problems/Problem 10

Problem

The figure below is a map showing $12$ cities and $17$ roads connecting certain pairs of cities. Paula wishes to travel along exactly $13$ of those roads, starting at city $A$ and ending at city $L$ , without traveling along any portion of a road more than once. (Paula is allowed to visit a city more than once.)

!! Someone with good Latex or Asymptote skills please help !!

How many different routes can Paula take?

$\textbf{(A) } 0 \qquad\textbf{(B) } 1 \qquad\textbf{(C) } 2 \qquad\textbf{(D) } 3 \qquad\textbf{(E) } 4$

Solution

Note the following route, which isn't that hard to discover:

!! Someone with good Latex/Asymptote skills please help !!

Look at the two square "loop"s. Each one can be oriented in one of two directions (lower left: either go down or left first; upper right: either go right or up first). Therefore, the answer is 1 route * 2 * 2 = $\boxed{\textbf{(E) } 4}$ . Note that no choice is larger than it.

2019 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 9	Followed by Problem 11
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All AMC 12 Problems and Solutions

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2019 AMC 12B Problems/Problem 10

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