Hard Question from UMD Math Competition 2014

There are three underground gopher nests in a field; call them A, B, C. There are tunnels between A and B, between A and C, and between B and C. A gopher counts that there are 89 ways to get from A to B and there are 82 ways to get from A to C. The gopher tries to count how many ways to get from B to C, but the number is greater than 99. Since the gopher cannot work with 3-digit numbers, it cannot count them. Help out the gopher and determine how many ways there are to get from B to C. (Note: A way to get from A to C is either a tunnel directly from A to C or a tunnel from A to B and then a tunnel from B to C. Similar definitions apply for ways to get from A to B and ways to get from B to C.)

a. 120
b. 171
c. 178
d. 302
e. 802

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