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How many ways can a round trip be done if the return trip must differ by at least 1 road?

find_the_fun

Active member
Feb 1, 2012
166
I don't understand the answer for part c of the following question

question.png

The answer key gives 14x13 as the solution to part c. I understand there are 14 ways to get to point C but depending on which road can no longer be used, there is anywhere between 10 and 13 ways to return home. For example, say R8 was taken to get to C. Then there are 14-1 ways to make the return trip (just don't use R8). However, if R1R5 is used then we can't use either R1 (so now there are 3x3+2=11 ways to make the trip) or R5 (so now there are 2x4+2=10 ways to make the trip). What is wrong with my reasoning?
 

Evgeny.Makarov

Well-known member
MHB Math Scholar
Jan 30, 2012
2,502
As I understand the problem statement in c), if Linda takes R1R5 to get from A to C, there is a single trip she is not allowed to take back: R5R1. All other trips are allowed.