Two Towns (chpt.2)
Turns out, there are lots of different ways you can take from Arrowfront to Boulderfort.
If you start at Arrowfront (i.e. point A), you can drive along the edges of the pathway shown above. However, you can only drive along the same edge once . Despite that, you may pass through the same point more than once .
Also, once you reach Boulderfort (i.e Point B) for the first time, you will need to stop immediately and enter the town.
How many different routes can you take?
The answer is 27.
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1 solution
The total number of routes you can take from Point A to Point B is:
(The number of ways from point A to the center point) x (The number of ways from center point to point B)
Now we consider 2 things. We call the center point C.
1. The number of ways from point A to C
This is equal to 9, since there are 3 direct ways from point A to C and 6 other ways from point A to C, which passes through point C twice.
2. The number of ways from point C to B
There are only 3 ways, since the question states that you must stop immediately once you've reach point B.
Therefore the answer is 3 x 9 = 27.