gmatt1476 wrote:
The map above shows the trails through a wilderness area. If travel is in the direction of the arrows, how many routes along the marked trails are possible from point A to point B ?
A. 11
B. 18
C. 54
D. 108
E. 432
PS24831.01
Attachment:
2019-09-21_1417.png
We see that the diagram has a horizontal line symmetry (if we draw a horizontal line through A and B). Therefore, if we find the number of routes from A to B in the upper half of the diagram, we can just multiply that by 2 to obtain the total number of routes from A to B in the entire diagram.
In the upper half of the diagram, counting each point starting from A and ending at B, we have 1, 3, 3, 3 and 1 routes between each pair of consecutive points, therefore, the number of routes is 1 x 3 x 3 x 3 x 1 = 27. Multiplying this by 2, we have a total of 54 routes from A to B.
Answer: C
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