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Question:
what is the total number of ways to reach from A to B in the network given ?
book's answer = 4x2x2x1=16
my answer= 4 x (4x2)x (4x2) x (2x1)
why my answer is wrong ?
my logic: see. the 2,3 level has 4 nodes ..and each of them have 2 ways...so, i did 4x2
similary, the last level before the end point has 2 nodes and they have 1 way so, i did 2x1
why my answer is wrong ?...why the number of nodes are not taken into count in the book's answer ?
2006-07-22 17:35:03 · 3 answers · asked by sanko 1 in Science & Mathematics ➔ Mathematics
The book is right. You are looking for the number of distinct paths (at least one edge different) from A to B with the rule that you NEVER go along the same edge twice(no backtracking)!
Going from A to B takes 4 moves.
A to level 1: 4ways (to 4 nodes)
Each of these 4 nodes is connected to 2 nodes, so there are 4x2 = 8 ways to reach the 2nd level. The 4 nodes at level 2 are also connected to 2 more nodes (level 3). So there are 4x2x2 = 16 ways to reach the 2 nodes connected to B. But once these 2 nodes are reached there is only one way to point B, so the answer is 4x2x2x1 = 16. Note: there are 16 ways to reach the two nodes connected to B, but there are only 8 ways to reach each of these 2 nodes (16 total).
2006-07-22 18:02:29 · answer #1 · answered by Jimbo 5 · 4⤊ 0⤋
This is why questions like this really bug me. You're given a simple question "What is the total number of ways to reach from A to B in the network given?", and if you answer the question truthfully, it's an infinite number of ways, because you can start forming circles through the paths, and depending on how many times you take the circles, you can count forever. But, you will get the question wrong if you do that, and if you explain yourself, your teacher will call you a smart Alec and will still mark the question wrong.
Why should we assume that there isn't any backtracking or using the same line twice? Where does it say that? Why should we assume that? Who's making this stupid questions where you trap people into situations where they are benefited from using screwed up logic!!!
2006-07-23 03:12:01 · answer #2 · answered by Michael M 6 · 0⤊ 0⤋
you need to give us some more rules for this problem
I can count many more ways to get from A to B than either your answer or the books answer
do you have to always move directly toward B?
are you allowed to re-use a line segment?
etc
I think the key to this is in the specific rules
2006-07-23 00:52:05 · answer #3 · answered by enginerd 6 · 0⤊ 0⤋