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Finding Paths

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Finding Paths

by wilderness » Fri Jul 18, 2008 1:38 pm
Hi,

Does anyone have any general formula how to attack a problem like this. I solved it by counting each of the possible shortest ways. But of course if there had been 10 streets and 20 avenues my method would not be useful. I have a feeling that it has got something to do with combinations but I have no further idea. What do you think


The right answer is 10.
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Re: Finding Paths

by parallel_chase » Fri Jul 18, 2008 3:16 pm
wilderness wrote:Hi,

Does anyone have any general formula how to attack a problem like this. I solved it by counting each of the possible shortest ways. But of course if there had been 10 streets and 20 avenues my method would not be useful. I have a feeling that it has got something to do with combinations but I have no further idea. What do you think


The right answer is 10.

No matter which route X take to get to Y, X will have to cross 2 avenues and 3 streets.

No. of ways X can take to get to Y = 5!
No. of ways X can cross avenues = 2!
No. of ways X can cross streets = 3!

Therefore 5! / (2! 3!) => 10
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Re: Finding Paths

by asigheartau » Fri Jul 18, 2008 7:56 pm
parallel_chase wrote:
wilderness wrote:
No. of ways X can take to get to Y = 5!

How do you determine that?
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by Ian Stewart » Sat Jul 19, 2008 12:14 am
See solution here:

www.beatthegmat.com/og-195-197-unsolved ... 12321.html

Yes, it can be solved for any size of grid.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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