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February 13th, 2010, 04:39 AM   #1
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fair coin tossing, and choosing directions.

I was reading up some introductory discrete probability to use in analyzing randomized algorithms, and I was trying to solve this problem, but couldn't quite nail it.

Your city is planned in the form of an infinite grid of crossings. You start from your house, and walk aimlessly. You have a fair coin with you, which you toss to find out which direction to go. You can't turn and walk back, so at each junction you have three choices of direction(front, left, right). Describe a method(give an experiment involving coin tossing) which would let you choose each direction with an equal probability of 1/3.

My idea is to toss the coin twice, and decide as follows : if you get 2 heads go left, if a tail and a head, then go straight, if a head and a tail, then go right(the order in which you get head and tail matters). If you get two tails, then toss again.

Can someone tell me if this is right?(Is there a better solution?) Or any other ideas about how to approach this problem?

Thanks in advance!
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February 13th, 2010, 12:23 PM   #2
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Re: fair coin tossing, and choosing directions.

Quote:
Originally Posted by thehaltingproblem
Can someone tell me if this is right?(Is there a better solution?) Or any other ideas about how to approach this problem?
Yes, it's right. I would consider it the best answer, though depending on how you measure it there could be others just as good or better.
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February 14th, 2010, 04:30 AM   #3
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Re: fair coin tossing, and choosing directions.

Thanks! I'm post a better solution/analysis if I find one.
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February 14th, 2010, 04:31 AM   #4
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Re: fair coin tossing, and choosing directions.

Thanks! I'll post a better solution/analysis if I find one. (sorry for the typo in the last post!)
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February 14th, 2010, 01:20 PM   #5
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Re: fair coin tossing, and choosing directions.

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Originally Posted by thehaltingproblem
Thanks! I'll post a better solution/analysis if I find one. (sorry for the typo in the last post!)
You don't have to repeat the post. Just click on the "edit" of your post and you can correct what you had already posted.
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