It Can Take a While to Wander Home (Math Chat)
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http://www.maa.org/features/mathchat/mathchat_12_16_99.html  


Frank Morgan, MAA Online  
Solution to the challenge: How fast do you get home with a random walk on the line? in the plane? in threespace? in nspace? Eric Brahinsky reports that the median number of steps to get home is 24 on the line, about 32 in the plane, and infinite in higher dimensions. On the line, you have a 50 percent chance of retracing your first, departure step to return home in 2 steps, and a 50 percent chance of requiring 4 or more steps. (Of course the total number of steps home must be even.) New challenge: Justin Smith calls 5939 a "right" prime because it remains prime after dropping any number of digits from the right: 5939, 593, 59, and 5 are all prime. How many right primes are there less than 1000? Is there a largest right prime?  


Levels:  High School (912), College 
Languages:  English 
Resource Types:  Problems/Puzzles, Articles 
Math Topics:  Graph Theory 
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