It Can Take a While to Wander Home (Math Chat)
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|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 three-space? in n-space? Eric Brahinsky reports that the median number of steps to get home is 2-4 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 (9-12), College|
|Resource Types:||Problems/Puzzles, Articles|
|Math Topics:||Graph Theory|
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