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 Making a Multiple of Four (Posted on 2014-04-30)
I want to make a multiple of four in a curious way: First I choose a random integer 1 to 4, each equally likely. If I get the '4', I stop immediately and that is my number. As long as I do not have a multiple of four, I continue to choose more random integers 1 to 4, keeping track of the running total. When the running total is a multiple of four, then I stop.

What is the expected number of random integers I need to get my multiple of four and what is the expected value of the running total?

Variation: The first random integer is the same, but the second and subsequent integers are equal to, one less, or one more than the previous integer. (If the previous random integer was 3, then I would choose one of 2, 3, or 4.)

In this case what is the expected number of integers needed and what is the expected total?

 No Solution Yet Submitted by Brian Smith No Rating

 Subject Author Date part 2 simulation Charlie 2014-04-30 14:38:53 re(2): Or maybe I'm simple (part I spoiler) Steve Herman 2014-04-30 14:13:33 re: Or maybe I'm simple (part I spoiler) Charlie 2014-04-30 12:42:26 Or maybe I'm simple (part I spoiler) Steve Herman 2014-04-30 11:55:13 Not so simple Steve Herman 2014-04-30 10:56:42 Part I Solution, Part II Question tomarken 2014-04-30 10:33:57

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