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Happy PI Day Problems

2012 Problem:

You have three pies of diameter 9 inches. Without cutting any of the pies a brilliant genie places two of the pies on a circular table, such that the center of mass of each pie is directly over the table. The genie agrees to grant your wish if you can place the third uncut pie ENTIRELY on the table such that it does not overlap with either of the first two pies. How big must the table’s diameter be, such that you are guaranteed to be able to earn your wish?

2011 Problem:

As Gabby was both doing math problems and making a pi-day pie last night, she dropped her pencil onto the pie. Her pie is a perfect circle and her pencil is the same length as the radius of the pie. Assuming the pencil is lying flat on top of the pie and that the center of the pencil is over the pie itself (otherwise it wouldn't balance!), what is the probability that part of the pencil extends beyond the edge of the pie?
(Express your answer in terms of π!)

I think this one is harder than last year's problem, but it can be done without any real calculus, although a calculus concept is sort of required...

2010 Problem: If you randomly slice a perfectly circular pie 3 times, each slice along a diameter, thus making 6 pieces of pie that meet at the center, what is the probability that at least 1 piece of the pie is greater than one quarter of the entire pie? Hint: The answer is not 1/2 and it can be done without calculus, but calculus may make it easier.. Contact me if you want to check your answers.	My Halloween 2009 Pumpkin

©2011 Susa H. Stonedahl