Math Problems, Probability Problems

Problem of the Day: 1/20/13

If seven evenly matched competitors run a race, in how many ways can they place 1st, 2nd, and 3rd?

Solution to yesterday’s problem:

Let’s use an annotated version of the diagram:


Knowing that the side length of the total square is 2 ft, we can say that the segments to either side of the octagon’s sides are 0.5 ft each. This makes four triangles, each with a base and height of 0.5 feet. Expressing their combined area gives




The final answer is that there is 0.5 square feet left in the square.


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