Solution: Thanksgiving Spread

I'm planning on having lots of family over for Thanksgiving this year and want to serve a delicious and attractive spread. I've got an bow tie shaped table like in the figure below that I want to fill with six platters. The table is 24 feet long, 11 feet at the widest and 1 foot at the narrowest, right in the middle. I'd like to garnish the edges of the platters with some trim, how much trim do I need? In other words, what is the total circumference of the six circles in the diagram below?

Answer: I think this most people thought this one was hard, or else they just had too much turkey on Thankgiving and forgot to turn in a solution. The key point is that you do not need to figure out the individual radii of the circles! That would be hard. Just call the diameters d1, d2, d3, d4, d5 and d6 and observe that d1 + d2 + d3 + d4 + d+ d6 = 24. Now since the formula for the circumference of a circle of diameter d is πd, we have that the total circumference is:

πd1 + πd2 + πd3 + πd4 + πdπd6 = π(d1 + d2 + d3 + d4 + d+ d6) =   24π  

Correct Solutions: Nathaniel Blake