# Math 8_ October 1

Happy October!

On Oct. 1 we…

* Worked to determine relationships between polygons and triangles

*Worked toward discovering a formula for the sum of interior angles

*Discussed “why” the sum of interior angles of a triangle is always 180 degrees.

The homework from that day, due Oct 2 is: Sum of Interior Angles in a Polygon

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Anyone who can solve the riddle (prove with pictures) gets a prize! Bring the answer to my class!

Three mathematicians are applying for a job. There are five hats, three white, two black. They’re lined up, and a hat is placed on each. The first person in line cannot see any hat; the second in line sees only the hat of the person in front of him; the third person sees only the hats of the two people in front of her. The first person to correctly figure out what color hat he has gets the job; you guess wrong and you are killed. Assume these are INTELLIGENT mathematicians, and that they will do the logically correct thing at each stage — if something can be deduced, they will figure it out. After a long pause, the first person, who cannot see any hats, says he knows the color of his hat. What is the color, and how does he know?

Good luck!

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