Puzzler of the week

[Scott MacLean]

This week's puzzler:

This puzzler is from the wonderful world of mathematics. Ed and his two sons, Biff and Skip, have been hired to paint the floor of a merry-go-round. They want to make sure they measure the floor area exactly, because they don't want to buy any extra paint.

The carousel, of course, is a circle.

Here's the catch: In the middle of the carousel is a smaller circle, which contains all the machinery for the carousel. An annulus, in other words.

Ed tells Biff, "We need to know the area of the carousel, including the area of the big outer circle that we're going to paint and the area of the inner circle where there's nothing but the machinery.

"Once we have the areas of both circles we can subtract the inner circle from the other circle and we'll know how much paint we need."

Biff goes to the carousel and says to himself, "I can't do this. All the machinery is in the middle. I can't get to the center to measure the diameter." He thinks, "I'll cheat. The old man will never know!" Biff measures a straight line from one edge of the carousel to the other edge, not going through the center.  In other words he's going to make what's called a chord of the big circle.

Any line that goes from one edge of the circle to the other that isn't a diameter is a chord. As luck would have it, the tape measure touches the inner circle, or in geometric terms, is tangent to the inner circle at one point.

Biff returns to his dad and says, "I couldn't do what you wanted me to do. I got this measurement and it's 70 feet." The old man administers a swift dope slap. He says, "How the heck are we going to figure this out. We don't know either diameter."

The other brother Skip says "I think I can figure it out. "

Can he or can't he?


Last week's puzzler:

I was on a holiday recently and my car was in need of petrol.

I was on a secondary road, and I turned into a self-service gas station. I pulled up to one of the minipumps, and absentmindedly reached for the nozzle.

I was just about to fill up my tank, when I happened to notice that the gasoline was a little expensive.

In fact, it was $4.59 a gallon. I said, "Whoa. What kind of vehicle uses this stuff?"

I looked around. There was a vehicle on the lift and I knew immediately why this gasoline was $4.59 a gallon.

Here's the question: What did I see?

The answer:

What I saw on the lift was a car that had numbers on it... a racecar.

Its doors were welded shut, and it had no glass. It was in fact a racecar. And this guy must have been the local gas station where all the racecar drivers -- there must have been a track nearby -- came to get their gas. This gas was 110 octane.


_______________________
Scott MacLean
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http://www.nerosoft.com