原创 Three puzzles to ponder

I've been thinking of a few puzzles that I'd like to share. Let's start with a bit of an "old chestnut" just to get our brains oiled up and ready for action...

Puzzle #1: OK, suppose you have a planet that's 20km in diameter. Let's assume that this planet is perfectly spherical. In fact let's assume that it's made out of stainless steel and has been polished like a mirror (hey, it's our planet, we can assume what we like).

Now, suppose we have a very large ball of red string and we loop it all around our planet's equator. Now suppose we have a large ball of green string and we loop this around the equator also, but this time we use lots and lots of wooden sticks to keep the green string exactly one meter above the ground.

So, how much longer will the green string be compared to the red string?

Puzzle #2:  Have you heard that Car Talk program on National Public Radio (NPR). It's hosted by two brothers called Frick and Frack (I have no idea if these are their real names) and it's a lot of fun. Anyway, I was listening to the show a couple of weekends ago whilst driving around and they posed an interesting problem that was submitted by the owner of a big tractor-trailer.

It seems that the fuel gauge on this guy's tractor-trailer is broken, so he has been reduced to using a stick to see how much fuel he has left in his tank. Purely for the sake of this discussion, let's assume that his tank is 1m long and 50 cm in diameter as reflected in the illustration below.

So if he makes a mark on the stick 50 cm from the bottom, then this would represent a full tank. And if he makes a mark on the stick 25 cm up from the bottom then this would represent 1/2 a tank. So what he is asking is where he should put the marks corresponding to 1/4 and 3/4 of a tank.

Puzzle #3: Have you seen the four-part mini-series of television programs called Aftermath. The idea is that they postulate something happening like the population of the world doubling overnight or all of the oil that's still in the ground suddenly disappearing ... and then they consider what would happen.

One of these programs was titled Aftermath: When the Earth Stops Spinning. The idea is to consider what would happen if the world suddenly started to slow down its spinning over the course of five years. I saw thsi program on TV and it was very interesting. Anyway, this set me to thinking...

Let's assume that the circumference of the world is exactly 24,000 miles at the equator. We know that the earth spins round once every 24 hours, so at the equator this is 24,000 miles in 24 hours, which equates to 1,000 miles per hour.

The point is that, if you are standing at the equator, the spin of the world is sort of trying to throw you off (if you see what I mean). So, assuming that someone has a mass of exactly 100kg if we were to weigh him at the North or South Pole – and also that our guy has access to a really sensitive and accurate weighing scale, what would the reading on the weighing scale be if our subject was standing on it at the equator?