I'm posting one puzzle, riddle, math, or statistical problem a day. Try to answer each one and post your answers in the comments section. I'll post the answer the next day. Even if you have the same answer as someone else, feel free to put up your answer, too!

Saturday, October 22, 2005

Consider two round coins of equal size. Imagine holding one still so that it does not move and then rolling the other coin around it, making sure that it does not slip. The rims are kept touching at all times. How many times will the moving coin have rotated after it has completed one revolution of the stationary coin? Don't try it until you have thought about it. You may be surprised.

What it comes down to, is the circumference of the second coin as it circles around the first coin.

Definitions: First coins sits still. Second Coin circles the first.

Let's say you place the second coin above the first. Make sure the coin is heads up. Start rotating. When the second coin reaches the bottom of the first, it is once again heads up.

But if you look at it closely, the second coin started out by touching the first coin at it's bottom. When it reaches the bottom of the first coin, it is touching the first coin at it's top! So it has only rotated half-way. But since you are an outside observer (this is where it gets complicated by relativity), you see it as having rotated once, because of where you are observing it from.

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Once.

ReplyDeleteMost people believe that the answer will be once and are therefore surprised to discover that the truth is in fact twice. Try it and you will see.

ReplyDeleteI tried it out and it is twice, but WHY? Can you explain the theory behind it? Enviroman Says

ReplyDeleteSupport Enviroman

What it comes down to, is the circumference of the second coin as it circles around the first coin.

ReplyDeleteDefinitions: First coins sits still. Second Coin circles the first.

Let's say you place the second coin above the first. Make sure the coin is heads up. Start rotating. When the second coin reaches the bottom of the first, it is once again heads up.

But if you look at it closely, the second coin started out by touching the first coin at it's bottom. When it reaches the bottom of the first coin, it is touching the first coin at it's top! So it has only rotated half-way. But since you are an outside observer (this is where it gets complicated by relativity), you see it as having rotated once, because of where you are observing it from.