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# Rolling a coin

## Question

We have two identical coins. And we roll the one on the left halfway around the other coin, so it rotates without slipping against the other coin, so that it ends up on the right of the other coin. It has rolled over a length of only half its circumference, and yet it has made one complete rotation. Which way is the head of the coin facing?

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No need to spoiler.

If it has made a complete revolution, (and it has) it's facing the same "way" after as before.

Maybe I'm missing something.

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No need to spoiler.

If it has made a complete revolution, (and it has) it's facing the same "way" after as before.

Maybe I'm missing something.

I think you have to determine what the coins are to determine which way the head is facing. If the rotating coin were a US cent, then the head faces to the viewer's right. Nearly all other US coins (except for very recent mintings) have heads that face to the viewer's left. I suppose that you have to use the circumferences of the coins to find out which pair would satisfy the other conditions of the OP.

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No need to spoiler.

If it has made a complete revolution, (and it has) it's facing the same "way" after as before.

Maybe I'm missing something.

I think you have to determine what the coins are to determine which way the head is facing. If the rotating coin were a US cent, then the head faces to the viewer's right. Nearly all other US coins (except for very recent mintings) have heads that face to the viewer's left. I suppose that you have to use the circumferences of the coins to find out which pair would satisfy the other conditions of the OP.

I guess that's what was meant. I just pointed out that after a complete revolution the facing "way" is unchanged.

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oops I accidentally included the answer in my question . Often when people think of this problem without actually trying it they believe that the coin only rotates halfway or 3/4's of the way and don't realize that the coin makes a complete rotation. My mistake guys.

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