3 Coin Rotation Problem
- Author:
- Brad Ballinger
- Topic:
- Rotation
Suppose three coins are lined up, touching each other.
We hold one of the end coins still.
We rotate the middle coin around the fixed coin, without slippage.
We keep the third coin in contact with the second, so it too turns without slippage.
If the turning coins go once around and end up in their original positions, how many times do they rotate?
The classic version of this puzzle uses only two coins.
The answer in both versions depends on the relative sizes of the coins.
Version 1
Suggestion: Don't touch the diagram below until you've thought about the problem a little.
I've tried to limit the diagram so that it can't quite show you the answer, but even so, I was very surprised by what it showed me.
If I was a little less scrupulous, I might modify this to make a rotation version of an area rearrangement puzzle.
Version 2
In this version, use sliders a, b, and c to set each circle's circumference.
Slider n sets the number of color bands that each circle is divided into.
If you're just getting started, my advice is to set a, b, and c how you like them and then either leave n at 1 or the maximum value on its slider, whichever you prefer.
Other values of n might cause problems. Checking the "override color guard" box makes these problems more likely. Can you explain the glitch?