The puzzle is as follows:
Assume that you have three coins over a rectangular table as it is indicated in the picture from below. These three coins are identical in diameter which is 3 cm and tangent to each other. Suddenly a fourth coin coin equal to the previous ones in size and shape is made to roll tangentially around the others without sliding until reaching its original position. How many turns did this coin made?
The given choices are:
- 3 turns
- 4 turns
- 1 turn
- 2 turns
This puzzle comes from a late 1970s APA IQ test timed cards adapted from Leon Thurstone and Catell's on psychometric measure.
I'm not sure if the question itself is okay or not. As the size of the table is given but I didn't use it.
What I tried to do was to calculate the length around those three coins and I concluded that it is $3\times 1.5 \pi$.
The number of turns given by that fourth coin would be:
$3\times 1.5 \pi\,cm\times\frac{1\,\textrm{turn}}{2\pi\times 1.5\,cm}$
This gives me:
1.5 turns. But it doesn't appear in any of the choices. What could be wrong here? Perhaps the size of the table contributes to the solution?
It would be helpful if answers included a drawing to spot which part I'm missing, because the more I look into this I can't find where I got it wrong.