This riddle is (at least for me) very hard to imagine...

You have an appliance like this:

There are two cogwheels in a box. The bigger one has 24 teeth and it is tightly attached to the center of the box (it doesn’t turn or move). The smaller one has 8 teeth and it rotates around the bigger wheel. How many times does the smaller wheel turn compared with the box when it turns once around the bigger wheel?



Three times is wrong but ratio between numbers of teeth is important.

Two tightly attached wheels is something different from one wheel rotating around the other.



The smaller wheel turns around 4 times.

Imagine the two wheels turning next to each other. While bigger wheel turns once (24 teeth) small one turns three times (3 x 8 teeth) to the other side.

Now we want the big wheel to stop and the small wheel to turn around the big one. There it makes one additional turn on the way around the big wheel. If you can’t imagine that you can try with two coins. If you hold one and roll the other around the first one it doesn’t turn once but two times.

Still didn’t get it? Disassemble some clockwork and try it.