🚀 go-pugleaf

In article <C1IyDB.2K5@fastrac.llnl.gov> dan@danberg.llnl.gov (Dan Bergmann) writes:
>Two circles are next to each other and touching at one point (one is NOT
>inside the other). The larger circle has twice the radius of the smaller
>circle. The smaller circle rolls around the large one until it comes back
>to its original starting position. How many revolutions does it make about
>its center?

I've certainly heard this before, and it seems to me it ought to be in
the rec.puzzles archive (I couldn't find it either).

SPOILER ahead...



The answer is 3.

The way I look at it is as you roll the circle around the larger one,
turn your head at the same time so that the small circle always appears
on top.  Suppose the small circle was supposed to roll counterclockwise
around the larger one.  Then what you will see instead is one clockwise
revolution of the larger circle and two counterclockwise revolutions
of the small circle.

But now you have seen the larger circle move when it shouldn't have.
To restore the correct number of revolutions of the large circle (i.e.
0) you must turn your head back so both circles turn counterclockwise
one time.  This is the third such revolution for the small circle.

This situation is analogous to the difference between the number of
solar days in a year (~365.25) and the number of sidereal days
(~366.25).

-- David Karr (karr@cs.cornell.edu)