Surly Game time: Can You Figure Out this Puzzle

[TwiceHorn 31,624]

14 minutes ago, Not a cat said:

Help me out here.  I've read up on this and it's still not clicking why the extra rotation occurs- the sites I see simply say because the center of A is rotating around the center of B but I'm still not getting it.

So if B rotated around A it would be 4/3?

Sincerely, a liberal arts major 

It's because for circle A to travel around the circumference of circle B, its CENTER must traverse 360 degrees, rather than a point on the circumference.  And its center is at 4/3r.

So you have to set the circumference of circle b equal the circumference of the imaginary circle traversed by the center, which has a radius 4/3r, and the multiplier n for the number of rotations.

[Not a cat 5,726]

Ok, now that makes sense.  Thanks

[AeroHorn 755]

Another way to see it is to replace the circle B with a point. Now, the circle B is just turning around a point that is located on its circumference (the common point between the two circles in the diagram, call it C). Now, the circle B is going around point C, but during the full rotation, the point C hasn't moved. 

So, a circle going around any path adds one extra rotation to the number of rotations corresponding to the distance of the path. You can also see it by replacing circle B with a square. When the circle A reaches a corner of the square, its point of contact doesn't move but it rotates by 90 degrees. It crosses 4 corners amounting to an extra full rotation (360 degrees).

[WithoutAClue 15,478]

Holy necro bump Batman!

Rather than start a new thread I'm bumping this one. I ran across this logic problem and thought it was worth sharing.

Can You Solve Albert Einstein’s Famous House Riddle?

It took me longer than it should have to solve it but I'm old and haven't done logic problems in a while.

enjoy.