Borromean Rings

Borromean rings are rings in the 3-dimensional space, linked in such a way that if you cut any of the three rings, all of them will be unlinked (see the image below). Show that rigid circular Borromean rings cannot exist.

Assume the opposite. Imagine the rings have zero thickness and reposition them in such a way, that two of them, say ring 1 and ring 2, touch each other in two points. These two rings lie either on a sphere or a plane which ring 3 must intersect in four points. However, this is impossible.

Broken Window

One snowy night, Sherlock Holmes was in his house sitting by a fire. All of a sudden a snowball came crashing through the window, breaking it. Holmes got up and looked out just in time to see three neighborhood kids who were brothers run around the corner. Their names were John Crimson, Mark Crimson, and Paul Crimson.

The next day Holmes got a note on his door that read:

“? Crimson. He broke your window.”

Which of the three Crimson brothers should Sherlock Holmes question about the incident?

He should question Mark. The note read: “QUESTION MARK Crimson. He broke your window.”