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.”

Roll a Pencil

You roll a 5 sided pencil on the table. On one of its sides, it is written “HB Pencil”, the others are blank. What is the chance that the side with text on it ends up straight on top?

The chance is 0%. Since the pencil has an odd number of sides, it is impossible that any of them ends up straight on top.

Cut the Paper

You have a sheet of paper and a rectangular piece cut from it, as shown in the picture. What is the easiest way to cut the paper into two pieces with equal areas?

Make a cut through the centers of the small and the big rectangle. The cut will split both the area of the big and the small (absent) rectangle by half, and therefore will do the same to their difference – the given sheet of paper.

Cogwheels

There are two cogwheels on a table. The bigger one has 10 teeth and is fixed to the table. The smaller one has 5 teeth and revolves around the bigger one. If the smaller cogwheel makes one full rotation around the bigger cogwheel, how many rotations will it make with respect to the table?

The answer is three rotations in total. Two because of the ratio 10:5, one more because of the movement of the smaller cogwheel.