Cut the Pizza

Cut a circular pizza into 12 congruent slices, such that exactly half of them contain crust.

Remark: We say that a slice contains crust if it shares an arc with the boundary of the pizza (with non-zero measure).

First, cut the pizza into 6 congruent circular triangles, and then split each of them in half, as shown on the image below.

The Gun and the Recording

One day, the police found a man dead inside a hut. In his left hand, he was holding a gun. In his right hand, he had a recording device. When the recording was played, the police heard the man talking about how horrible his life was and how he wanted it to end. The recording ended with a gunshot. The police was about to call it a suicide until a detective pointed out a very important clue. What was it?

If the person shot himself and died, he wouldn’t have been able to stop the device from recording further.

Rewarded and Fired

A very rich man has many servants in his mansion. One day as he is about to travel, his night watchman warns him not to board his flight. “I had a dream last night that the plane crashed,” the watchman tells him. The rich man is annoyed at first, but since he is also superstitious himself, he decides not to take the flight.

Later that day as he is watching the news, he sees that his plane did, in fact, crash. He goes over to thank and reward his servant, and then fires him. Why?

The watchman has been sleeping at work instead of guarding the mansion, so that’s the reason he gets fired.