Trotsky’s Killer

August 20, 1940

Leon Trotsky, an enemy of Josef Stalin, had been in exile for 11 years. On this day, a Soviet assassin entered Trotsky’s house in Mexico City and hit him in the head with an ice axe. He died the next day.

Here is a group of suspects who were rounded up. Each wrong suspect has one different feature from the correct suspect. Who killed Trotsky?

The killer of Leon Trotsky was Ramón Mercader.

Plinks, Plonks, and Plunks

If all plinks are plonks and some plunks are plinks, which of these statements must be true?

  • All plinks are plunks.
  • Some plonks are plunks.
  • Some plinks are not plunks.

Remark: “Some” means more than 0.

The first statement says that the set of plonks contains the set of plinks, and the second statement says that there is at least one plunk-plink. Therefore, that plunk-plink must also be a plonk, and the second statement is true.

The first and the third statements, however, do not need to be true. Indeed, it is possible that there is a plink that is not a plunk, or that all plinks are plunks.

A Dream Last Night

The director of a company wakes up early for a morning flight. He realizes that he forgot some papers at work and goes there. In the office, he meets the night watchman who is leaving for home. The watchman stops the director and tells him that he shouldn’t fly. “I had a dream last night,” the watchman says, “I saw you crash. I saw you die sir, please do not fly today.”

The director listens to the advice of the watchman and decides not to travel. On the next day, the director returns, gives the watchman a generous bonus, and then he fires him. Why?

The plane indeed crashed, so the watchman saved the director’s live. However, apparently, he has been sleeping during his shift, which is the reason the director fires him.

Murdered Wife

One night, a man received a call from the Police. The Police told the man that his wife was murdered, and that he should get to the crime scene as soon as possible. The man immediately hung up the phone and drove his car for 20 minutes. As soon as he got to the crime scene, the Police arrested him, and he got convicted for murder.

How did the Police know that the man committed the crime?

The police did not tell the man where the crime scene was.

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Five Points in a Square

There are 5 points in a square 1×1. Show that 2 of the points are within distance 0.75.

Split the unit square into 4 small squares with side lengths 0.5. At least one of these squares will contain 2 of the points. Since the diagonals of the small squares have lengths less than 0.75, these 2 points must be within such distance.