Full of T
What begins with T, ends with T, and is full of T?
SOLUTION
The answer is TEA POT.
53 Bicycles and a Dead Man
There is a room with a table, 53 bicycles, and four men. One of the four men is dead. How did he die?
SOLUTION
The “bicycles” are the (famous) Bicycle playing cards. The four men were playing poker, but one of them was cheating with an extra card, so he got killed.
The Ark
How many species of animals did Moses take on the Ark with him?
SOLUTION
None. It was Noah’s ark, not Moses’.
Raise Me None
Raise me none and I am unbeaten.
Raise me once and I am excessive.
Raise me twice and I am forward.
Raise me thrice and I am eaten.
All said right, but wrongly spelled.
Who am I?
SOLUTION
The answer is the NUMBER 2:
2⁰ = 1 (“one”), which is unbeaten;
2¹ = 2 (“too”), which is excessive;
2² = 4 (“fore”), which is forward;
2³ = 8 (“ate”), which is eaten.
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.
SOLUTION
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.
Lost Without Moving
In 1972 there was a chess game between two famous players. One of them lost the game without moving any pieces. How?
SOLUTION
It was the game in 1972 between Bobby Fischer and Boris Spassky, when Bobby Fischer’s clock ran out of time. Fischer himself even did not appear for the game due to his protest against the cameras installed in the playing hall.
Envelopes with Numbers
You are given 2 sealed envelopes with numbers inside. You are told that one of the numbers is twice as much as the other one. You grab one of the envelopes and right before you open it, you make the following calculation:
“If this envelope contains X inside, then the other envelope contains either X/2 or 2X inside. Since the chance that the other envelope contains a larger number is exactly 50%, the expected money I will get after switching is X/4 + X = 1.25X > X. Therefore, I should switch!”
Clearly, this reasoning is wrong, since you can’t possibly deduce which envelope of the two contains a larger number. Where is the mistake?
SOLUTION
The trick is that conditionally on the fact that your envelope contains X, it is not true that the other envelope has 50% chance of containing either X/2 or 2X. The reason is that it is impossible that all amounts of dollars appear in the envelopes with the same probabilities (densities). Thus, for example, if it is very unlikely that an envelope contains more than 1000, and you open an envelope with 800 inside, you will not think that the other envelope has 50% chance of containing 1600.
Movie Conundrums 7
Can you recognize which famous movies are depicted by these images?
SOLUTION
- St. Elmo’s Fire
- The Sum of All Fears
- Moonraker
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?
SOLUTION
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.