David Justice and Derek Jeter were professional baseball players. In 1997 they had the following conversation:
David: Did you know that in both 1995 and 1996 I had better batting averages than you?
Derek: No way, my batting average over the last two years was definitely higher than yours!
It turned out that both of them were right. How is it possible?
SOLUTION
This is the so called Simpson’s paradox. The reason it occurred is that during 1996 both players had high averages and Derek Jeter had many more hits than David Justice. In 1996 both players had low averages and David Justice had many more hits than Derek Jeter. You can see their official statistics below.
There is a common 9-letter word in the English language, such that if you keep removing its letters one by one, the resulting 8 words are still valid. What is this word?
Remark: The removed letters do not need to be from the beginning or the end of the word.
SOLUTION
The word is STARTLING -> STARTING -> STARING -> STRING -> STING -> SING -> SIN -> IN -> I.
A bus driver was heading down a street in Colorado. He went right past a stop sign without stopping, turned left where there was a “no left turn” sign, and went the wrong way on a one-way street. Then he went on the left side of the road past a cop car. Yet, he didn’t break any traffic laws.
Why not?
SOLUTION
The bus driver was not driving his bus, he was walking.
A man was moving to a new house. He rented a moving truck, put all his belongings in it, and drove to his new place. He entered the garage with the truck and took all his belongings out of the truck. When he tried to exit the garage with the truck, he couldn’t. Why?
SOLUTION
The empty truck was just slightly taller than the garage door. When it was packed with items, the truck’s height got lower, so the man could enter the garage. Once the items were unpacked, the truck was once again taller than door, so it couldn’t get out.
First, print and cut the pieces below. Then, arrange them so that they form a triangle and then rearrange them so that they form a square.
SOLUTION
The solution is shown below.
What is fascinating about these dissections is that one can transform into the other by keeping the pieces attached to each other in a chain and simply rotating them around the hinge points.
There are 5 houses and each of them has a different color. Their respective owners have different heritages, drink different types of beverages, smoke different brands of cigarettes, and look after different types of pets. It is known that:
The Brit lives in the red house.
The Swede keeps dogs as pets.
The Dane drinks tea.
Looking from in front, the green house is just to the left of the white house.
The green house’s owner drinks coffee.
The person who smokes Pall Malls raises birds.
The owner of the yellow house smokes Dunhill.
The man living in the center house drinks milk.
The Norwegian lives in the leftmost house.
The man who smokes Blends lives next to the one who keeps cats.
The man who keeps a horse lives next to the man who smokes Dunhill.
The owner who smokes Bluemasters also drinks beer.
The German smokes Prince.
The Norwegian lives next to the blue house.
The man who smokes Blends has a neighbor who drinks water.
The question is, who owns the pet fish?
SOLUTION
The German owns the pet fish.
Since the Norwegian lives in the leftmost house (9) and the house next to him is blue (14), the second house must be blue. Since the green house is on the left of the white house (4), the person living in the center house drinks milk (8), and the green house’s owner drinks coffee (5), the fourth house must be green and the fifth one must be white. Since the Brit lives in the red house (1) and the Norwegian lives in the leftmost house (9), the leftmost house must be yellow and the center house must be red. Therefore, the colors of the houses are: YELLOW, BLUE, RED, GREEN, WHITE.
Since the Norwegian from the yellow house smokes Dunhill (7), the man from the blue house must keep a horse (11). The person smoking Blends cannot be in the red house, because this would imply that the person in the green house keeps cats and the Swede keeps dogs in the white house (2, 10). However, in this case the Dane must be drinking tea in the blue house (3) and the person smoking Blends does not have a neighbor drinking water (5), which is a contradiction (15). Also, the person smoking Blends cannot be in the green house, because this would imply that the person in the white house drinks water (15), the Dane lives in the blue house (3), and the German and the Swede live in the last two houses. Since the German smokes Prince (13) and the Swede keeps dogs (2), there is nobody who could smoke Bluemaster and drink beer (12). The person smoking Blends cannot be in the white house either, because this would imply that the person in the green house drinks water (15), when in fact he drinks coffee (5).
Therefore, the person smoking Blends must be in the blue house, and then the German and the Swede must live in the last two houses (2, 13). Since the person who smokes Bluemasters drinks beer (12), this must be the Swede with his dogs in the white house (2). The only option for the person who smokes Pall Mall and raising birds (6) is the red house. Then the Norwegian must keep cats (10) and the German is left with the pet fish in the green house.
A woman was standing in her hotel room, when somebody knocked on the door. When she opened the door, there was a man who said that he has mistaken his door, apologized, and continued down the corridor. When the woman closed the door, she called security to warn them about the thief. Why did she think the man was planning to rob her?
SOLUTION
If the man really thought this was his room, he wouldn’t have knocked on the door.
Alex and Bob are playing a game. They are taking turns drawing arrows over the segments of an infinite grid. Alex wins if he manages to create a closed loop, Bob wins if Alex does not win within the first 1000 moves. Who has a winning strategy if:
a) Alex starts first (easy) b) Bob starts first (hard)
Remark: The loop can include arrows drawn both by Alex and Bob.
SOLUTION
In both cases, Bob wins. An easy strategy for part a) is the following:
Every time Alex draws an arrow, Bob draws an arrow in such a way that the two arrows form an L-shaped piece and either point towards or away from each other. Since every closed loop must contain a bottom left corner, Alex cannot win.
For part b), Bob should use a modification of his strategy in part a). First, he draws a horizontal arrow. Then, he splits the remaining edges into pairs, as shown in the image below. If Alex draws one arrow on the grid, then Bob draws its paired arrow, such that the two arrows point either towards or away from each other. The only places where a loop can have a bottom left corner are where Bob drew the first arrow or the grid points directly above it. However, if a loop has a bottom left corner there, then it is easy to see that it must have at least one more bottom left corner elsewhere, which is impossible.
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