Rich and Poor
Who is richer – the richest among the poor or the poorest among the rich?
SOLUTION
The poorest among the rich is richer than the richest among the poor. That is because any rich person is by default richer than any poor person.
Category: Brain Teasers
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1988 Pennies
Why are 1988 pennies worth more than 1983 pennies?
SOLUTION
For the same reason 20 pennies are worth more than 15 pennies. 1983, 1988 are the numbers of pennies, not the years they have been made.
Maze Design
How can you design a maze in just 10 seconds, which can not be solved in under 5 seconds?
SOLUTION
Just quickly draw a maze in the shape of a spiral. The other person must be twice as fast as you in order to solve it.
Square Cake
There is a square cake at a birthday party attended by a dozen people. How can the cake be cut into twelve pieces, so that every person gets the same amount of cake, and also the same amount of frosting?
Remark: The decoration of the cake is put aside, nobody eats it.
SOLUTION
Divide the boundary of the cake into twelve equal parts, then simply make cuts passing through the separation points and the center. This way all tops and bottoms of the formed pieces will have equal areas, and also all their sides will have equal areas. Since all pieces have the same height, their volumes will be equal as well.
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?
SOLUTION
The answer is three rotations in total. Two because of the ratio 10:5, one more because of the movement of the smaller cogwheel.
Mystery Mate
White plays and mates Black in one move. However, there is a mystery in this position that has to be revealed first.
SOLUTION
The mystery is that someone has just placed one extra black pawn on the board – there are 9 in total. Also, no matter which one is the added pawn, there always exists a mate in one move.
If the extra pawn was a7 – Qb6
If the extra pawn was b7 – Kc6
If the extra pawn was c4 – Qb4
If the extra pawn was d3 – Qe4
If the extra pawn was e3 – Bxf2
If the extra pawn was f7 – Ke6
If the extra pawn was g6 – Rg4
If the extra pawn was h3 – Rh4
Wobbling Table
A perfectly symmetrical square 4-legged table is standing in a room with a continuous but uneven floor. Is it always possible to position the table in such a way that it doesn’t wobble, i.e. all four legs are touching the floor?
SOLUTION
The answer is yes. Let the feet of the table clockwise are labeled with 1, 2, 3, 4 clockwise. Place the table in the room such that 3 of its feet – say 1, 2, 3, touch the ground. If foot 4 is on the ground, then the problem is solved. Otherwise, it is easy to see that we can not put it there if we keep legs 2 and 3 in the same places. Now start rotating the table clockwise, keeping feet 1, 2 and 3 on the ground at all times. If at some point foot 4 touches the ground as well, the problem is solved. Otherwise, continue rotating until foot 1 goes to the place where foot 2 was and foot 2 goes to the place where foot 3 was. Foot 3 will be on the ground, but this contradicts the observation that initially we couldn’t place legs 2, 3 and 4 on the ground without replacing feet 2 and 3.
Prank the Professors
Three professors fell asleep under a tree. At some point a prankster passed by and painted their faces with black dye. When the professors woke up, each of them saw the others’ faces and started laughing at them. After a while though, they stopped laughing, realizing that their own faces were painted as well. How did they deduce that?
SOLUTION
Let us denote the professors with A, B and C. The thought process of A would go like this: “If my face is not painted, then B will see that C is laughing at him and will realize immediately that he is being pranked. However, B was laughing for a while and therefore my I must being pranked as well.”. Then A will stop laughing and the same will happen with the other two professors B and C.
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Repetitive
You have two groups of words:
- black, word, English, brief, noun, grandiloquent, last
- white, number, Russian, long, verb, unpretentious, first
To which group does “repetitive” belong?
SOLUTION
The first group contains self-explanatory words (known as autologicals), the second group does not. Therefore “repetitive” should belong to the first group.
Chocolate Bar
Louis has a bar of chocolate 4×6 which is marked into 24 little squares. At each step, he breaks up one of its pieces along any of the marked horizontal/vertical lines. Show that no matter how he does that, it will always take the same number of steps until the chocolate is broken into single 1×1 pieces.
SOLUTION
Every time he splits the chocolate, the number of pieces increases by 1. Therefore it will always take him 23 steps to split it into single pieces.