Max Friedrich William Bezzel (1824 – 1871) was a German chess composer who created the eight queens puzzle in 1848.
Place 8 queens on a chessboard, so that no two of them attack each other. For an extra challenge, make sure that no three of them lie on a straight line.
The original puzzle has 12 unique solutions, up to rotation and symmetry. With the additional restriction imposed, there is only one solution.
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 question is, who owns the pet fish?
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.
King Arthur and his eleven honorable knights must sit on a round-table. In how many ways can you arrange the group, if no honorable knight can sit between two older honorable knights?
The answer is 1024 ways, up to rotation around the table. To see this, note that the youngest honorable knight must sit right next to King Arthur – there are two possible places for him. Then, the second-youngest knight must sit right next to this group of two. Once again, there are two possible places for him. Continuing like this, we see that for all honorable knights, except for the oldest one, there are two possible spots on the table. Multiplying two to the power of ten out, we get 1024.
This is a non-transitive dice set, i.e. every dice in it is weaker than some other dice. Can you design a non-transitive set with only 3 dice?
Remark: “Weaker” means that it loses more often than it wins.
The simplest solution is given by:
2, 2, 4, 4, 9, 9;
1, 1, 6, 6, 8, 8;
3, 3, 5, 5, 7, 7.
Another solution is given by the so-called “Miwin’s dice”. They are as follows:
1, 1, 3, 5, 5, 6;
2, 3, 3, 4, 4, 5;
1, 2, 2, 4, 6, 6.
You have a drawer with 10 pairs of black socks and 10 pairs of white socks. How many times do you need to blindly reach inside the drawer and take out a sock, so that you get a matching pair?
Only 3 times. Once you have two socks of the same color, they already form a matching pair.
Who is richer – the richest among the poor or the poorest among the rich?
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.
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?
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.
You are given 3 boxes – one labeled “Apples”, one labeled “Bananas”, and one labeled “Apples and Bananas”. You are told that the labels on the boxes have been completely mismatched, i.e. none of the three labels is put on its correct box. How can you open just one box and pick a random fruit from it, so that after seeing the fruit, you can guess correctly the contents of every box out of the three?
Open the box labeled “Apples and Bananas”. If you pick a banana from it, then the box labeled “Bananas” will contain apples, and therefore the box labeled “Apples” will contain apples and bananas. Similarly, if you pick an apple from it, then the box labeled “Apples” will contain bananas, and therefore the box labeled “Bananas” will contain apples and bananas”.
Jack is looking at Anne, but Anne is looking at George. Jack is married, but George is not. Is a married person looking at an unmarried person?
The answer is YES. If Anne is unmarried, then Jack is married and is looking at an unmarried person. If not, then she is married and is looking at an unmarried person.
“If there is a vowel written on one side of a card, then there is an even number written on the other side.”
How many of these four cards do you need to flip in order to check the validity of this sentence?
What would the answer be if you know that each card contains one letter and one number?
You need to flip all cards except for the second one. If each card contains one letter and one number, then you need to flip only A and 7.
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