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Simple logic puzzles

Logic puzzles can also be found in the books of Sullian, Carroll (see menu).

1) You are a biochemist working with a twelve-acid centrifuge. This is a device that has 12 slots of the same size around the central axis into which you place samples of chemicals that you need to mix. When the machine is turned on, the samples rotate around the central axis and turn into a homogeneous liquid. To ensure that the samples mix well, they must be placed in 12 slots in a balanced manner. For example, if you want to mix 4 substances, then they can be placed in slots 3, 6, 9, and 12 (it is assumed that the slots are numbered, as well as the numbers on the clock). Can five substances be mixed in such a centrifuge? Answer

2) 97 baseball teams participate in the annual tournament. In this tournament, the winner is selected according to the old exclusion system. That is, these 97 teams are divided into pairs and the teams of each pair play against each other. After the losing teams are eliminated, the winners are again divided into pairs, etc. How many games do you need to play to determine the champion? Answer

3) How many flowers do I have if all of them except two roses, all but two are tulips, and all but two are daisies. Answer

4) Any group of 6 people consists of 3 common acquaintances, or 3 common strangers. Prove it. Answer

5) You want to send a valuable item to a friend. You have a box that is larger than the item itself. You have several key locks. The box has a ring (loops) that is larger than would be enough for the lock. But your friend has no keys to any of your locks. What to do?
Note: You cannot send the key in an unlocked box, as it can be copied. Answer

6) Two boxes labeled "A" and "B". The inscription on box "A" reads: "The inscription on box" B "is true and the gold in box" A "". The inscription on box "B" reads: "The inscription on box" A "is not true and the gold in box A". Assuming gold is in one of the boxes, tell me which one. Answer

7) Prove that in Moscow there are at least two people with the same amount of hair on their heads, if it is known that the maximum amount of hair in a person is 100,000. Answer

8) In some country there are two cities. In one of them live only people who always tell the truth, in the other - only those who always lie. They all go to visit each other, i.e. in either of these two cities one can meet both an honest man and a liar. Suppose you are in one of these cities. How, by asking one single question to the first person you come across, determine which city you are in — the city of the honest or the city of liars? Answer

9) Suppose that you are a prisoner who is suddenly granted the right to go free, but only if you cope with this task: you have two doors, one of them leads to freedom, the other is the road to death. Two guards are sitting, one of them being a liar, and the second always telling the truth; you don’t know which of them is who. You should, asking only one question to one of the guards, determine the path to freedom. What question do you ask? Answer

10) While the three wise men slept under a tree, a mischievous child painted their heads red. Waking up, every sage discovered the work of the hands of a child on the heads of his friends. Naturally they began to laugh. Suddenly one was silent. Why? Answer

11) You have two jars of pills marked "A" and "B". On the day you need to eat one pill from each jar, if you eat more than one pill, you will die. Once you took one pill from jar "A", and when you began to shake the pill out of jar "B", two pills accidentally fell out. Now you have three pills on your hand that are completely indistinguishable in appearance. How to get out of this situation with the least losses? Answer

12) "The headmaster objects to the cancellation of the decision to ban the control of hairstyles." How to understand this? Can I walk with any hairstyles? Answer

13) How to make it so that you love someone yourself, and so that this someone also loves you? Answer

14) What question can logicians answer “No”? Answer

15) A wolf cub, a monkey and a hippopotamus came to the carousel, on which the machine and the airplane were spinning. Each of the friends wanted to ride on that, and on the other. The machine and the airplane contained only one passenger. During the trip, each of the friends at once rolled on a typewriter and on an airplane. In the first call, the monkey rolled on a plane, and the wolf cub - on a typewriter. During the second approach, a wolf cub rode on a plane.
Who and what rode during the third call? Answer

16) Fill in the blank to get a true sentence (the last word may have to be changed so that the phrase sounds correctly in Russian):