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Simple logic puzzles

Also logical puzzles can be found in the books of Smalian, Carroll (see the menu).

1) You are a biochemist working with a 12-centrifuge centrifuge. This device, which has 12 slots of the same size around the central axis, in 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 become a homogeneous liquid. To be sure that the samples are well mixed, they should be placed on 12 slots in a balanced manner. For example, if you want to mix 4 substances, 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). Is it possible to mix five substances 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 losing the 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 for two roses, all but two are tulips, and all but two are daisies. Answer

4) Any group of 6 people consists of either 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 locks with keys. The box has a ring (loop) that is more than enough for the lock. But your friend's keys are from none of your lock. What to do?
Note: You can not send a key in an unlocked box, as it can be copied. Answer

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

7) Prove that in Moscow there are at least two people with the same amount of hair on the head, 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 only people live who always speak the truth, in the other only those who always lie. They all go to visit each other, i.e. in any of these two cities you can meet as an honest man, so a liar. Suppose you are in one of these cities. How, after asking a single question to the first comer, to determine which city you were in - to the city of honest or to the city of liars? Answer

9) Let's say that you are a prisoner who was suddenly given the right to go free, but only if you cope with this task: there are two doors in front of you, one of them leads to freedom, the other - the road to death. Two guards sit, one of them being a liar, and the other always telling the truth; you do not know which one is who. You should, having asked only one question to one of the guards, determine the road to freedom. What question do you ask? Answer

10) While the three sages were sleeping under a tree, a mischievous child painted their heads in red. Waking up, every sage discovered the child's handiwork on the heads of his friends. Naturally they began to laugh. Suddenly, one stopped talking. Why? Answer

11) You have two jars with pills labeled "A" and "B". In the day you need to eat one pill from each jar, if you eat more than one pill, then you will die. Once you took one pill from the jar "A", and when you began to shake the pill from the can of "B", two pills accidentally dropped out. Now you have on your arm three pill completely indistinguishable in appearance. How to get out of this situation with the least loss? Answer

12) "The school principal objects to the cancellation of the decision to ban the control of the hair." How to understand this? Can I go with any haircuts? Answer

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

14) On what question the logician can not answer "No"? Answer

15) A wolf cub, a little girl and a hippo came to the carousel, on which the car and the airplane flew. Each of them wanted to roll on both, and on the other. The machine and airplane contained only one passenger. For three arrivals each of the men paused in a car and on a plane. In the first call, the little girl pushed on the plane, and the wolf cub on the typewriter. At the time of the second call a wolf cub was riding on a plane.
Who and what went for a drive on the third visit? Answer

16) Fill in the pass to get a true sentence (the last word, you may have to change, so that the phrase correctly sounded in Russian):
IN THIS PROPOSAL ... LETTER. Answer