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Simple logic puzzles

Also, logic puzzles can be found in the books of Smallian and Carroll (see menu).

1) You are a biochemist working with a twelve-nozzle centrifuge. This device, which 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 be sure that the samples are well mixed, they must be placed in 12 slots balanced. 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 by the old exception system. That is, these 97 teams are divided into pairs and the teams of each pair play against each other. After losing teams are eliminated, the winners are again divided into pairs, etc. How many games need to play to determine the champion? Answer

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

4) Any group of 6 people consists of either 3 common friends 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), which is more than enough for a lock. But your friend has the keys to none of your locks. What to do?
Note: You cannot send a key in an unlocked box, as it can be copied. Answer

6) Two boxes are labeled "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" says "The inscription on the box" A "is not true and the gold in the box A". Assuming that 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 the head, if it is known that the maximum amount of hair in a person is 100,000. Answer

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

9) Assume that you are a prisoner who is suddenly granted the right to be released, but only if you are able to cope with this task: you have two doors, one of them leads to the will, the other is the road to death. Two guards are sitting, one of them being a liar, and the other is always telling the truth; you do not know which one is who. You must, by asking just one question to one of the guards, determine the path to freedom. What question will you ask? Answer

10) While the three wise men were sleeping under a tree, the naughty child painted their heads red. Waking up, every sage discovered the handiwork 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, labeled "A" and "B". On the day you need to eat one pill from each jar, but if you eat more than one pill, you will die. Once you took one pill from the jar “A”, and when you started to shake the pill out from the jar “B”, two pills accidentally fell out. Now you have three pills on your hand completely indistinguishable in appearance. How to get out of this situation with minimal losses? Answer

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

13) How to do so to love someone yourself, and so that someone loved you too? Answer

14) What question does the logician not answer "No"? Answer

15) The wolf cub, the little bear and the hippopotamus approached the carousel, on which the machine and the airplane were turned. Each of the friends wanted to roll on that and on the other. The machine and the airplane could accommodate only one passenger. During the trip, each of the friends at times rolled on a typewriter and on a small airplane. In the first approach, the little car slipped on an airplane, and the little wolf - on a typewriter. During the second call on the airplane rode a cub.
Who rode on what and the third time on what? Answer

16) Fill in the pass to get a true sentence (the last word may have to be changed in order for the phrase to sound correct in Russian):
IN THIS OFFER ... LETTERS. Answer