Gentlemen bought a camel. A seller said to him that the camel knew the three commands: “Phew!” – go,  “Hi!” – run, “Amen!” – stop. Gentleman said: “Phew!” and the camel went, then he said : “Hi!” and the camel ran. Suddenly the gentleman saw that the camel ran toward a precipice, but he forgot how to stop the camel. Understanding that his death was inevitable, he began to pray and said at the end of the prayer: “Amen!”. The camel stopped on the precipice edge. The gentleman wiped sweat from the forehead and said: “Phew!”.

Three friends went to a sage and asked to judge them. They bought together 18 lambs. The first man paid a half of the whole cost, the second – a third and the last – 1 / 9 of the whole cost. They wanted to divide the lambs, but so that all the lambs were alive. The sage said to them: “I can judge you, but I want to get one of the lambs as a reward”. The men agreed. Then the sage gave 9 lambs to the first man, 6 lambs – to the second man, 2 lambs – to the last man andtook 1 lamb for himself. As a result all of them were satisfied. What was a cause of the situation ?


S o l u t i o n.  A cause of this situation was that these three men paid:

In the middle of the XX century Russia was a country, where all people knew mathematics perfectly. In 1965 one newspaper wrote: ”Do you know that a cost of 0.25 liter of vodka, raised to the power, equal to a cost of 0.5 liter of vodka is the number p with accuracy of three first digits ?”. You can convince in this fact yourself, if to consider that a bottle of 0.25 liter of vodka cost 1.49 ruble, and a bottle of 0.5 liter of vodka cost 2.87 ruble in 1965. Check!

Achilles runs after a turtle. Achilles’ velocity is 10 times more than turtle’s velocity. First moment the distance between them is equal to100 m. Achilles runs these 100 m, a turtle creeps 10 m. Achilles runs this 10 m, a turtle creeps 1 m. Achilles runs 1 m, a turtle creeps 0.1 m. Achilles runs 0.1 m, a turtle creeps 0.01 m, and so on. Hence, Achilles will never catch up a turtle ! Explain, please this paradox, known as Zenonian one.


S o l u t i o n.   A cause of this paradox consists in dividing continuous time into
parts. We consider smaller and smaller time intervals and receive
the paradox as a result. Actually, Achilles will outrun a turtle,
of course! Assume that Achilles runs 100 m in 10 seconds, then
in next 10 seconds he will run else 100 m, and a turtle will creep
this time only 20 m.

Once a group of 8 guests was taking seats around a big table in a restaurant during a long time. An owner watched this and then said that he agreed to feed them gratis on condition that they would take seats newly every day. How long will he feed them gratis on this condition ?


S o l u t i o n.   This is a classic problem of theory of combinations. Each combination
of guests around a table is a permutation, so the number of all
possible permutations is equal to

8! = 40320 days ≈ 110 years.

Thus, the owner agrees to feed them gratis for 110 years!.

Two friends meet. One of them says:
-  Yesterday I was in a circus and saw a trained boa. His length is 8 meters from a head to a tail and 9 meters from a
tail to a head.
-  It’s impossible!
-  Why? Don’t you know that from Monday to Sunday there are 7 days, and from Sunday to Monday there is only 1 day.

London. Midnight. It’s raining. Can one believe in a weather forecast, that in 72 hours a weather in London will be sunny ?


S o l u t i o n.   No, one can’t, because in 72 a midnight will be again, and a sunny weather in a middle latitude may be only in the daytime.

A thief penetrated into a flat and saw a huge immovable dog and a parrot, sitting  in the cage. The parrot said:
-  You are welcome!
A thief was afraid at the beginning, but then he calmed down, because the dog made nothing. Capturing jewels and money he wanted to go away and asked the parrot at the end:
-  Well, don’t you know other words, foolish bird ?
The parrot answered:
-  Bite him, boy!

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