Rough automatic draft, low quality: expect mistakes and awkward wording. It will be replaced by a better translation. Original →
64
TASKS. GAMES, EXPERIENCES
What do you do, reader, in your free time? Do you sort out your stamp collection, take up photography, play football? Probably both, and three… But, among other things, you - we are sure of this - still love to solve various problems: simple and complex, gray and spring, instructive and entertaining. This is a very exciting thing - solving problems, it is gymnastics for the mind, and gymnastics is also necessary for a future engineer or scientist, like physical exercises, which everyone was obliged to do in the morning.
A very interesting collection of problems was recently published, under the title “Your Free Time”*). Its authors - V.N. Bolkhovitinov, B.I. Koltovoy and I.K. Lagovsky collected their tasks into one book, which they published at different times in the magazines “Technology for Youth”, “Young Technician”, “Science and Life”. When compiling the collection, we also used problems and problem ideas published in various foreign magazines and collections.
The book “Your Free Time” has several sections: “Psychological Workshop”, “Logical Problems”, “Mathematical Documents”, “Designer’s Problem Book”, “Laboratory Exercises at Home” and others. Almost all problems included in the collection contain solutions or answers.
By completing the tasks of the book “Your Free Time”, solving the problems placed there, you will get more convenience, and one can only regret that the collection was published in a relatively small edition - only 10,000 copies. (For comparison, we point out that only the reader «Kvant», who absolutely love solving problems, is more than two hundred thousand).
To ensure that what was previously presented about the book being solved was more complete, we present several problems taken from the collection “Your Free Time”.
Calbra problem
The fitter noticed that the control checks the accuracy of machining a round hole with a diameter of 3 cm, lowering into it 2 caliber plugs with a diameter of 2 and 1 cm. Then the traces suggested, in order to increase the accuracy of control of the shape of the hole, along with these 2 calibers, lower 2 more, which should fit tightly to the walls and to both first calibers.
Calculate the diameter of the calibers that suggest adding traces. Try to do without using trigonometry. (Of course, both new calibers will be the same size.*)
Two bars
In Transcaucasia, the sashite tree grows, which is 1.2 times heavier than water. A block was prepared from it and a block of the same volume was made from dry linden, which is 1.2 times lighter than water.
The bars were tied together and lowered into the water. The linden block was at the bottom, and the sashite block was at the top. The first one sank completely, and the second one to 5/6 of its height.
Turn the bars over: the bottom was made of sashite, and the top was made of linden.
To what height did the linden block sink?
Tourism
A group of tourists of 100 people went abroad. 10 of them knew neither a little nor French. 75 knew German. 83 people knew French. How many tourists spoke both foreign languages?
Rejected report
The inspector of the group for studying population demand submitted the following report to the canteen trust:
Number of respondents: 100 people.
Of these: 78 people drink coffee, 71 people drink tea, 48 people drink coffee and tea.
The report was rejected. Why?