12 Soviet problems that only the smartest can solve

2024 Author: Malcolm Clapton | [email protected]. Last modified: 2023-12-17 03:44

Test your wits!

1. How to divide?

Two friends cooked porridge: one poured 200 g of cereal into the pot, the other - 300 g. When the porridge was ready and the friends were going to eat it, a passer-by joined them and took part in the meal with them. Leaving, he left them 50 kopecks for it. How should buddies share the money they receive?

The majority of those who solve this problem answer that the one who added 200 g of cereal should get 20 kopecks, and the one who added 300 g should get 30 kopecks. This division is completely unfounded.

We must reason like this: 50 kopecks were paid for the share of one eater. Since there were three eaters, the cost of all porridge (500 g) is 1 ruble 50 kopecks. The one who poured 200 g of cereal contributed 60 kopecks in monetary value (because 100 g costs 150 ÷ 500 × 100 = 30 kopecks). He ate 50 kopecks, which means he needs to be given 60 - 50 = 10 kopecks. The one who contributed 300 g (that is, 90 kopecks in money) should receive 90 - 50 = 40 kopecks.

So, out of 50 kopecks, one should take 10, and the other 40.

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2. Book price

Ivanov buys all the literature he needs from a bookseller he knows with a 20% discount. From January 1, the prices of all books have been increased by 20%. Ivanov decided that he would now pay for the books as much as the rest of the buyers paid before January 1. Is he right?

Ivanov will now pay less than the rest of the buyers paid before January 1. It has a 20% discount on the price increased by 20% - in other words, a 20% discount off 120%. That is, he will pay for the book not 100%, but only 96% of its previous price.

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3. Chicken and duck eggs

The baskets contain eggs, some chicken eggs and others duck eggs. The number of eggs is 5, 6, 12, 14, 23, 29. "If I sell this basket," the merchant thinks, "then I will have exactly twice as many chicken eggs as duck eggs." Which basket did he mean?

The seller was referring to a basket of 29 eggs. The chickens were in baskets 23, 12, and 5; duck - in baskets, numbering 14 and 6 pieces. Let's check. There were 23 + 12 + 5 = 40 chicken eggs in total. Duck eggs - 14 + 6 = 20. There are twice as many chicken eggs as duck eggs, as required by the condition of the problem.

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4. Barrels

6 barrels of kerosene were delivered to the store. The figure shows how many buckets of this liquid were in each barrel. On the first day, two buyers were found; one bought 2 barrels entirely, the other - 3, and the first person bought half as much kerosene as the second. So I didn't even have to uncork the barrels. Of the 6 containers, only one remains in the warehouse. Which one?

The first customer bought 15-bucket and 18-bucket barrels. The second one holds 16 buckets, 19 buckets and 31 buckets. Indeed: 15 + 18 = 33, 16 + 19 + 31 = 66, that is, the second person had twice as much kerosene as the first. A 20-bucket barrel remained unsold. This is the only possible option. Other combinations do not give the desired ratio.

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5. Million products

The product has a weight of 89.4 g. Imagine in your mind how much a million such products weigh.

You must first multiply 89.4 g per million, that is, by a thousand thousand. We multiply in two steps: 89.4 g × 1,000 = 89.4 kg, because a kilogram is a thousand times more than a gram. Further: 89.4 kg × 1,000 = 89.4 tons, because a ton is a thousand times more than a kilogram. The required weight is 89.4 tons.

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6. Grandfather and grandson

- What I will say happened in 1932. I was then exactly as old as the last two digits of the year of my birth express. When I told my grandfather about this ratio, he surprised me with the statement that the same thing happens with his age. It seemed to me impossible …

“Impossible, of course,” a voice interjected.

- Imagine, it is quite possible. My grandfather proved it to me. How old was each of us?

At first glance, it may really seem that the problem is incorrectly composed: it turns out that the grandson and grandfather are of the same age. However, the requirement of the problem, as we shall now see, is easily satisfied.

The grandson was obviously born in the 20th century. The first two digits of the year of his birth, therefore, 19. The number expressed by the rest of the digits, when added to itself, should be 32. This means that this number is 16: the year of birth of the grandson is 1916, and he was 16 years old in 1932.

His grandfather was born, of course, in the 19th century; the first two digits of the year of his birth - 18. The doubled number expressed by the rest of the figures should be 132. This means that this number itself is equal to half 132, that is, 66. The grandfather was born in 1866, and in 1932 he was 66 years old.

Thus, both the grandson and grandfather in 1932 were as old as the last two digits of the year of birth of each of them express.

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7. Non-changeable bills

One lady had several dollar bills in her purse. She had no other money with her.

1. The lady spent half of the money on buying a new hat, and paid $ 1 for a refreshing drink.
2. Going to a cafe for breakfast, the woman spent half of her remaining money and paid another $ 2 for cigarettes.
3. With half of the money left after that, she bought a book, then on the way home she went to a bar and ordered a cocktail for $ 3. As a result, $ 1 remained.

How many dollars did the lady have initially, if we assume that she never had to change the existing bills?

Let's start solving the problem from the end, that is, from the third point. Before buying a cocktail, the lady had 1 + 3 = 4 dollars. If she bought the book for half of the remaining money, then before buying the book she had 4 × 2 = 8 dollars.

Let's move on to point 2. The lady paid $ 2 for the cigarettes, that is, before purchasing them, she had 8 + 2 = 10 dollars. Before buying cigarettes, the woman spent half of the money available at that time on breakfast. So, before breakfast, she had 10x2 = $ 20.

Let's move on to the first point. The lady paid 1 dollar for a refreshing drink: 20 + 1 = 21. This means that before buying the hat she had 21 × 2 = 42 dollars.

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8. Three workers dug a ditch

Three workers were digging a ditch. At first, the first of them worked half the time it took for the other two to dig the entire ditch. Then the second person worked half the time it took the other two to dig the entire ditch. Finally, the third participant worked half the time it took for the other two to dig the entire ditch.

As a result, the work was completely completed, and 8 hours have passed since the beginning of the process. How long would it take all three diggers to dig this ditch, working together?

Let the other two work simultaneously with the first participant. According to the condition, during the operation of the first, two others will dig half of the ditch. In the same way, while the second is working, the first and the third will dig more half-ditches, and while the third is working, the half-canals will provide the first and the second. This means that in 8 hours all together they would have dug a ditch and another one and a half ditches, a total of 2, 5 ditches. And the three of them will dig one ditch in 8 ÷ 2, 5 = 3, 2 hours.

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9. African earrings

There are 800 women among the population of a certain African village. Three percent of them wear one earring each, half of the women who make up the remaining 97% wear two earrings, and the other half do not wear earrings at all. How many earrings can be counted in the ears of the entire female population of the village? The problem should be solved in the mind, without resorting to improvised computational tools.

If half of 97% of the villagers wear two earrings, and the other half do not wear them at all, then the number of earrings per this part of the population is the same as if all local women wore one earring each.

Therefore, when determining the total number of earrings, we can assume that all the inhabitants of the village wear one earring, and since 800 women live there, then there are 800 earrings.

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10. Chief walking

For one boss, who lives in his dacha, a car came in the morning and took him to work at a certain time. Once this boss, deciding to take a walk, left 1 hour before the arrival of the car and walked towards him. On the way, he met a car and arrived at work 20 minutes before its start. How long did the walk last?

Since the car only "won" 20 minutes, then the distance from the place where she met the boss to his dacha and back she would have covered in 20 minutes. This means that the driver had 10 minutes before the dacha, and since the passenger left the house an hour before the car arrived, the walk lasted 60 - 10 = 50 minutes.

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11. Oncoming trains

Two passenger trains, both 250 m long, go towards each other at the same speed of 45 km / h. How many seconds will pass after the drivers meet before the conductors of the last carriages meet?

At the moment the drivers meet, the distance between the conductors will be 250 + 250 = 500 m. Since each train travels at a speed of 45 km / h, the conductors approach each other at a speed of 45 + 45 = 90 km / h, or 25 m / s. The required time is 500 ÷ 25 = 20 s.

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12. How old?

Imagine that you are a taxi driver. Your car is painted yellow and black and you have been driving it for 10 years. The bumper of the car is badly damaged, the carburetor and air conditioner are junk. The tank holds 60 liters of gasoline, but is now only half full. The battery needs to be replaced: it does not work well. How old is a taxi driver?

From the very beginning, the problem says that you are a taxi driver. This means that the driver is as old as you are.

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This selection is based on materials from the book "" by I. Gusev and A. Yadlovsky. In it you can find the best puzzles, without which not a single scientific and educational publication of the Soviet Union could do at one time.