The seller sells a hat worth 10p suitable buyer. Hat problem by Leo Tolstoy. Did you manage to figure it out?

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Lev Nikolaevich Tolstoy, as you know, was not only a “great Russian writer”, but also a talented teacher (by the way, 4brain has something useful for teachers). His approach was an individual attitude to each student and the absence of traditional school discipline. In the Yasnaya Polyana school, the children sat where they wanted, for as long as they wanted, and for as long as they wanted. The main task of the teacher, according to Tolstoy, was to interest students in various examples, life tasks, and if there is interest, then the child himself will want to learn and learn more (here is such a “Tolstoy”).

And one of the examples of the ability to interest students was the famous problem about the hat, and this problem has reincarnated today and has become a real Internet meme. The condition of the task is:

The seller sells a hat. Worth 10 r. The buyer comes up, measures and agrees to take it, but he only has a banknote of 25 rubles. The seller sends the boy with these 25 rubles. exchange for a neighbor. The boy comes running and gives 10+10+5. The seller gives a hat and change of 15 rubles. After some time, a neighbor comes and says that 25 rubles. fake, demands to give her money. What should I do. The seller climbs into the cash register and returns the money to her. How much was the seller deceived (including the cost of the hat)?

At first glance, the conditions are simple, but practice shows that there are more wrong answers than correct ones. And if you want to test yourself, try to find the answer yourself before you go to the solution ( clue: there are no tricks in the task that are designed to divert attention, and there is also no dual interpretation of terms).

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Answer and solution

Before showing you the solution to this problem, I would like to note that there are many solutions. But I noted that it is rare to find such a solution that could prove its truth for absolutely any person the first time.

The most popular solution goes something like this:

The seller gave the buyer 15 rubles from his pocket and a hat that costs 10 rubles. And the saleswoman should not be taken into account at all, since he took 25 rubles from her and returned it back. That is, the correct answer is 25 rubles.

Some conclusions seem doubtful to me, because they are (that is, a number of premises are omitted for them). Therefore, let's try to understand the situation using a simple accounting form:

Indeed, it turns out that the seller, compared to the initial situation (before all transactions), remains:

Without a hat
Without 15 rubles at the box office (compared to the amount that was originally)

I would also like to note that often, when people give an initially wrong solution, they begin to engage in demagogy. For example, they find fault with the word "deceived", saying that perhaps the buyer did not know that he was giving counterfeit money (but in this case, those who produced the counterfeit bill were deceived). Or they say that in the end, the seller must return a counterfeit bill, which is also worth something. Naturally, any task is a model of a life situation and it does not describe all the subtleties, but allows any words to be interpreted as you like.

But many of these arguments are rather weak, which allows us to say that the correct solution to this problem is still.

In addition to the fact that Lev Nikolaevich Tolstoy was a great Russian writer, he was also known as a talented teacher. His approach was the absence of traditional school discipline and an individual approach to each student. In the Yasnaya Polyana school, the children sat where they wanted, for as long as they wanted, and for as long as they wanted. The main task of the teacher, according to Tolstoy, was to interest students in various examples and life tasks, and if there is interest, then the child himself will want to learn and learn more.

According to legend, this problem was invented by Leo Tolstoy for the second grade of a parochial school. Now only 30% of high school students, only 20% of university students, and only 10% of employees of banks and credit institutions can solve it correctly. The condition of the task is:

The seller sells a hat. Worth 10 r. The buyer comes up, measures and agrees to take it, but he only has a banknote of 25 rubles. The seller sends the boy with these 25 rubles. exchange for a neighbor. The boy comes running and gives 10+10+5. The seller gives a hat and change of 15 rubles. After some time, a neighbor comes and says that 25 rubles. fake, demands to give her money. What should I do. The seller climbs into the cashier and returns the money to her. How much was the seller deceived?

At first glance, the solution lies on the surface. However, the task is misleading for many and causes a lot of controversy.

Solution

In fact, there are many solutions. The "classic" answer goes like this:

If this answer confused you, let's try to explain the solution using the example of an accounting form.

September 11, 2015 10:06

By Fabiosa

nnm.me

The seller sells a hat. Worth 10 r. The buyer comes up, measures and agrees to take it, but he only has a banknote of 25 rubles. The seller sends the boy with these 25 rubles. exchange for a neighbor. The boy comes running and gives 10+10+5. The seller gives a hat and change of 15 rubles. After some time, a neighbor comes and says that 25 rubles. fake, demands to give her money. What should I do. The seller climbs into the cashier and returns the money to her. How much was the seller deceived?

At first glance, the solution lies on the surface. However, the task is misleading for many and causes a lot of controversy.

Solution

In fact, there are many solutions. The "classic" answer goes like this:

If this answer confused you, let's try to explain the solution using the example of an accounting form:

In fact, it turns out that the seller, compared to the initial situation (before all transactions), remains:

without a hat;
without 15 rubles at the box office (compared to the amount that was originally).

Here is such a wise problem from Leo Tolstoy, which to this day causes a lot of controversy!

The main task of the teacher, according to Tolstoy, was to interest students in various examples, life tasks, and if there is interest ...

Lev Nikolaevich Tolstoy, as you know, was not only a "great Russian writer", but also a talented teacher. His approach was an individual attitude to each student and the absence of traditional school discipline.

In the Yasnaya Polyana school, the children sat where they wanted, for as long as they wanted, and for as long as they wanted. The main task of the teacher, according to Tolstoy, was to interest students in various examples, life tasks, and if there is interest, then the child himself will want to learn and learn more (this is such a “Tolstoy maieutics”).

And one of the examples of the ability to interest students was the famous problem about the hat, and this problem has reincarnated today and has become a real Internet meme.

The condition of the task is:

The seller sells a hat. Worth 10 r.

The buyer comes up, measures and agrees to take it, but he only has a banknote of 25 rubles.

The seller sends the boy with these 25 rubles. exchange for a neighbor.

The boy comes running and gives 10+10+5. The seller gives a hat and change of 15 rubles.

After some time, a neighbor comes and says that 25 rubles. fake, demands to give her money.

What should I do. The seller climbs into the cash register and returns the money to her.

How much was the seller deceived (including the cost of the hat)?

At first glance, the conditions are simple, but practice shows that there are more wrong answers than correct ones. And if you want to test yourself, try to find the answer yourself before you go to the solution ( hint: there are no tricks in the problem that are designed to divert attention, and there is also no dual interpretation of terms)

Answer and solution

The most popular solution goes something like this:

Some conclusions seem doubtful to me, since they are enthymemes (that is, a number of premises are omitted for them). Therefore, let's try to understand the situation using a simple accounting form:

Indeed, it turns out that the seller, compared to the initial situation (before all transactions), remains:

Without a hat
Without 15 rubles at the box office (compared to the amount that was originally)

Or they say that in the end, the seller must return a counterfeit bill, which is also worth something. Naturally, any task is a model of a life situation and it does not describe all the subtleties, and the peculiarities of our language allow any words to be interpreted in any way.

But many of these arguments are rather weak, which allows us to say that the correct solution to this problem is still: 25 rubles.published