Question

Плиз!Очень срочно!Не игнорьте Дед Мазай засеял морковью 50 рядок, причём на каждой у него выросло не больше 40 морковок.Докажите,что найдутся грядки,где число выросших морковок совпадёт. С легендой плиз

Answer 1

Так как число грядок превышает число 40, то колво морковок должно совпасть не менее 10 раз

Answer 2

Problem Statement

The problem states that Grandpa Mazai planted 50 rows of carrots, with no more than 40 carrots growing in each row. The task is to prove that there will be at least two rows where the number of grown carrots is the same.

Proof by Pigeonhole Principle

To prove that there will be at least two rows with the same number of grown carrots, we can use the Pigeonhole Principle. The Pigeonhole Principle states that if you have more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon.

In this case, the rows of carrots are the pigeonholes, and the number of grown carrots in each row is the pigeons. We have 50 rows (pigeonholes) and a maximum of 40 grown carrots in each row (pigeons).

Since we have more rows (50) than the maximum number of grown carrots in a row (40), by the Pigeonhole Principle, there must be at least two rows with the same number of grown carrots.

Therefore, we have proven that there will be at least two rows where the number of grown carrots is the same.

Example

To illustrate this, let's consider a simplified example with only 5 rows and a maximum of 4 grown carrots in each row:

| Row | Number of Grown Carrots | |-----|------------------------| | 1 | 3 | | 2 | 2 | | 3 | 4 | | 4 | 1 | | 5 | 3 |

In this example, we can see that rows 1 and 5 both have 3 grown carrots. This demonstrates that there are indeed at least two rows with the same number of grown carrots.

Conclusion

Using the Pigeonhole Principle, we have proven that in Grandpa Mazai's case, where he planted 50 rows of carrots with no more than 40 carrots growing in each row, there will be at least two rows where the number of grown carrots is the same.