Question

Имеется тысяча билетов с номерами 000,001,002,...,998,999 и сто ящиков с номерами 00,01,02,...,98,99. билет разрешается опускать в ящик, если номер ящика получается зачёркиванием одной цыфры в записи номера билета. может ли после некоторого раскладывания всех билетов по указанному правилу хотя бы один ящик оказаться пустым

Answer 1

Нет не может быть ведь

Answer 2

Нет,ну может быть,потому что все цифры совпадают!

Answer 3

Problem Analysis

The problem involves 1000 tickets numbered from 000 to 999 and 100 boxes numbered from 00 to 99. A ticket can be placed in a box if the box number can be obtained by crossing out one digit in the ticket number. The question is whether, after distributing all the tickets according to the given rule, it is possible for at least one box to be empty.

Solution

To solve this problem, we can use the Pigeonhole Principle, which states that if n items are put into m containers, and n > m, then at least one container must contain more than one item.

Let's consider the boxes as containers and the tickets as items. We need to determine if it's possible to distribute the tickets into the boxes such that at least one box remains empty.

Application of Pigeonhole Principle

The Pigeonhole Principle can be applied as follows: - There are 100 boxes and 1000 tickets. - Each ticket can be placed in one of 9 possible boxes (obtained by crossing out one of the digits). - By the Pigeonhole Principle, if there are more "pigeons" (tickets) than "pigeonholes" (boxes), at least one box must contain more than one ticket, and therefore at least one box will be empty.

Conclusion

Based on the application of the Pigeonhole Principle, it is not possible to distribute all the tickets according to the given rule without leaving at least one box empty. Therefore, after distributing all the tickets according to the given rule, at least one box will be empty.

I hope this explanation helps! If you have further questions or need additional clarification, feel free to ask.