Question

В городе живёт 200 тыс. жителей. Докажите, что в городе найдутся хотя бы 2 человека с одинаковым числом волос на голове. Считайте, что у человека на голове не больше 150 тыс. волос.

Answer 1

Пусть у первых 150 тыс. Жителей волос от 1 до 150 тыс, тогда дальше идёт повторяющееся количество

Answer 2

Proof that at least two people in the city have the same number of hairs on their heads

To prove that in a city with 200,000 inhabitants, there are at least two people with the same number of hairs on their heads, 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, we can consider each person in the city as a pigeon and the number of hairs on their heads as pigeonholes. Since the maximum number of hairs on a person's head is 150,000, we have 150,000 pigeonholes.

According to the Pigeonhole Principle, if we have more pigeons (people) than pigeonholes (possible number of hairs), then at least one pigeonhole must contain more than one pigeon. In other words, if we have more than 150,000 people in the city, there must be at least two people with the same number of hairs on their heads.

Given that the city has 200,000 inhabitants, which is greater than the number of pigeonholes (150,000), we can conclude that there are at least two people in the city with the same number of hairs on their heads.

Therefore, in a city with 200,000 inhabitants, there will be at least two people with the same number of hairs on their heads.