Question

под крышкой каждой бутылки мехмат-колы нарисована одна из трех картинок:звездочка,карандаш или рожица.Если собрать две крышки с одинаковыми картинками то их можно обменять в буфете на шоколадку.Сколько бутылок надо купить, чтобы точно получить две шоколадки?

Answer 1

Рассмотрим самый "крайний" случай (то есть когда попадаются сначала 3 разных бутылки). Вытаскиваем 3 разных бутылки: у нас 3 разных крышки. Надо вытащить еще одну бутылку, и тогда к любой из крышек добавится одна такая же. Далее еще один крайнй случай: попадается та крышка, номинал который уже есть в кол-ве 2 штук. Но если вытащить еще одну бутылку, то крышка присоединится к одной такого же цвета. Итого 5 бутылок

Answer 2

Problem Analysis

In this problem, there are three possible pictures that can be found under the cap of each bottle of Mehmatakola: a star, a pencil, or a smiley face. If two caps with the same picture are collected, they can be exchanged for a chocolate bar at the cafeteria. The task is to determine how many bottles need to be purchased in order to guarantee receiving two chocolate bars.

Solution

To solve this problem, we need to consider the worst-case scenario, which is that we collect caps with different pictures until we have enough to exchange for two chocolate bars.

Let's analyze the possible scenarios step by step:

1. First bottle: When we purchase the first bottle, we have no caps to exchange, so we cannot get any chocolate bars.

2. Second bottle: When we purchase the second bottle, we have one cap. Since we don't have any other caps, we cannot exchange it for a chocolate bar.

3. Third bottle: When we purchase the third bottle, we have two caps. In the worst-case scenario, these two caps will have different pictures. Therefore, we still cannot exchange them for a chocolate bar.

4. Fourth bottle: When we purchase the fourth bottle, we have three caps. In the worst-case scenario, at least two of these caps will have different pictures. Therefore, we still cannot exchange them for a chocolate bar.

5. Fifth bottle: When we purchase the fifth bottle, we have four caps. In the worst-case scenario, at least three of these caps will have different pictures. Therefore, we still cannot exchange them for a chocolate bar.

Based on this pattern, we can conclude that we need to purchase at least five bottles in order to guarantee receiving two chocolate bars. This is because we need to collect at least four caps with the same picture, and the worst-case scenario is that the first four caps we collect will have different pictures.

Conclusion

To guarantee receiving two chocolate bars by exchanging caps from Mehmatakola bottles, you need to purchase at least five bottles.

Please let me know if you need any further assistance!