Question

Укажите наименьшее число яблок, которые нужно одновременно взять из ящика (не заглядывая в него), что бы среди них оказалось хотя бы 2 яблока одного сорта, если в ящике находятся:а) двух сортовб) трех сортовв) четырех сортов г) n сортовЖелательно с решением. Заранее спасибо :3

Answer 1

1) 3 яблока;2) 4 яблока;3) 5 яблок;4) n+1 яблок.Объяснение: если доставать яблок столько же, сколько и сортов, то они могут быть все разных сортов.Если же достfвать яблок на одно больше, чем количество сортов, и даже если все кроме последнего разных сортов, то последнее обязательно будет одного и того же сорта с каким-нибудь из остальных.

Answer 2

Finding the Minimum Number of Apples

To find the minimum number of apples needed to ensure at least 2 apples of the same type are selected without looking into the box, we can use the concept of the Pigeonhole Principle.

a) Two Types of Apples: To ensure at least 2 apples of the same type are selected from a box containing two types of apples, we need to take 3 apples simultaneously. This is because if we take 2 apples, they could be one of each type, but taking a third apple guarantees that at least 2 will be of the same type.

b) Three Types of Apples: In a box containing three types of apples, we need to take 4 apples simultaneously to ensure at least 2 apples of the same type are selected. This is based on the Pigeonhole Principle, where if there are more pigeons than pigeonholes, at least one pigeonhole must contain more than one pigeon.

c) Four Types of Apples: For a box containing four types of apples, we need to take 5 apples simultaneously to guarantee at least 2 apples of the same type are selected. This is because with 4 types, taking 4 apples could result in one of each type, but taking a fifth apple ensures at least 2 will be of the same type.

d) n Types of Apples: For a box containing n types of apples, we need to take (n+1) apples simultaneously to ensure at least 2 apples of the same type are selected. This follows the same logic as the previous scenarios, where the number of apples needed is one more than the number of types to guarantee at least 2 of the same type.

Therefore, the minimum number of apples needed to ensure at least 2 apples of the same type are selected from a box containing: - Two types of apples is 3 apples. - Three types of apples is 4 apples. - Four types of apples is 5 apples. - n types of apples is (n+1) apples.

I hope this helps! If you have further questions, feel free to ask!