A basket of fruits is being arranged out of apples, bananas and oranges . What is the smallest number of pieces of fruit that need to be put into the basket to ensure that there are at least 8 apples or at least 6 bananas or at least 9 oranges ?
So my teacher solved this using the strongform of the pigeonhole principle , and arrived at 21 as the answer . But I applied only common sense and stated the answer is 6, since if you put in just 6 bananas into the basket , the condition is satisfied . Incase all 3 fruits need to be there , the answer is obviously 8 . Aparently that is incorrect . Help me out , Am I blind to something in this sum or is my teacher too stuck up in her own ways ?
(Also , how am I supposed to ask world problems ? They dont fit into the title of a question)
The question is asking you to prepare for a worst-case scenario, not a best-case scenario. Imagine a game where you're not the one in charge of choosing the fruits - your opponent is in charge, and they don't want you to win. The opponent can get away with choosing 20 fruits (7 apples, 5 bananas, and 8 oranges) before the 21st fruit finally forces your condition to be satisfied.