# least number of items required to satisfy one of three given conditions?

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 teacher didn't explain the problem correctly. If you can't see into the basket and you can't influence how the bag boy picks fruit and all you know is "there are n pieces of fruit" what is the smallest number that will let you know for certain. If you are told: 12 fruit. It's possible you have 8 oranges and 4 apples. So no go. You need more than 12. – fleablood Sep 28 '16 at 6:53
• My man , there cannot exist ANY number that will let me know for certain that the 'bag boy' has satisfied the condition . Say I'm told he has put 749 pieces of fruit in the basket . He could have just picked 749 bananas . Or 747 bananas , 1 orange and 1 apple . – Nikhil Kapoor Sep 28 '16 at 13:04
• " He could have just picked 749 bananas" which is at least six bananas. "Or 747 bananas , 1 orange and 1 apple" which is at least six bananas. "My man". I'm not your man. – fleablood Sep 28 '16 at 16:43
• Alright then ... My Woman , I now get your point . least number of fruits ... that makes sense . My earlier comment was indeed quite silly . In my defence , my teacher could have worded the question better . – Nikhil Kapoor Sep 30 '16 at 12:21