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)

  • $\begingroup$ 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. $\endgroup$ – fleablood Sep 28 '16 at 6:53
  • $\begingroup$ 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 . $\endgroup$ – Nikhil Kapoor Sep 28 '16 at 13:04
  • $\begingroup$ " 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. $\endgroup$ – fleablood Sep 28 '16 at 16:43
  • $\begingroup$ 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 . $\endgroup$ – Nikhil Kapoor Sep 30 '16 at 12:21

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.

  • $\begingroup$ Wait what ? I really must respectfully disagree . How can a maths question be about opinion ? the question gave a condition , and I satisfied it . Thats all that there is to it , no ? $\endgroup$ – Nikhil Kapoor Sep 28 '16 at 6:37
  • $\begingroup$ The answer is 0. If the basket already has the fruit in it you don't need to put any more fruit into it. So nyah, nyah to you. You aren't the only one who can be a snot - nose know it all punk. the question was ambiguously worded. Adriano explained what it should be. Nothing to do with opinion. $\endgroup$ – fleablood Sep 28 '16 at 7:08
  • $\begingroup$ Oh I'm sorry , I did not know the question explicitly stated the basket already has fruits . $\endgroup$ – Nikhil Kapoor Sep 28 '16 at 12:59
  • $\begingroup$ The point being you misunderstood the quesition. Adriano explained it perfectly but rather than listen and try to learn the math your instructor is trying to teach, you insist that your smart ass interpretation had to be right because some how because math isn't about "opinions", word problems once stated don't have to mean what you don't want them to mean. So I made a joke where I smart-assedly reinterpreted the question for my own purposes. $\endgroup$ – fleablood Sep 28 '16 at 16:48
  • $\begingroup$ The question is: You have a basket of fruit that can have any combination of apples, bananas, and oranges. Your are told how many fruit in it. From that you can conclude you must have either at least six bananas, or at least nine oranges, or at least eight apples. What is the least number so that you can (correctly) make such a conclusion based only on the number? $\endgroup$ – fleablood Sep 28 '16 at 16:53

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