10 thoughts on “Pigeonhole Principle – 4

  1. This is exactly what I was searching for. I have come across similar questions and was not sure how to solve them. Thanks a lot and keep up the good work 🙂

  2. When cubes there are only 5 possible remainders… How did you find this out ? Is there a method to find this because this could be very helpful during exams. Or is it just trial and error ?

  3. Hi J! I found your post really helpful.. but I am not getting the solution of q1. If it was asked to have the minimum number of boxes with the same number of oranges, then the answer would had been 4 , am I right? Your post probably has an error in the final answer part.. 🙂

    • No, the minimum value would have been 0. There could be 0 boxes having a particular number! But this is a different question – it is asking for a minimax, that is, the minimum value of the maximum possible number. Read the earlier 3 posts again.

      Let me phrase it differently. Suppose I say, you want to find the mode of the distribution, what could be the least possible value for the mode? You will find that it could be 5 but not less.


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