SOLUTION: Suppose there are 40 students in a class. Is there a month in the year in which at least 4 students were born?

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Question 1183662: Suppose there are 40 students in a class. Is there a month in the year in which at least 4 students were born?
Found 2 solutions by Solver92311, ikleyn:
Answer by Solver92311(821)   (Show Source): You can put this solution on YOUR website!


If there are 40 students and only 12 months in which any of them could have been born, then the average number of birthdays per month is three and one-third. Since you cannot have a third of a birthday, it will be better to consider integer division of 40 by 12, namely a quotient of 3 and a remainder of 4. Those four must have been born in a month or months that already have 3 birthdays, so yes, at least one month has 4 birthdays. In fact, if 4 is the most birthdays in any given month, then there are 4 months that have 4 birthdays each.


John

My calculator said it, I believe it, that settles it

From
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Answer by ikleyn(52908)   (Show Source): You can put this solution on YOUR website!
.

As it is worded,  printed,  posted and presented,  this formulation is  INCORRECT  and is good for re-cycling,  ONLY.


The correct formulation is as follows:

            Suppose there are  40  students in a class.  Prove that
            there is a month in the year in which at least  4  students were born.


The solution is in couple of lines. 

    If we assume, in opposite, that the number of birthdays is no more than 3 in each of 12 months of the year,

    then the total number of students in the class is no more than 3*12 = 36.


    It contradicts to the given part that the number of students in the class is 40.


    The contradiction proves the statement.



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