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):
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
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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.
