Posted by **skye** on Monday, July 30, 2012 at 8:13pm.

At a certain hospital, 89 children were born in the month of June. If more children were born on the fifteenth of June than on any other day in June, what is the least number of children that could have been born on the fifteenth of June?

The number of days is not given, is it possible to solve this problem without it?

- sat math -
**MathMate**, Monday, July 30, 2012 at 8:34pm
There are 30 days in June, and 89 children born.

Suppose 60 of the 89 were spread over 30 days evenly, so every day, there are two newborns, leaving 28 to be distributed over 29 days.

If the remainder is spread out over the remaining days, so some have 3 and some have 2 newborns a day, then the least number of newborns on the 15th is 4 for this to happen (best case).

On the other hand, do not confuse with the problem of "what is the least number of children born on the 15th so that no matter what happens, there are more newborns on the 15th than any other day?"

In this case, the answer would be (89+1)/2=45 (worst case)

- sat math -
**skye**, Monday, July 30, 2012 at 9:44pm
thanks! :)

- sat math :) -
**MathMate**, Monday, July 30, 2012 at 9:55pm
You're welcome!

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