Discussion
Suppose that for any group of n people has the property that at least two of them have birthdays that occur on the same day of the week. Then which one of the following must be the value of n ?
Answer: A
The value that must work is 10.
There are 7 days of the week. By the pigeonhole principle, any group of 8 or more people must contain two born on the same day of the week, while a group of 7 or fewer can have everyone on a different day.
So the property is guaranteed only when \(n \ge 8\). Of the options, only 10 qualifies. With 7, 6 or 5 people each person can have a different day, so the property can fail.
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