What is the smallest number of a class to guarantee that two students have their birthdays on the same day of the week?

Question

My answer: k=7 days in a week r=2 according to the GPP(Generalized pigeonhole principle) the smallest number N=k(r-1)+1

N=7(2-1)+1=8

therefor 8 will be the smallest number.

is this correct?

Answer 1

Yes. If there are seven people, then they may all have one day of the week for themselves. If there are more than seven (i.e. at least eight) then someone will have to share. In my opinion, you shouldn't really need a formula to come to this answer, but whatever floats your boat.