If k is a positive integer and k + 1 objects are placed into k boxes, then at least one box contains two or more objects.

Example: if a theater holds 1300 people, how many seats need to be filled to ensure that at least two people have the same first and last initials?

Our first initial we have 26 options

Our last initals we have 26 options

Therefore 26^2 ways to make first and last initials.

If we have 26^2 people, everyone could fill up all those possible sets of initials

If we add 1 = 26^2 +1, someone will have the same first and last initials as somebody else. Therefore the solution is 26^2 +1

Reply to Thread

First initial we have 36 options

Last initial we have 36 options

Therefore 36^2 to make first and last initials or 1,296.

If we just add one we'd get 1,297 combinations with at least one having the same first and last as everyone else.So certainly your 1300 seat theater will still have at least one first and last initial in common.

Here's my question:If we filled every seat in the theater shouldn't the other 3 also have an initial in common with someone else?