Counting Problem?

I have a counting problem that I'm grappling with:





A professor gives a multiple choice (a,b,c,d) quiz with ten questions. Assume no questions can be left blank. How many students are needed in the class to guarantee that three students turn in identical answer sheets?





Any help with this problem is appreciated.

Counting Problem?
10 questions, each with four possible responses.





There are 4^10 total possible answer sheets.





To guarantee three have identical answer sheets you need


2*(4^10) + 1


students. This is a worst-case scenario, as with 2*4^10 students it is possible that each possible answer sheet occurs twice. So, with one more you can pigeon-hole it. Hope this helps.
Reply:Just 3, they could be looking over each others shoulder!
Reply:I am not sure of my answer. I don't know if this problem could be solved as is!

boots