how many distinct, positive integers would we have to choose from the numbers 1,2,3,...,2014 to guarantee that some pair of the chosen values has a difference that is a multiple of 5? (Pigeonhole Principle)

Question

anonymous · Answer

choosing 1 and 6 would work

anonymous · Answer

Yes, but the question is asking what is the minium number of values that we have to choose to guarantee that at least 2 of them has a difference that is a multiple of 5, not just pick two values with a difference that is a multiple of 5.