Functional equation dependent on a constant

Functional equation dependent on a constant

Understand the problem Find all real numbers  for which there exists a non-constant function  satisfying the following two equations for all i)  andii)  Source of the problem Baltic Way 2016 Topic Functional Equations Difficulty Level Easy Suggested Book Functional...
Pigeonhole principle exercise

Pigeonhole principle exercise

Understand the problem We are given  sets of size  each. The size of the intersection of any two sets is exactly . Prove that all the sets have a common element. Source of the problem Austrian-polish mathematical Olympiad 1978 Topic Combinatorics Difficulty Level Easy...
Lottery tickets

Lottery tickets

Understand the problem Each lottery ticket has a 9-digit number, which uses only the digits 1, 2, 3. Each ticket is coloured red, blue or green. If two tickets have numbers which differ in all nine places, then the tickets have different colours. Ticket 122222222 is...