4

Part of 2005 Korea Junior Math Olympiad

Problems(1)

11 students in a test, for any 2 qestions exactly 6 solved 1 correctly

Source: KJMO 2005 p4

11

students take a test. For any two question in a test, there are at least

6

students who solved exactly one of those two questions. Prove that there are no more than

12

questions in this test. Showing the equality case is not needed.