problems in competition
Source: Italy TST 2000
September 27, 2008
combinatorics unsolvedcombinatorics
Problem Statement
On a mathematical competition problems were given. The final results showed that:
(i) on each problem, exactly three contestants scored points;
(ii) for each pair of problems, exactly one contestant scored points on both problems.
Prove that if , then there is a contestant who got points on each problem. Is this statement necessarily true if n \equal{} 7?