MathDB
Examination

Source:

June 27, 2012
invariantpigeonhole principle

Problem Statement

A group of 6767 students pass their examination consisting of 66 questions, labeled with the numbers 11 to 66. A correct answer to question nn is quoted nn points and for an incorrect answer to the same question a student loses nn point.
a) Find the least possible positive difference between any 22 final scores b) Show that at least 44 participants have the same final score c) Show that at least 22 students gave identical answer to all six questions.
Back to ProblemsView on AoPS