Question 55
1. $67$ students write an exam. The exam consists of $6$ multiple-choice questions, all of which have to be answered with yes or no. Each student answers all $6$ questions. A correct answer to the $k$-th question gives $k$ points, a wrong answer $-k$ points.
a) Show that at least two students filled out the exam sheet equally.
b) show that at least four students scored the same number of points.
a) Show that at least two students filled out the exam sheet equally.
b) show that at least four students scored the same number of points.