MathDB

14 students attend the IMO training camp. Every student has at least

k

favourite numbers. The organisers want to give each student a shirt with one of the student's favourite numbers on the back. Determine the least

k

, such that this is always possible if:

a)

The students can be arranged in a circle such that every two students sitting next to one another have different numbers.

b)

7

of the students are boys, the rest are girls, and there isn't a boy and a girl with the same number.

Problem Statement