KURSCHAK 1948

Knowing that $23$ October $1948$ was a Saturday, which is more frequent for New Year's Day, Sunday or Monday?

A convex polyhedron has no diagonals (every pair of vertices are connected by an edge). Prove that it is a tetrahedron.

Prove that among any $n$ positive integers one can always find some (at least one) whose sum is divisible by $n$ .