49th Eötvös Competition Problems 1945

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

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

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