48th Eötvös Competition Problems 1944

1.  Prove that 46²ⁿ⁺¹ + 296·13²ⁿ⁺¹ is divisible by 1947.

2.  Show that any graph with 6 points has a triangle or three points which are not joined to each other.

3.  What is the smallest number of disks radius ½ that can cover a disk radius 1?