olymmath

KURSCHAK 1947

Kürschák Competition 1947.

Other problems

Problem 1

Prove that 462n+1+296⋅132n+146^{2n+1} + 296 \cdot 13^{2n+1} is divisible by 19471947 .

Problem 2

Show that any graph with 66 points has a triangle or three points which are not joined to each other.

Problem 3

What is the smallest number of disks radius 12\frac12 that can cover a disk radius 11 ?