TH-TMO 2016 Problem 10

A Pattano coin is a coin which has a blue side and a yellow side. A positive integer not exceeding $100$ is written on each side of every coin (the sides may have different integers). Two Pattano coins are identical if the number on the blue side of both coins are equal and the number on the yellow side of both coins are equal. Two Pattano coins are pairable if the number on the blue side of both coins are equal or the number on the yellow side of both coins are equal. Given $2559$ Pattano coins such that no two coins are identical. Show that at least one Pattano coin is pairable with at least $50$ other coins