## Task 2 - 270922

In a "Hungarian domino game" with the numbers $0,1, \ldots, 9$, each tile is divided into two halves, each half bearing one of the numbers.

In a game, all combinations of any two of the numbers $0,1, \ldots, 9$ appear exactly once (including those where the same number appears on both halves of a tile).

A "chain" is formed by placing several tiles next to each other such that adjacent halves of neighboring tiles always bear the same number (domino game rule).

A chain is called "closed" if the two tile halves at the free ends of the chain also bear the same number (so that the chain, if it consists of enough tiles, can be led back to its beginning and closed there).

a) Determine the number of all tiles belonging to a "Hungarian domino game"!

b) Determine the maximum number of such tiles from a game that can form a closed chain!