Catalan Numbers

The Catalan numbers, named for the Belgian mathematician Eugène Charles Catalan, are a sequence of natural numbers that are important in combinatorial mathematics. The sequence begins:

1, 1, 2, 5, 14, 42, 132, ...

The Catalan numbers are solutions to numerous counting problems which often have a recursive flavour. In fact, one author lists over 60 different possible interpretations of these numbers. For example, the nth Catalan number is the number of full binary trees with n internal nodes, or n+1 leaves. It is also the number of ways of associating n applications of a binary operator as well as the number of ways that a convex polygon with n + 2 sides can be cut into triangles by connecting vertices with straight lines.

Eight Eight=1000

1. 888+88+8+8+8=1000
2. 8+8/8(8*8*8-8)-8=1000
3. 8888-888/8=1000