Abstract: Godel's discoveries during the early 20th century, regarding the strength of axiomatic systems in mathematics, marked the end of the Hilbert program. It ended the era in which many believed that mathematics could be finitely formalized. However, Godel's results are existence results, much like Cantor's proof of the existence of transcendental numbers. It was not until the 1980's that examples of natural independence phenomena were discovered. The result presented in this talk is one of them. It can be viewed as a game played on a finite tree. It is a completely finitistic combinatorial true statement whose truth cannot be determined using only finitistic arguments.