Hales–Jewett theorem
In mathematics, the Hales–Jewett theorem is a fundamental combinatorial result of Ramsey theory, named after Alfred W. Hales and Robert I. Jewett, that concerns the degree to which high-dimensional objects must necessarily exhibit some combinatorial structure. An informal geometric statement of the theorem is that for any positive integers n and c there is a number H such that if the cells of a H-dimensional n×n×n×...×n cube are colored with c colors, there must be one row, column, or certain diagonal (more details below) of length n all of whose cells are the same color.