This short chapter serves as a yet one more example of how the p-adic ergodic theory is applied to a “non-dynamical” area of mathematics, the combinatorics, namely, to the theory of Latin squares. Latin squares are used in a number of applications, from games to experiment design, password distribution in public networks, etc. In this chapter, we explain how to contract large Latin squares and pairs of orthogonal Latin squares which can be implemented as straight line programs (SLP) even on very weak computers or in constraint environment.