Combinatorial Explosion

The number of Latin squares as a function of the order (independent of the set from which the entries are drawn) (sequence A002860 in the OEIS) provides an example of combinatorial explosion as illustrated by the following table. One example in a game where combinatorial complexity leads to a solvability limit is in solving chess (a game with 64 squares and 32 pieces). Adding another boolean variable B will give the system four possible states, A = true and B = true, A = true and B = false, A = false and B = true, A = false and B = false.

Source: en.wikipedia.org