Combinatorial explosion is the term applied to certain kinds of problem where the complexity grows very rapidly. This arises when all combinations of, even relatively small, sets of elements need to be considered. For example, imagine we are looking at choices of flavours in ice-cream sundaes (ignoring how much, it is a very generous gelateria). If we have two flavours, strawberry and banana, then there are only four options: plain strawberry; plain banana; strawberry and banana; and (for the restrained) none at all. If there are three flavours, there are 8 options; for four flavours 16; and for a gelateria with a dozen flavours more than 4096.
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