Consider another illustration. The two letters X and Y can be combined in four different two-letter combinations (XX, XY, YX and YY). They can be combined in eight different ways for three-letter combinations (XXX, XXY, XYY, XYX, YXX, YYX, YXY, YYY), sixteen ways for four-letter combinations, and so on. The number of possible combinations grows exponentially—22, 23, 24, and so on—as the number of letters in the sequence grows. Mathematician David Berlinski calls this the problem of “combinatorial inflation,” because the number of possible combinations “inflates” dramatically as the number of
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