Answer:  The professor simply assumes to be fake any series that does not include at least one run of 6 heads in a row or six tails in a row.

The trick is based on Bayes' theorem, which informs us that any truly random flip of a coin will generally (don't know exact %) include a run of six.  But that's not how our pattern-fixated minds think of randomness, so runs this long look non-random to people faking results.

See also:  Random Coin Flips 2

Source:  Leonard Mlodinow, "The Drunkard's Walk:  How Randomness Rules our Lives"

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