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You might look for algorithms that, though not guaranteed to run quickly, seem likely to do so most of the time.

Joey: So you really did graduate from computer engineering? Unfortunately, proving inherent intractibility can be just as hard as finding efficient algorithms.

The theory of NP-completeness provides many straightforward techniques for proving that a given problem is "just as hard" as a large number of other problems that are widely recognize as being difficult and that have been confounding the experts for years.

Armed with these techniques, you might be able to prove that the bandersnatch problem is NP-complete and march into your boss's office and announce: I can't find an efficient algorithm, but neither can all these famous people.

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