&gt;  Nobody sorts by comparing all N! permutations and picking the correct one. (Well, I certainly don&#x27;t.)<p>You can usually make a problem seem <i>harder</i> than it actually (from a complexity point of view) is by phrasing it in terms of directly picking from permutations or combinations.<p>An example: finding the longest common substring for N strings can also be phrased as picking from a quadratic number of of substrings, but has a linear-time algorithm (using suffix trees).