Patterns in multiple-choice tests

An urban legend is that some multiple choice tests are written with patterns or codes in the answers. For example, a test of 12 questions, each question having four possible answers, could supposedly have a cyclical answer sequence of:

:D, B, C, A, D, B, C, A, D, B, C, A

The sequence "DBCA" is repeated. Another possibility is a sequence which would be a palindrome:

:A, C, B, B, D, A, A, D, B, B, C, A

A similar belief is the possible hidden meaning(s) behind answer "runs", strings of the same letter:

:A, D, C, D, B, A, A, A, A, A, D, C

Despite the lack of a true pattern, a sequence like this is conspicuous due to the very small probability that a string of five A's could occur randomly. However, it is important to note that this sequence is no more or less likely (assuming that the probability of each of A, B, C, or D being chosen is 0.25) than any of a huge number of much less 'conspicuous' sequences of the same length, eg.:

:A, C, D, A, B, B, C, B, D, B, C, D

Runs of identical answers often cause anxiety in students, who believe due to human misconceptions of randomness that such sequences are statistically unlikely. For this reason, some large-scale tests such as the SAT deliberately avoid runs of four or more identical answers, using them less often than they would occur statistically in a uniformly random sequence. This phenomenon has been documented by test preparation services such as The Princeton Review, who advise students to carefully review such sequences for possible incorrect answers.

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