Given a sequence consisting of the whole numbers 1, 4, 9, 16, 25, 36, and 49, what number comes next in the sequence?
The most likely answer is 64–the next number in a sequence of squares of consecutive integers, starting with 1.
Such sequence puzzles are a staple of textbook exercises, brainteaser collections, and various intelligence and aptitude tests. Some sequences are easy to figure out, some have multiple interpretations, and others can require considerable head-scratching before the pattern becomes evident.