A reasoning problem in which the task is to connect nine dots, arranged in a square, by four straight lines drawn without lifting the pen from the paper and without retracing any lines (see illustration). If symmetric solutions are considered equivalent, then it is a well-defined problem, and it should be easy, because there are only a few possibilities to try, but it is difficult in practice for psychological reasons. Fewer than 5 per cent of undergraduate students manage to solve it in two minutes, and most are convinced by then that no solution exists. It is often used to illustrate lateral thinking and is a perfect example of ‘thinking outside the box’. It was first discussed by the US psychologist Norman R(aymond) F(rederick) Maier (1900–1977) in an article in the Journal of Comparative Psychology in 1930. See also problem solving.
Nine-dot problem. On the left are shown nine dots to be connected by four straight lines, without lifting the pen from the paper and without retracing any lines. The solution, shown on the right, should be easy but is very hard in practice.