A particularly complex or challenging problem or puzzle.

A brainteaser regarding probability, in which a game show contestant picks a door to win a prize. One door conceals a car; the other two conceal goats. After the contestant picks a door, the host opens one of the two remaining doors which reveals a goat. Counterintuitively, it is then in the contestant's interests to switch to the remaining door.

A conspiracy theory postulated by David Icke in which the government (or another higher power) manipulates the population by introducing a problem and then using their own means to solve that problem.

(astronomy) The problem of calculating the motion of three celestial bodies that interact with each other gravitationally

(economics) The situation where those who benefit from goods or resources do not pay for them, resulting in a lack of funding and subsequent underprovision.

A geometric puzzle involving calculating the width of an alley based on the height at which two ladders cross when propped diagonally across it.

The problem posed by ironic process theory, where (for example) explicitly trying not to think about a white bear makes one more likely to think of it.

A visibility problem in computational geometry, dealing with whether a number of points in a polygon can collectively "see" (by line segments akin to a person's line of sight) the whole interior of the polygon.

(calculus) the problem of solving a (set of) ordinary differential equations accompanied by the requirement that the function sought (and possibly also one or more of its derivatives), taken for some value, equals some other specific value; graphically, (for example) the problem of finding that antiderivative of some function that passes through a particular point

(computing theory) The undesirable situation where a large number of processes waiting for an event are awoken whenever the event occurs, and then engage in a conflict over which process handles the event.