The need to make a decision between alternatives that are both desirable.

A kind of puzzle in which there is one common factor in a first set of diagrams that is missing from a second set. The solver (possibly a computer program) must identify this factor.

(quantum mechanics) The unresolved problem of what causes a wavefunction to collapse into an eigenstate, or whether wavefunctions collapse at all.

The situation where a spam filter or search engine blocks or modifies content because the text contains a string of letters shared with an obscene word.

(mathematics) The challenge of proving that the only solution of the Diophantine equation :∑ₙ₌₁ᴺn²=M²; with N > 1 is when N = 24 and M = 70.

(computing theory) A question in some formal system with a yes-or-no answer, depending on the values of input parameters.

(object-oriented programming) The ambiguity that arises when two classes B and C inherit from A, and a further class D inherits from both B and C, so that if there is a method in A that B and/or C has overridden, and D does not override it, it is unclear which version of the method D should inherit.

(mathematics) A mathematical problem, asking whether a room with mirrored walls can always be illuminated by a single-point light source, allowing for repeated reflection of light off the mirrored walls. It was solved in 1958: there are such rooms that cannot be thus illuminated.

(social planning) A problem that is difficult or impossible to solve because of incomplete, contradictory, and changing requirements that are often difficult to recognize.

(idiomatic) A problem expected with any new and untried product, system, or venture