Instead, to solve such a puzzle, the solver must find a solution that satisfies the given conditions.
Conway's Game of Life and fractals, as two examples, may also be considered mathematical puzzles even though the solver interacts with them only at the beginning by providing a set of initial conditions.
Many of the puzzles are well known because they were discussed by Martin Gardner in his "Mathematical Games" column in Scientific American.
Mathematical puzzles are sometimes used to motivate students in teaching elementary school math problem solving techniques.
The fields of knot theory and topology, especially their non-intuitive conclusions, are often seen as a part of recreational mathematics.