Magproblem

Magproblem is a term used in puzzle communities to describe a family of logic puzzles that model magnetic constraints and polarity. The word is informal and not standardized, but it appears in online forums, puzzle collections, and teaching materials as a concise label for puzzles where arrangement and orientation of magnetic-like elements must satisfy a set of clues.

Typical structure and rules of magproblems involve a grid or graph in which magnets or magnet-like units occupy positions and carry a binary polarity. Clues specify how many poles of a given type must appear in particular rows or columns, or how magnets must be oriented relative to neighbors. Solutions require assigning placements and polarities so that all clues are satisfied and the overall configuration is internally consistent. Variations exist: some puzzles use domino‑shaped magnets occupying two adjacent cells with opposite poles, others treat polarity as an abstract property without physical magnets, and some include additional constraints such as forbidden adjacencies or symmetry requirements.

Solving magproblems draws on logical deduction and constraint propagation. Solvers often use techniques such as parity reasoning, process of elimination, and pattern recognition to reduce possibilities. When straightforward deduction is insufficient, computational methods like backtracking, constraint programming, or SAT solvers may be employed to find a valid configuration or prove that none exists. Magproblems are used in puzzle books, classroom activities, and programming problem sets to illustrate reasoning under constraints and to teach techniques from the broader field of constraint satisfaction problems.

Related topics include logic grid puzzles and constraint satisfaction problems in computer science. Magproblems vary in complexity and presentation, but share a common goal of reconciling local polarity rules with global consistency.