Board puzzles with algebra of binary variables – link to Integer linear programming

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These puzzles are based on algebra with binary variables taking a pair of values, for example, (no, yes), (false, true), (not exists, exists), ('''0''', '''1'''). It invites the player quickly establish some equations, and inequalities for the solution. The [[Partition of a set|partitioning]] can be used to reduce the complexity of the problem. Moreover, if the puzzle is prepared in a way that there exists [[Unique (mathematics)|a unique solution only]], this fact can be used to eliminate some variables without calculation.
These puzzles are based on algebra with binary variables taking a pair of values, for example, (no, yes), (false, true), (not exists, exists), ('''0''', '''1'''). It invites the player quickly establish some equations, and inequalities for the solution. The [[Partition of a set|partitioning]] can be used to reduce the complexity of the problem. Moreover, if the puzzle is prepared in a way that there exists [[Unique (mathematics)|a unique solution only]], this fact can be used to eliminate some variables without calculation.


The problem can be modeled as [[Linear program#Integer unknowns|binary integer linear programming]] which is a special case of integer linear programming.<ref>Schrijver 1986</ref>
The problem can be modeled as binary [[integer linear programming]] which is a special case of integer linear programming.<ref>Schrijver 1986</ref>