Monopoles Formal Description [spoilers]

Monopoles: Problem Statement

• Given: n rooms. A set 1..m of monopoles to place.

• Find: A list S of n sets with the following properties:

  • Each monopole is placed:

    forall i in {1..m} .
        exists j in {1..n} .
            i in S[j]
    

  • No monopole is in two places:

    forall i in {1..m} .
        forall j, k in {1..n} .
            j ≠ k → i not in S[j] or i not in S[k]
    

  • Sums exclude monopoles:

    forall i in {1..n} .
       forall j, k in {1..m} .
           j ≠ k → j not in S[i] or k not in S[i] or j + k not in S[i]