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]
      
Last modified: Sunday, 1 November 2020, 11:48 PM