# 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