Question 12
Beaver’s country has 36 cities arranged as the 6×6 square grid below. Two cities are adjacent if their squares share a vertex.
Each city is either densely populated (gray) or sparsely populated (white). Every year their populations change by these rules:
- A dense city remains dense if exactly 2 or 3 adjacent cities are dense; otherwise it becomes sparse.
- A sparse city becomes dense if exactly 3 adjacent cities are dense; otherwise it remains sparse.
How many dense cities are there after two years?
Each city is either densely populated (gray) or sparsely populated (white). Every year their populations change by these rules:
- A dense city remains dense if exactly 2 or 3 adjacent cities are dense; otherwise it becomes sparse.
- A sparse city becomes dense if exactly 3 adjacent cities are dense; otherwise it remains sparse.
How many dense cities are there after two years?