Question 12
The beavers like using Bomino tiles. These tiles are decorated by colouring cells grey on a $3\times3$ grid according to these rules:
- Every grey cell must share an edge or a vertex with at least one other grey cell.
- Every grey cell shares an edge with at most one other grey cell.
- A tile with $n$ grey cells is called an $n$-Bomino.
- Two tiles are considered the same if one can be rotated or flipped to obtain the other.
Below are examples of a 2-Bomino and a 4-Bomino.
How many different 3-Bomino tiles are there?
- Every grey cell must share an edge or a vertex with at least one other grey cell.
- Every grey cell shares an edge with at most one other grey cell.
- A tile with $n$ grey cells is called an $n$-Bomino.
- Two tiles are considered the same if one can be rotated or flipped to obtain the other.
Below are examples of a 2-Bomino and a 4-Bomino.
How many different 3-Bomino tiles are there?