Problem #18: Matches on a Goban
I have a box with 21 matches and a single coin. I discovered that the coin fits (almost) perfectly inside one of the squares of the board, and that the matches have a length that they take up three squares if placed vertically or horizontally.
Find a way to put all the matches and the coin on the board such that each square is touched by exactly one match or has the coin on top of it.
For example, one could start as in the following picture:
[N.B.: It is not a trick question: the matches don’t have to lie partly outside of the board, nor do any of the matches have to cover more than three squares, nor do they have to lie in a position that isn’t horizontal or vertical]
Bonus
Is there a way to fill the board with the matches when the coin is placed as in the picture above?