Devise a two-player game based on 3-coloring a tiling of kites and darts.

Hi Antreas,

Here is a portion of the K&D that the kids and I start with. We play
only within the boundary, but one could also expand the boundary
dynamically as needed. (As I mentioned, we play on the computer by
clicking colors with a mouse, so that is easy.)

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Player 1 goes first (now THAT is original) by filling any available
tile with one of 3 agreed upon colors. I'll use red, yellow and green.
Player 1 goes first below with a red kite. Subsequent legal moves are to
color only tiles that are edge-adjacent to those already colored, and
never to color two adjacent tiles the same color. So the second move
must be yellow or green on any of the 4 tiles adjacent to the first red
kite.

I'll let Player 2 take a green kite. Player 1 then has many choices, but
chooses a yellow dart. So here are the first three moves:

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Not very interesting so far. Notice though, that there is a kite
adjacent only to the green and yellow tiles that can only be colored
red. Maybe Player 2 will stumble near this trap --- you win if you
create an uncolored tile that is surrounded by 3 different colors,
thereby destroying the 3-coloring of the tiling. (Remember, JHC
conjectures that all of these can be 3-colored.)

Player 2 fills the "ace" --- a novice! But that is not a bad move.
Player 1 tries to sucker his opponent and colors a green kite:

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But Player 2 is not such a novice after all and traps Player 1 by
coloring an adjacent red kite and claiming a dart (which is then colored
blue --- it's easier for us to color our captures than to initial them):

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At this point we could either say that Player 2 has won the game and
begin again (which I like --- it is more "pure" a game), or continue,
leaving the capture tiles on the board. When doing the latter, we have
decided that after capturing a tile, the victor may move again, which
occasionally results in a few consecutive captures. Also, we don't allow
the captured tile to be considered "colored", so a play adjacent to a
captured tile must also be adjacent to a colored tile. The former game
is interesting despite appearing to be short. When I play with Katy
(15), the games are sometimes long --- a few dozen or so moves. (She
wins about 40%, I'd say!) With 10-year-old Patrick, we usually play the
2nd method. I am not particularly good at this sort of thing, but I
still win about 90% with Patrick! I have yet to play with a
mathematician!

So does it make sense? This is the first time I have tried to explain
it, and I haven't tried to give an indication of how subtle and pretty a
game I have found it to be. But as I said, I have yet to really test it.

Let me know what you think. Want to play a quick transcontinental game?

-- Rick