Circles and Quadrants

A forum for good logic/math puzzles.

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krazykate
Posts: 296
Joined: Tue Jun 03, 2008 3:40 am UTC

Circles and Quadrants

Postby krazykate » Sat Oct 04, 2014 3:27 pm UTC

The first piece may be placed in any circle on the board. From then on, each piece must be placed in the quadrant corresponding to the color of the circle from the previous play. Pieces may not be placed in overlapping circles (e.g. If there's a piece in the blue circle in the center of the cross in the green quadrant, then the red, green, and two yellow circles that form the cross are 'blocked'). If a player has no legal moves in the quadrant that they have to play in, that player must take all the pieces from that quadrant and skip their turn. The next player can place in any quadrant. The game is over when a certain number of pieces have been played, and the winner is the player that has taken the fewest pieces.

Having playtested it with a friend a couple times, we went through a bit of the decision tree and were able to work out that this game is not very fun to play. We weren't able to find a solution though, mainly due to the sheer number of opening moves as well as the asymmetry and seeming randomness of the board layout.

So now you guys can have a shot at it. The last time I posted a logic game, it turned out that it was based on an older, more established one that had long since been discussed and solved. I'm curious to see if I'm in a similar situation here. Is there a solution that works for any board layout and turn count? Is there any reason for this specific layout?

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