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Dots and Hexagons I'm sure you know the game of Dots and Boxes already, but maybe you know it by another name. It's a game for two players usually (although more than two can play), and is often played by children because the rules are quite easy. All you do (on your turn) is to join two next-door dots on the grid, drawing a line and trying to complete a box. Each time you make a box, you must take another turn. If you fail to make a box, the other (or next) player then takes his turn to draw a line. The winner is the one with the most boxes when all the boxes have been claimed. Usually you'll put your initials in each box you complete as you play the game. You can choose to play on any size grid; here's a sample:
The rules are actually open to some interpretation; if you can complete a box, are you obliged to? The question is important when you are filling in a string of boxes - are you allowed to stop two boxes before the end of the string and force your opponent to give you the next string of boxes? It's a matter of taste - if you are allowed to stop, then the game becomes more like sudden death; the first player to get a string of 3 boxes will win in the majority of games. Alternatively you could make a rule that says that any box that can be completed must be completed. But then the fun of your opponent genuinely missing a chance has gone :). You could say that all boxes must be completed, if the opponent demands it. That's probably the best, if you don't like the sudden death version. It also means that each player will most likely get a similar number of boxes - there probably won't be a 'big winner' and a 'big loser'. That's safer if children are playing ;). The choice of rules (in advance! ;) ) can be important - for instance, if near the end of the game there is one string of 3 boxes waiting to be claimed, two of 4, two of 7 and one of 9, then under the 'sudden death' rules, the player who claims the first string of 3 claims all the rest of the boxes and will win; however under the 'must complete' rules that player will claim 3, then 4, then 7 boxes (14 total), and the other will claim 4, then 7 then 9 boxes (20 total). (Technical note: I'm talking simple 'linear' strings of boxes here). The game plays really well for children, and yet can be played quite seriously, if you want to exercise the brain cells. At the simple level, the winner appears to be a matter of chance; at the analytic level, the winner will probably be the first one who can analyse the end game correctly. It's not a game to rival, say, chess or Go - it would yield much more easily to a computer program, and there is presumably a winning strategy for one player or the other (albeit pretty complicated). However it is a game that is worthy of further study - even if you only want to make sure your kids beat you at it when appropriate ;). Apparently the 'must complete' version of the game has been solved mathematically (1966), but the other 'sudden death' version is still 'unsolved'. So why are we talking about boxes here in the Hall of Hexagons? Are we square here? Of course not! Anything that can be done with boxes can be done better with hexagons, can't it? Of course it can. Let me introduce ... Dots and Hexagons which you play by joining dots on the grid and (OK, you guessed) trying to make hexagons.
The only reason this hasn't been thought of before is that it's not that easy to draw a hexagonal grid. Obviously what you need to try this out is something ready made you can print out. Ta-da! There 4 grids in each file. As a game it actually plays pretty well - better than Dots and Boxes in my view. Also of course it's new, so you have to think a bit and watch out in case you make silly mistakes. It occurs to me that it would be fun to try Dots and other shapes. I seem to recall trying Dots and Triangles a long time ago, and it didn't really work well; but what about Dots and Pentagons, played on a dodecahedron in 3-D? Or Dots and Pentagons and Hexagons, played on a soccerball? (I've forgotten what the soccerball's called properly, but it's what you get when you chop the corners off an icosahedron).
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