>> boll@CS.ColoState.EDU (dave boll) describes a new game:
>>> The board: A MxN rectangle of dots.
>>> The play : Players alternate making moves, last one able to move wins
>>> A move: A move in this game consists of drawing a straight line
>>> connecting two (previously untouched) dots. The line may not cross
>>> any previously drawn line, nor can it pass thru one dot on the way
>>> to another. Each dot can have at most one line touching it.
>> ...
>>> Anyway, has anyone ever heard of a game like this? Thoughts?
>>
>> Someone descibed a similar game about a month or two ago. With this game
>> it's pretty clear immediately that player 1 can win on any MxN board if M
>> or N is even:
>>
>> + + + +
>> /
>> + + / + +
>> /
>> + + + +
>>
>> From here, any move that player 2 makes can be "mirrored" by player 1; player>> 2 MUST run out of moves first. Is there a similar easy winning strategy on
>> oddxodd boards?
>On boards with odd sides with no common factor, you can connect a line between
>two corners with the same effect.
This is rubbish. A line between two corners on a board with odd sides always
goes throught the central dot, so is not a legal move. This move is legal
(and the first move of a winning "mirror" strategy, as described above) on
an MxN board if (M-1) and (N-1) have no common factor. However, this
requires that one of (M-1) and (N-1) is odd, so one of M or N is even; so
this construction is less general than the construction above.
There can be no simple "mirror" strategy on an odd sided board: the first move
touches two dots, leaving an odd number of dots, which can not be divided into
