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        riddles >> medium >> Mutilated Go Board
        
(Message started by: THUDandBLUNDER on Jan 4^th, 2004, 3:21am)

Title: Mutilated Go Board
Post by THUDandBLUNDER on Jan 4^th, 2004, 3:21am

OK, a mutilated mini-go board.

The four corners of the 11x11 board are removed. The object is to place four stones on the corners of a square. The square formed may have edges that are parallel to those of the board or may be tilted (see below). How many possible squares can be thus formed?

Title: Re: Mutilated Go Board
Post by towr on Jan 4^th, 2004, 7:52am

unless I'm mistaken the answer is ::[hide]1173[/hide]::
For an m-size board (m [ge] 2) with the corners missing it would be ::[hide](m^4 - m^2 - 48 m + 84)/12[/hide]::
Unless, of course, I'm mistaken, in which case it wouldn't be.. ;)

Title: Re: Mutilated Go Board
Post by THUDandBLUNDER on Jan 4^th, 2004, 9:33am

Quote:

Unless, of course, I'm mistaken

...or your source is mistaken. :P

Title: Re: Mutilated Go Board
Post by towr on Jan 4^th, 2004, 9:52am

I didn't use any sources this time..
I just examind the problem, and generalized for other cases, and tried to deduce a formula.

Title: Re: Mutilated Go Board
Post by TimMann on Jan 4^th, 2004, 2:05pm

Quibble: The diagram is drawn improperly if you want this to be a Go board. Go is played on the intersections of the lines, not inside the squares. (Also, the stones are black and white, not black and red.) Drawing the diagram properly wouldn't change the problem any, though. You'd make it one row and one column smaller to keep it 11x11 when counting intersections instead of squares.