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5x5 Arithmetic solver
From: |
Vincent Belaïche |
Subject: |
5x5 Arithmetic solver |
Date: |
Thu, 19 May 2011 22:21:53 +0200 |
Dear Dave,
Please find herein attached a contribution to the 5x5 game. This is an
arithmetic solver based on a matrix inversion in a (Z/2Z)^25 vector
space.
Note that will work only with a reasonably recent version of Calc
because that needs a bug fix on matrix inversion for matrix of Z/2Z
modulo forms.
The code works only for 5x5 grid size for the time being. I think that
it is feasible to make it general to work for any size or for any
pattern (I had in mind like replacing the 5-toggles cross by some other
pattern like a V or Y or X pattern). However this would need some
further thinking.
Also, this contribution could be improved in several other minor aspects
like:
- showing only one or a limited number of click positions for suggestion
instead of all of them --- that could be based on some sort criteria
to select the position(s) to show, for instance give priority to the
positions that toggle more positions
- or by updating the solution incrementally after the first matrix
inversion rather than invert the matrix again every time a new
suggestion is required by the user --- even with just a 5x5 matrix the
inversion takes some time, at least on my machine --- but that may be
due to this that I am using MSWindows instead of GNU Linux ;-) ---
- or hiding the suggestions after some configurable time, like one
or two second, or more
Nevertheless I believe that this solver makes this game significantly
more funny for my tired brain, as clicking on s (to require a
suggestion) and then trying only to remember the position where to
click, is quite enough thinking of that kind for me.
Very Best Regards,
Vincent.
PS: The Calc code has been reviewed by Jay.
5x5.tgz
Description: Binary data
- 5x5 Arithmetic solver,
Vincent Belaïche <=