Beefy Boxes and Bandwidth Generously Provided by pair Networks
Just another Perl shrine
 
PerlMonks  

Re^4: magic squares

by Limbic~Region (Chancellor)
on Apr 08, 2009 at 15:28 UTC ( #756364=note: print w/ replies, xml ) Need Help??


in reply to Re^3: magic squares
in thread magic squares

tilly,
Yes, this is exactly what I was guessing at. There are also constraints as to what x, y and z can be within the confines of this puzzle. I didn't have a chance last night to work on this though because the following entered my mind as I was leaving work

X+Y X+Z X-Y-Z X-2Y-Z X X+2Y+Z X+Y+Z X-Z X-Y Terms: X, X+Y, X-Y, X+Z, X-Z, X+Y+Z, X-Y-Z, X-2Y-Z, X+2Y+Z X+Y X-2Y+Z X+Y-Z X-Z X X+Z X-Y+Z X+2Y-Z X-Y Terms: X, X+Y, X-Y, X+Z, X-Z, X+Y-Z, X-Y+Z, X+2Y-Z, X-2Y+Z Terms in common: X, X+Y, X-Y, X+Z, X-Z Terms not in common: X+Y+Z VS X+Y-Z AND X-Y-Z VS X-Y+Z X-2Y-Z VS X-2Y+Z AND X+2Y+Z VS X+2Y-Z

I haven't convinced myself that you don't need to iterate over other series of equations. Still thinking on it though.

Update: In fact, I think I can show that your statement "By rotating and reflecting we can make the largest corner be x+y" is not in fact true - consider the following square:

X+Y X-Y-Z X+Z X-Y+Z X X+Y-Z X-Z X+Y+Z X-Y
You have X+Y and X+Z both in a corner so you need to make a relationship between them to determine which is the largest value. Also, I noticed that I showed it is possible to have X+Y+Z in a corner and am now convinced that multiple series of equations must be iterated (though you can re-use the values for X, Y and Z).

Cheers - L~R


Comment on Re^4: magic squares
Select or Download Code
Re^5: magic squares
by tilly (Archbishop) on Apr 08, 2009 at 16:08 UTC
    It is ugly, but I used the above logic to code up a reasonably efficient solution. On my machine it runs in about 0.01s:
      tilly,
      Thanks! After having read your code and your proof I see why it wasn't immediately obvious to me. I was stuck looking at it a different way. I stubbornly had to convince myself that my way was in fact correct. After I did, I realized we were saying the same thing. This is the frustrating part - I sometimes can't get out of my own way.

      Unfortunately, I now lack all ambition to implement my solution.

      I only got interested in the problem because glancing at the commentary of existing posts - a number thought brute forcing was necessary. I had a hunch that this wasn't true.

      Cheers - L~R

Log In?
Username:
Password:

What's my password?
Create A New User
Node Status?
node history
Node Type: note [id://756364]
help
Chatterbox?
and the web crawler heard nothing...

How do I use this? | Other CB clients
Other Users?
Others avoiding work at the Monastery: (5)
As of 2015-07-02 06:44 GMT
Sections?
Information?
Find Nodes?
Leftovers?
    Voting Booth?

    The top three priorities of my open tasks are (in descending order of likelihood to be worked on) ...









    Results (30 votes), past polls