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tcsoccerman Server Help Squatter
Age:26 Gender: Joined: Jan 15 2007 Posts: 694 Location: Atlantis Offline

Posted: Fri Oct 17, 2008 5:49 pm Post subject: Mathmatical Number Game Problem 




Goal: To try and fill in all the squares without going over one that is already filled by counting to 100.
Directions: Using a 10x10 graph (100 squares), write a 1 in the top left. Now you can either move horizontally 3 squares (4,1) and write in the next number, verically 3 squares (1, 4) or diagonally 2 squares (3,3). Continue doing so until you have filled all squares once. There is 15 million different incorrect solutions and 2 correct solutions.
I'm going to try and make a program to find the solution.
This whole problem came from my math teacher, who said they'd give us a car if we can find the solution. Evidently a past student's dad was a software developer and made a program to find this solution. He had the program running a couple days and the kid actually got the car, a convertible. I think they're even telling the truth.


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SamHughes Server Help Squatter
Joined: Jun 30 2004 Posts: 248 Location: Greenwich Offline

Posted: Fri Oct 17, 2008 9:32 pm Post subject: 




So you can go vertically 3 squares in any direction, and diagonally 2 squares in any direction?
Well, just so you know, I found a solution, by hand, in about five minutes.


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tcsoccerman Server Help Squatter
Age:26 Gender: Joined: Jan 15 2007 Posts: 694 Location: Atlantis Offline

Posted: Fri Oct 17, 2008 10:17 pm Post subject: 




and what would that be?! i think we have a communication problem.


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SamHughes Server Help Squatter
Joined: Jun 30 2004 Posts: 248 Location: Greenwich Offline


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SamHughes Server Help Squatter
Joined: Jun 30 2004 Posts: 248 Location: Greenwich Offline

Posted: Fri Oct 17, 2008 10:49 pm Post subject: 




You know there are more than 2 solutions, because there's 2 ways to get from A to B and then you can reflect both solutions around the diagonal, giving 4 solutions.
Maybe the rules are tighter than I read them to be.


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tcsoccerman Server Help Squatter
Age:26 Gender: Joined: Jan 15 2007 Posts: 694 Location: Atlantis Offline

Posted: Sat Oct 18, 2008 1:10 pm Post subject: 




Yeh i didn't explain it well enough you got the wrong interpetation.
I'll try again
You've got a 10x10 grid (100 squares).
The goal is to fill all of the grid up with the numbers 1100.
You start by marking a "1" at 1,1 in top left corner.
From there you can either go horizontal 3 (4,1), vertical 3 (1,4) or diagonal 2 (3,3).
Now you would make a 2 where you chose to go. lets say 4,1.
Now you continue that faschion (either go horizontal 3 (4,1), vertical 3 (1,4) or diagonal 2 (3,3)) and mark a 3, 4, 5.... up to 100.
If at anytime you end up on a gridpoint that is already filled in with a number, you have to choose a different path. You can't overwrite. (This is the "catch").
That should be a little harder.


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SamHughes Server Help Squatter
Joined: Jun 30 2004 Posts: 248 Location: Greenwich Offline

Posted: Sat Oct 18, 2008 10:48 pm Post subject: 




Um, what did you say that's different than what you said before?
Are you able to go vertically and horizontally in any direction? Are you able to go diagonally in any direction? Or just down and to the right?
These questions you haven't answered. And if the answer is yes to the first two, then my solution is correct.


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tcsoccerman Server Help Squatter
Age:26 Gender: Joined: Jan 15 2007 Posts: 694 Location: Atlantis Offline

Posted: Sun Oct 19, 2008 11:36 am Post subject: 




Maybe you do have the answer, lets make sure.
That image is a good example of the rules. (That is only an 8x7 grid though, it should be 10x10). Like i said, you just keep doing that until you fill it all up.
Also look at 6, and note that from 6 i could NOT go up because then i would be at 3.
Does that clarify?
numbergame.bmp  177.83 KB
File downloaded or viewed 26 time(s)


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SamHughes Server Help Squatter
Joined: Jun 30 2004 Posts: 248 Location: Greenwich Offline

Posted: Mon Oct 20, 2008 9:13 pm Post subject: 




So to be clear, from square 6 there are 6 possible squares one could visit next?


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tcsoccerman Server Help Squatter
Age:26 Gender: Joined: Jan 15 2007 Posts: 694 Location: Atlantis Offline

Posted: Tue Oct 21, 2008 3:37 pm Post subject: 




yes


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YonatanNaamad Newbie
Joined: Mar 22 2009 Posts: 5 Location: Troy Offline

Posted: Sun Mar 22, 2009 7:26 pm Post subject: Prolog solution 




Hey. It's my first post, and I know it's a bump of an old post, but whatever.
Anyway, here's some Prolog code that could theoretically come up with a solution to the problem.
in(H,[H_]).
in(H,[_T]) : in(H,T).
append([],A,A).
append([AB],C,[AW]) : append(B,C,W).
vs([A,Y],[X,Y],L) : A > 3, X is A3, not(in([X,Y],L)).
vs([A,Y],[X,Y],L) : A < 8, X is A+3, not(in([X,Y],L)).
vs([A,B],[A,Y],L) : B < 8, Y is B+3, not(in([A,Y],L)).
vs([A,B],[A,Y],L) : B > 3, Y is B3, not(in([A,Y],L)).
vs([A,B],[X,Y],L) : A > 2, B > 2, X is A2, Y is B2, not(in([X,Y],L)).
vs([A,B],[X,Y],L) : A > 2, B < 9, X is A2, Y is B+2, not(in([X,Y],L)).
vs([A,B],[X,Y],L) : A < 9, B > 2, X is A+2, Y is B2, not(in([X,Y],L)).
vs([A,B],[X,Y],L) : A < 9, B < 9, X is A+2, Y is B+2, not(in([X,Y],L)).
gvs(_,0,_,[]).
gvs(S,N,L,[AB]) : N > 0, M is N1, append(L,[S],NL), !, vs(S,A,NL),gvs(A,M,NL,B).
solve(N,B) : gvs([1,1],N,[],B). 
To run it, you just call solve(100,B). I'm running it on my server now to see what the results are. It can find solutions for the first 90 moves pretty quickly.
(PS. Soccerman's post count is pretty beast)


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tcsoccerman Server Help Squatter
Age:26 Gender: Joined: Jan 15 2007 Posts: 694 Location: Atlantis Offline

Posted: Sun Mar 22, 2009 9:13 pm Post subject: 




lol, i just ruined it.
anyways, that's too complex for me to know if what that code does is correct, but the fact that it's so complex makes me think that it is the right code. good work.


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Chambahs Power attack
Joined: Jun 19 2005 Posts: 820 Offline

Posted: Wed Mar 25, 2009 1:33 am Post subject: 




Sama has a passion for brain teasers that involve math or numbers. I remember his other "turn a name into numbers and ill figure out the equation game" he had us all doing.


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