A Tough Logical Puzzle- Requires Utilization of Mathematical Algorithms

[Jack Bateman]

A 6x6 grid features two different types of pieces: x's and o's. You are given three separate views of the same grid in a step by step progression. The number of pieces gradually decreases with each step and also change in location.

This is the layout of the grid progression:
http://www.eskimo.com/~miyaguch/hoeflin/n36.gif

So what is the fourth figure in this series? Meaning what would be the placement of the final piece(s) in the forth step of the 6x6 grid?

[davee123]

This has been answered here before-- but I don't see how mathematical algorithms are involved in obtaining the answer? It was simply a matter of figuring out the rules for the game, and applying them to the final board. What algorithms are you proposing to use in order to determine the result?

DaveE

[Jack Bateman]

Well as you can see, I am new to these forums, so I had no idea this question had been answered here before. Could you post a link so I could find the explanation as to how to solve it?

As for which algorithms to use, I did not know, which was why I was asking. It seems to me that this would be one approach to the problem, but apparently it is easier to approach it in the way you described, which would probably involve less analysis.

[Sakha]

Here (http://www.physicsforums.com/showthread.php?t=311608) is the thread with this puzzle.

[Jack Bateman]

Thanks for posting the link. It was pretty helpful.

I think the methodology is somewhat questionable, but nonetheless the solution is the only one that makes sense.

[davee123]

As for which algorithms to use, I did not know, which was why I was asking.

Damn, I thought perhaps you knew a better answer that was more methodical than the one that apparently applied. I didn't like that answer, primarily because it seemed like a coincidental one rather than a logical one. Oh well...

DaveE

[Jack Bateman]

Haha, sorry DaveE, I cannot think of another process that will successfully yield a different logical answer. Ideally I would have my friend who works in programming come up with a computerized method for attacking the problem, but he has far more important (or more precisely, less trivial) things to do with his time.

Based on the origin of the question, however, the answer seems to hold water. The process is likely correct too, interestingly enough. Simply due to the nature of other questions like this one, I suspect that the author would have expected an individual to approach this from the point of view of a game instead of subjecting it to rigorous mathematical analysis. That would be taking things a step too far. The item analysis for this question also supports this conclusion.

One method I tried to use to solve this problem was creating matrices based off of each grid or the progression from one to another, and observing the differences between each step (including by subjecting each matrix to simple mathematical processes to look for differences), but alas, this simply either further misdirects one from obtaining an accurate answer or does not follow the trend of the rate at which each "game piece" decreases.

But like I said, this would be over-thinking the question.