A Tough Logical Puzzle- Requires Utilization of Mathematical Algorithms

Click For Summary

Discussion Overview

The discussion revolves around a logical puzzle involving a 6x6 grid with two types of pieces, x's and o's, and the challenge of determining the placement of the final piece(s) in a series of grid transformations. Participants explore the applicability of mathematical algorithms in solving the puzzle, the methodology behind the solution, and the nature of the problem itself.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant presents a grid puzzle and asks for the fourth figure in the series, indicating a progression of piece placement.
  • Another participant questions the involvement of mathematical algorithms in solving the puzzle, suggesting it may be more about understanding the game's rules.
  • A participant expresses a desire for a link to a previous explanation of the puzzle, indicating they are new to the forum.
  • There is a suggestion that the methodology used to solve the puzzle is questionable, yet the solution seems to make sense to some participants.
  • One participant shares their attempt to create matrices to analyze the grid changes but finds it may complicate rather than clarify the solution.
  • Another participant reflects on the nature of the problem, suggesting it might be more appropriate to approach it as a game rather than through rigorous mathematical analysis.

Areas of Agreement / Disagreement

Participants express differing views on the necessity and effectiveness of mathematical algorithms in solving the puzzle. While some believe a straightforward approach based on game rules suffices, others seek a more methodical, algorithmic solution. The discussion remains unresolved regarding the best approach to the problem.

Contextual Notes

Participants note the potential for overthinking the problem and the limitations of applying rigorous mathematical methods to what may be a more intuitive game-like scenario.

Jack Bateman
Messages
12
Reaction score
0
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?
 
Last edited by a moderator:
Mathematics news on Phys.org
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
 
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.
 
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.
 
Jack Bateman said:
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
 
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.