Geometry Puzzle with 20 points in a cross pattern

  • Context: High School 
  • Thread starter Thread starter bob012345
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Discussion Overview

The discussion revolves around a geometry puzzle involving a cross pattern of 20 points. Participants explore how many points must be removed to ensure that no squares can be formed with the remaining points. The conversation includes attempts to determine the minimum number of points to remove and the exploration of various strategies for solving the problem.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest that removing 6 points might be sufficient to eliminate all squares, while others propose that 5 points could achieve the same result.
  • A participant mentions seeing 3 squares remaining after certain points are deleted, indicating that 8 points removed might be enough.
  • There are claims that a solution with 6 points was found, but it is not universally accepted as the minimum.
  • Several participants express uncertainty about the reliability of their methods, with some suggesting brute-force approaches or heuristics to verify solutions.
  • One participant discusses the potential for using a labeling system to track squares and points, while another mentions the complexity of the problem relating to the set cover problem in combinatorics.
  • There are references to using algorithms to solve the problem, indicating a computational approach to finding solutions.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the minimum number of points to remove, with multiple competing views on the effectiveness of different strategies and solutions. The discussion remains unresolved regarding the optimal approach.

Contextual Notes

Some participants note the limitations of their methods, including the reliance on brute-force searches and the complexity of verifying solutions. There are also mentions of unresolved mathematical steps and the dependence on specific configurations of points.

  • #31
Gavran said:
I do not understand your statement.
There are four squares and every square has four points. Every option must have at least one point from each of these four squares. That means there are $$ \binom{4}{1}\cdot\binom{4}{1}\cdot\binom{4}{1}\cdot\binom{4}{1}=4\cdot4\cdot4\cdot4=256 $$ different options which include one point from each of the four squares. If you exclude mirror and rotation options there will be ## 256/8=32 ## possibilities (the post #20).
If I remember, that was so two weeks ago, probably what I meant by the permutations, was the relative rotations of the squares with missing points which was quicker and easier than checking for mirroring cases first. My 64 drawings include the mirrored cases.
 
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  • #32
bob012345 said:
If I remember, that was so two weeks ago, probably what I meant by the permutations, was the relative rotations of the squares with missing points which was quicker and easier than checking for mirroring cases first. My 64 drawings include the mirrored cases.
Okay.
 

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