Geometry Puzzle with 20 points in a cross pattern

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SUMMARY

The forum discussion centers on a geometry puzzle involving 20 points arranged in a cross pattern, where participants seek to determine the minimum number of points, denoted as ##n##, that must be removed to prevent the formation of squares among the remaining points. The consensus indicates that removing 6 points is sufficient to eliminate all squares, while some participants suggest that 7 or 8 points may also achieve this goal. The discussion highlights various strategies, including brute-force methods using JavaScript and heuristic approaches, to verify solutions and explore the complexities of the problem.

PREREQUISITES
  • Understanding of geometric configurations and square formation
  • Familiarity with combinatorial optimization problems
  • Basic knowledge of algorithms, particularly greedy algorithms
  • Proficiency in programming, specifically JavaScript for brute-force solutions
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  • Research the set cover problem and its applications in combinatorial optimization
  • Explore heuristic algorithms for solving geometric puzzles
  • Learn about brute-force search techniques in algorithm design
  • Investigate geometric configurations and their properties in computational geometry
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Mathematicians, computer scientists, puzzle enthusiasts, and anyone interested in combinatorial geometry and algorithmic problem-solving will benefit from this discussion.

  • #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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