B Geometry Puzzle with 20 points in a cross pattern

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The geometry puzzle involves determining the minimum number of points to remove from a cross-pattern of 20 points to prevent the formation of any squares. Participants suggest various solutions, with some proposing that 6 points can be removed, while others argue that 7 or 8 may suffice. Discussions highlight the complexity of verifying solutions, often resorting to brute-force methods or heuristic approaches. The set cover problem is referenced as a relevant framework for solving the puzzle, emphasizing the combinatorial nature of the challenge. Ultimately, the consensus is that while 6 points can eliminate all squares, proving that 5 points are insufficient remains a critical aspect of the 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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