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This is the same question posted by webadventurer with one extra condition (number 5) that disallows the previous solution posted here.

(All credits go to webadventurer, including all images.)

Rules:

  1. Line must be straight.
  2. Line must be continuous.
  3. Line must not intersect itself.
  4. Line is allowed to take 45 degree turns to itself, for example:

angle rule

5. Line must not leave the square.

The dots:

dots

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2 Answers 2

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I mean, as long as the number of segments doesn't matter..

enter image description here

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This might be the intended answer. Only slightly out of the box.

enter image description here

Then of course, people want to know what is the minmum.

OK, I tried. I managed to go down to ...

21 lines instead of 25.

enter image description here

But somehow the apparent waste at the ends is not very satisfactory.

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  • $\begingroup$ Also a good answer! I decided to award Bass the tick as they have posted the answer first, though your answer is quite elegant. $\endgroup$
    – CatProgrammer
    Commented Sep 1, 2023 at 7:23
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    $\begingroup$ No problem. Actually his answer inspired mine. $\endgroup$
    – Florian F
    Commented Sep 1, 2023 at 7:36
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    $\begingroup$ @CatProgrammer: The next question is... what is the minimum number of bends? $\endgroup$
    – user21820
    Commented Sep 1, 2023 at 12:37
  • $\begingroup$ Surely "inside the square" still gives you some margin to go a little bit past the centres of the outer dots? $\endgroup$
    – Jaap Scherphuis
    Commented Sep 2, 2023 at 13:19
  • $\begingroup$ Maybe, but I am a bit purist. Taking the square of dots as the limit makes more sense. The frame around it is of an unspecified and arbitrary size. $\endgroup$
    – Florian F
    Commented Sep 2, 2023 at 20:28

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