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25 dots are drawn as a 5x5 regular square grid. Can you draw 3 triangles that pass through every dot? The corners of the triangles must lie on the dots, ie., they cannot lie outside the grid.

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I think this is the only solution.
(Edit: It isn't. See teedyay's answer for another solution.)

enter image description here

I found this solution mostly by trial and error, but I did keep in mind that

apart from the 9 triangle vertices there are 25-9=16 other vertices that need to lie on the 9 sides of the triangles, so on average the sides need to visit almost 2 extra vertices each. That makes it almost inevitable that all triangles have two axis-aligned sides and a third 45-degree side, and that one triangle covers two whole sides of the grid.

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    $\begingroup$ Correct and well done! I will post a harder version of this puzzle soon. $\endgroup$ Jun 28 at 5:17
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Here is an alternative solution to the one already found:

Alternative solution

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    $\begingroup$ Oh very nice! I didn't realise that there was another solution. $\endgroup$ Jun 28 at 14:43
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    $\begingroup$ After seeing the solution for the 7x7 version of the problem I should have realised that trick might apply here as well. Very well done for finding this! $\endgroup$ Jun 28 at 15:22
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Another symmetric solution:

enter image description here

This was found by noticing that @teedyay's solution has quite a bit of slack in it.

In fact, there are two more similar solutions:

enter image description here enter image description here

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