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