A seemingly easy logical question

[maverick_bih]

This looks like an easy one, but I haven't found anyone yet who has answered it correctly, including me...
So, the goal is (like shown in the picture), to connect all three circles to each of the three triangles (nine connections in total, i have managed eight). Give it a try. You can go around the triangles and circles with the lines, just as long as they DON'T cross.

∆ ∆ ∆

O O O

 

[Mensanator]

What picture?

 

[Gigasoft]

It's impossible. Let's call the triangles T1, T2, T3 and the circles C1, C2, C3. There will be a separated area on each side of the lines going from T1 to C1 to T2 to C2. Let's call one of these areas Ž and the other Đ. There will also be a line going from C1 to T3 to C2, subdividing one of the areas, let's say Đ, into two new areas, one touching T1 which we will call Æ and one touching T2 which we will call Ø, giving a total of three separated areas. T3 now neighbours areas Æ and Ø, T1 neighbours Ž and Æ and T2 neighbours Ž and Ø. No matter which of these areas C3 is in, only one of the points T1, T2 and T3 will be on the edge of this area.

 

[Martin Rattigan]

See attached gif.

 

[Tac-Tics]

See attached gif.

You could also do it in "two dimensions" on the surface of a torus (donut).