'Don't cross the streams'...in other words, don't do what's shown in the picture with this game posting?

FYI: any distribution of an equal number of red and blue dots, as long as no three are collinear, is solvable. Proof: consider the shortest possible circuit that reaches all dots and alternates between red and blue, regardless of crossings. Suppose the segments from r1 to b1 and r2 to b2 cross (direction does not matter here). Erase both segments and connect r1 to b2 and b1 to r2. The resulting graph is an alternating circuit that reaches all dots with a shorter total distance than the original. The proof is left to the reader.

@coveritwithgas: Nice attempt, but it is incorrect.

Counterexample: http://imgur.com/W0T33

The error in your proof is that reconnecting r1 to b2 and b1 to r2 sometimes results in two separate circuits instead of one circuit.

I stand corrected. Thanks.

I wish there was an "undo last move" feature. I'm on level 14 and I keep accidentally crossing the streams. It's becoming a game of physical finesse rather than a puzzle game, and I'm just about ready to rage quit.

Well, I guess power-of-post works for a ragequit fit too. I got past level 14 and am now happily up to level 19.

An undo feature would still be nice though ... :)

I agree with Barbara on her suggestion, "last move undo" button.