Wikipedia:Reference desk/Archives/Mathematics/2021 November 15

= November 15 =

Connect the dots
I play a simple game on my phone which I think has some very deep mathematical underpinnings. There's a grid (various sizes) like a chessboard. On the grid there are pairs of colored dots, each of which fills a grid square. The game is to draw lines (filling in grid squares) connecting pairs of dots, with no lines crossing and no grid square left uncovered by lines. Each game level presents a different grid size and/or arrangement of starting dots and/or number of starting dots. There is always (usually?) only one solution to the levels provided.

Is this a known mathematical problem in graph theory or knot theory or something? I'm not sure how best to look into the math behind this. Tdjewell (talk) 15:56, 15 November 2021 (UTC)


 * @Tdjewell: I believe you are describing the logic puzzle Numberlink (and possibly the app Flow Free based on it). I'm not really sure what specific mathematical question you have regarding the game, but according to our article, solving a given Numberlink puzzle is NP-complete. ev iolite   (talk)  16:08, 15 November 2021 (UTC)

Flow Free is in fact the app. Thank you for your response. That is exactly what I was looking for. — Preceding unsigned comment added by Tdjewell (talk • contribs) 16:18, 15 November 2021 (UTC)