What a great game!!

If you haven't already, you really ought to go check out planarity.net.  John Tantalo has really made a great game for us.  Here I share some strategy and some screen grabs from this game.  Here are some from a level 25 run


A great thing about planarity is that you just move the points around, and let your instinct tell you where to put them.  Move them back and forth and you'll get a feel for it.  After playing this game for a while, I realized that it doesn't really get harder at the higher levels - it only takes longer as there are more vertices.

But what is really going on?  Can we quantify how the mind solves this game?  The most straightforward approach is a nodal one.  Pick one vertex at random, and move it to the top of a clear area.  That will be your node 0.  Put all vertices which it connects below it in a line.  Now, for each of those nodes repeat the process, making sure that the edges above don't cross.  This may require that you re-order already placed nodes.  Here are a few pictures of games solved in this manner:

Nodal Solutions

Another way to solve the puzzles in a strict algorithm that is a bit fast for humans is to make a bounding shape.  To do so requires finding three or more vertices that can form a closed loop.  This is easier than you might think, even in the highest levels.    Once you have formed the closed loop, you can build a nodal solution (as described above) to the interior of the shape from each vertex.  Here are a few pictures of games solved in this manner:

'Closed Loop Solutions

An adaptive closed loop is solution is more like what the brain does automatically.. it builds closed shapes and pursues a nodal solution,  but when re-ordering the nodes becomes difficult a new bounding shape can be made in the exterior of the original one to speed up the process.  Here are a couple of examples:

Adaptive Closed Loop Solutions

Finally, there is the artisitc approach.  Here, we move the vertices as our aesthetic sense tells us in a pretty one.  In general the puzzle forces a certain pattern on us, and we build our picture from there. 

Artistic Solutions

Good luck, and happy planaritying!  I'd love to see your screengrabs - please send them to me and I'll post your picture and name - luke.saul[-\at-]gmail.com.