When I first started showing Tangle to people I noticed a common reaction. Level 1 and 2 were handled with ease but most people were afraid of Level 3. That led me to look at the difference in difficulty between Tangle’s levels.

There are multiple variables that determine the difficulty of a level. In general the graphs have an increasing number of vertices and edges, but the number of edges increases faster. But perhaps the biggest contributer to difficulty is the ratio of edges to vertices. It’s generally harder to untangle a vertex with four edges that is connected to three edges than a vertex with four edges connected to a vertex with two edges. The ratio of edges to vertices is what I ended up looking at most closely.

Consider the following graph:

The red line is Tangle’s the resulting ratio of edges to vertices for Tangle’s new level generation equations. The blue line is the ratio for the original. It became pretty apparent as to what was going on. Level 2 originally had much less complicated vertices because the vertices had fewer edges attached to them than even Level 1. While there were more vertices overall, making the level appear slightly harder, it wasn’t really a challenge to sort out the vertices. Everyone that I have introduced Tangle to after making the change to the red line has made a nice, smooth progression to and past Level 3.

One of the coolest parts about Tangle’s Online Leaderboard is its ability to create badges that players can put on their sites and blogs to show off their scores. Just click on any ranking, including the red 1st, 2nd and 3rd place stars on a Leaderboard listing and the Online Leaderboard will present the HTML to generate that badge.

As I’m posting this, the badge’s time is in first place for level 5. We’ll see how long that stands with the crazy times some people are putting up.

I’m extremely excited to be releasing Tangle today. Get it and play some games.

What is Tangle? The short answer is that Tangle is an addictive puzzle game where the player unscrambles a mess of tangled lines. The long answer is that Tangle is a game made around planar graphs. A planar graph is a graph that consist of vertices connected by edges that can be embedded into a plane so that no edges will intersect. Wikipedia has all the specifics, including how to mathematically prove a graph is planar.

Tangle has some great features that I’m very happy about.

• That sweet delicious app look that is so hip nowadays.
• An Online Leaderboard which can be accessed both through the web interface and in the game itself. The web interface is well worth poking around in.
• A theoretically limitless number of levels. Tangle randomly generates its levels with a formula for how many edges and vertices exist for each level and then creates a planar graph with those vertices and edges and rearranging the vertices on the board. The edges and vertices formulas ensure that valid planar graphs can be produced for any level.
• As a side effect of the way levels are created players will most likely never replay the same graph.
• Multiplayer where two or more players over a network are able to play identical graphs and are able to taunt each other about their playing through some text chat. It’s especially fun when challenging someone while video conferencing with them.
• If Normal mode is too easy for someone they can switch to Expert.
• Cool Core Graphics transitions which I plan on changing into some cool Core Animations when Leopard hits.
• Most importantly Tangle is fun and it’s challenging.

I hope people find a lot of fun in Tangle, I’ve had a blast writing it, watching people play it for the first time and now I’m loving releasing it so everyone can play it.

I’m also accepting multiplayer Tangle challenges, so comment here or email me or catch me on iChat if you want to challenge me.