## Tuesday, June 10, 2014

### Perfect Paths: Score 900 in Andromeda

A few people asked me: how can you score 900 in the Andromeda levels of Perfect Paths? They are simple puzzles, with an apparently obvious solutions; there doesn't seem to be much freedom in order to gain extra points. But on closer inspection, you can.

If you follow me on Twitter, you should have seen a retweet about a blog which shows solutions for (almost) all the levels in the game. Of course you'll not want to spoil the game by peeking at solutions, but if you're seriously stuck, this will get you going. Even if you do copy a solution, there's still a lot of fun to be had by making it better and shorter to earn extra points.

I already gave a few tips in my review of the game, but let's look at those again with specific examples.
The solution to the above puzzle seems obvious: just draw straight paths to the goals and be done with it. However, this is inefficient. The score you get depends on only two things: the number of arrows you use, and the number of steps taken by the solution. In the above case, the number of arrows is optimal: you can't do better than that. However, the order of the arrows is not optimal.

The blocks move following a 4-phase rhythm: UP, DOWN, RIGHT, LEFT. When for example you have two UP arrows one after the other, followed by a RIGHT arrow, this requires 7 steps: the block goes UP, then it stays still during the DOWN, RIGHT, LEFT phases, then it goes UP again, stays still during DOWN, finally goes RIGHT. So 4 steps are "wasted".
If instead the order of the arrows is UP, RIGHT, UP, the block ends in the same position as before, but in only 5 steps: goes UP, stays still during DOWN, goes RIGHT, stays still during LEFT, and finally goes UP. So you save 2 steps, potentially worth 2 extra points. Which is what happens if you change the solution to this one:
I said potentially, because the only thing that matters is how long it takes for the last block to reach the goal. If in a puzzle there are two blocks, and one of them does a very short path while the other takes a longer route, it doesn't matter how short the first path is. It's better to keep the paths balanced and make the blocks reach the goal at about the same time. Look at this for example:
Here the yellow block does an optimal path, but the blue block goes all over the place. It's possible to do better than this.

And to do really well in this level you have to take advantage of the most important element of the game: the ability to join and split blocks. Joining blocks is a major advantage because it allows you to move multiple blocks with a single command, saving on the number of arrows; but more importantly, it allows you to do things that are simply not possible for blocks moving alone. Look at this:
Here the two blocks will join, move together to the left, split; then the yellow block goes up pushing the blue one into its goal, and finally move to its goal. This solution is both more compact and shorter of the previous one, giving 13 extra points.

If you follow all these directions, you should easily be able to beat Andromeda with the remarkable score of... 899. That final extra point to reach 900 is still up to you. Try to find a different solution for the last puzzle which still uses joins and splits, but needs one less arrow.