There is one more SameGame implementation (besides the numerous ones discussed in my previous post) that I think deserves a separate posting: Cubes. There is also a lite version with only four levels to try it out, and a free ad-supported full version – though this free version does not (yet) seem to be available in all iTunes stores. As one might figure out from the illustration, Cubes is a 3 dimensional SameGame implementation. Although this seems to be just a little step further, this turns out to be a really capturing puzzle with good clarity.

Cubes has the classic objective of SameGame: remove as much as possible blocks by selecting groups of blocks (single blocks cannot be removed). The larger the group of blocks, the larger the number of points you will get. For some reason not known to me, for a group of n blocks you will get the unusual amount of n^{2}-3n+4 points. The reward is in line with most SameGame implementations, where the number of points is mostly slightly less than n^{2}. To pass a level, you need both to remove sufficient blocks, and reach a target score. Any surplus over the target will be transferred to the next level, making your live easier here.

The real nice twist of this puzzle is that (obviously) groups of block can wrap around the cube, or pass through the centre of the cube. And because the progressive scoring scheme, it really pays to carefully remove smaller groups to compile the largest groups of blocks possible. To the left you see a stage in which I have removed various smaller groups (obtaining 94 points in total so far) with the only goal to make a large cluster of blue blocks. This cluster has 34 connected block, which is enough to pass the target of 700, a shown in the illustration below (34 blocks is worth 1058 points). As you can also see, this is not enough yet to go on to the next level, because the green progress bar at the bottom indicates that I have not yet removed sufficient number of blocks. However, this second objective has until now not lead to problems in my experience.

Interacting with the puzzle is a joy on the iPhone. Swiping turns the blocks around, so you can see all sides to plan your next move. When you remove blocks (by double tapping) the ones not supported anymore will fall down in the direction of gravity (indicated by the arrow in the bottom right). Turning the iPhone changes the direction of gravity, which is practical, because it is often quicker to change gravity, than to move the blocks around until they are oriented as wished.

The whole puzzle consists of looking carefully at all sides, and try to predict what will happen if you remove a particular group of blocks. Because some blocks are hidden inside the cube, there is an element of chance in this puzzle, but I actually like this little bit of uncertainty and surprise. Only when larger clusters are removed (as illustrated in the last two screenshots) it becomes completely impossible to predict the outcome, and one simple has to wish for a good result.

Overall, I find this a highly interesting further development of SameGame. And it also shows a sequential removal puzzle that is completely inconceivable outside of a computer. I have not been able to find out anything about the developers of this variant (they call themselves Manta Research). Does anybody know more about them?

**[Update]** I made an error with the reward formula in the original version of this post. It has now been corrected.

**[Update 31 January 2009]** The developers explained the unusual reward formula as follows:

We tweaked the formula considerably during development to come up with something that would keep the gameplay balanced while still providing huge incentives to build the chain as large as possible but not the point where it gave ridiculous returns. We think we achieved that with this formula.

30 January 2009 at 12:20

Can’t figure out what it is the progress bar indicates. Is it a certain number of blocks? How many blocks must be removed for each level?

Thanks!

31 January 2009 at 10:50

I asked the developers, and they replied with the following explanation:

“The green progress bar indicates how many cubes must be removed before you can move to the next level. For obvious reasons you cannot possibly remove all cubes, particularly at higher levels with more colors, so there is a certain percentage of cubes that need to be cleared before you can move on. In general this percentage is between 80-85% of the cubes. At higher levels with more colors, we reduce the percentage because it naturally becomes more difficult to align colors and remove cubes near the end of the level.”

best

michael