Level 1: First steps

This game is about arranging that all blocks in a configuration have a specified number of neighbors. Let's try this with 1x1x1 blocks and reach three neighbors througout. The blocks turn transparent when they have enough neighbors.

1x1x1 to at least 3 neighbors

Since there will always be at least eight 1x1x1 blocks having no more that three neighbors, there is not so much we can do with them, until we reinroduce them as booster blocks later on. Let's aim for four neighbors now with a sligthly bigger block:

2x1x1 to at least 4 neighbors

We'll get to get to 5 neighbors with 1x1x2 later, but let's break that barrier first with a bigger block:

2x1x4 to at least 5 neighbors

Let's be more ambitious and get to 6:

2x1x2 to at least 6 neighbors

Ok, so now let's go back to five neigbors, but for the smallest block where this is possible:

2x1x1 to at least 5 neighbors

And now the big one: let's get to 7 neighbors throughout!

2x1x3 to at least 7 neighbors

Level 2: Turning blocks

This far, we have kept all blocks in the same direction. Allowing them to be turned gives many more options, and if the blocks are very excentric, we can rather easily arrange many neighbors:

1x1x8 to at least 9 neighbors

Even when the blocks are not so oblong, turning gives us better opportunities to arrange many neighbors.

1x1x4 to at least 6 neighbors

Here's another one:

1x1x3 to at least 6 neighbors

Let's see how short we can make the brick and still get to 7:

1x1x5 to at least 7 neighbors

Level 3: Exact matches in the plane

We now introduce two changes at once, changing the setup substantially. We require the blocks to all lie in the same layer, making the solution essentialy 2D. And we also stop accepting "too many" neighbors. The number of neighbors need to be exactly the goal.

1x1x2 to exactly 2 neighbors

Let's make it harder and go to 3:

1x1x2 to exactly 3 neighbors

And again, with cubes:

2x1x2 to exactly 3 neighbors