The Instant Insanity II is a sliding piece tower similar to Missing Link,
but with a goal pattern reminiscent of Instant Insanity.
It is a cylinder with 16 coloured tiles arranged in four equally spaced columns. The cylinder
has five layers, and the top and bottom layers can rotate around the main axis relative to the
middle block of three layers. The top layer has only two adjacent spots where a tile can be
placed, but all the other layers can contain four tiles.
Each tile has two colours. The face of the tile is of one colour, but there are two small indicator
areas on the left and right edges. The right indicator is the same colour as the face of the tile, and
the left indicator has a different colour. The aim of the puzzle is to arrange the tiles in the lower
four layers so that all four layers and all four columns show four distinct colours, and preferably to
do it so that adjacent indicators match in colour.
There are 16 distinct pieces and two spaces on a playing board with 18 locations, so that gives a total of 18!/2 = 3,201,186,852,864,000 positions, which are all attainable. There are two essentially unique solutions, but each can have their layers permuted in 4! ways, and the empty top layer can be rotate too, so there are really 2·4!·4 = 192 solved positions amongst the 3.2·10^{15} total.
There are essentially only two solutions, which are shown below.


It is of course possible to have the layers in a different order, and the orientation of the empty layer does not matter.
Even if you know the colour pattern you want to achieve, there is still the problem of actually manoeuvring the tiles to create that pattern. Assuming that the top layer is the one with only two slots, and that those two slots are empty, then the following move sequences are useful:
A.  Swap two tiles in the uppermost full layer: 


B.  Swap the top two tiles of the front column: 

C.  Swap the middle two tiles of the front column: 

Here is a short description of how to solve it. I will number the layers 1 to 5 from top to bottom.
Phase 1: Solve the bottom layer, layer number 5.
Phase 2: Solve the remaining layers