## On the Subject of Colour Shuffle

I thought this was supposed to be a revival of old Hypercolor? Where’s the damn hypercube???

The module shows 12 icosahedra, coloured with one of the colours in the diagram below. This is a result of two hidden internal sequences of binary colours — colours that have only 0 and 1 in their representation — blending.

Pressing the background will move all colours in both sequences from position `x`

to position `ax+b`

, where `a`

and `b`

are constant multipliers and offsets associated with each sequence, and `x`

being the position being taken into account. The positions on the module are cyclic. The internal sequences have the same zero-indexed starting position, and are read clockwise.

The goal of this module is to determine the two internal colour sequences, and the functions that they correspond to. After doing this, press the vertex you considered to be 0 to transition the module into submission mode. The module calculates its answer based on the vertex you pressed.

There are three stages in submission mode. In each stage, the vertex that was pressed to transition the module into submission will be coloured in a binary colour, where every other vertex will be grey. Count the number of occurrences of this colour in each internal sequence, and apply the function corresponding to the sequence, using that as `x`

. Then, take the sum of these results, and press the vertex corresponding to that number, going clockwise with 0 being the binary-coloured vertex. Advance through all three stages to disarm this module.

If an incorrect vertex is pressed, the module will strike and put the user back into the colour sequences shown before they transitioned, and any progress made within submission will be reset.