On the Subject of Reordered Keys

Seeing triple now, are we?

This module consists of 6 coloured keys, each of which is labelled with a coloured number.

These keys turn black when highlighted, and remain black when pressed.

The possible colours for both the keys and the numbers labelling them are: (R)ed, (G)reen, (B)lue, (C)yan, (M)agenta, and (Y)ellow.

Any of the numbers 1 - 6 may appear on each of the keys.

The information given by each key is used to locate two cells, each within a 6x6 grid, which in turn will be used to locate a cell in a third 6x6 grid, which will have a unique value in the range 1 - 6.

One of the six keys is a pivot, which is used to determine the correct configuration of keys to be submitted, and acts as the submit button for the current sequence of keys.

Pressing any two of the other keys will swap them and their values.

The module will reset if-

  • the pivot key is pressed.
  • any key is pressed after six swaps.

In six swaps or fewer, rearrange the keys until the configuration of key values is correct, avoiding forbidden configurations, and submit it by pressing the pivot key to advance to the next of two stages.

Submitting an incorrect configuration or failing to avoid forbidden configurations will cause a strike to be issued.

Step 1: Finding key values

The value of each key is found in Grid 3, the coordinates of which, are given by entries in the other two grids.

On Grid 1,

  • the column on the left refers to the colour of the key.
  • the row along the top refers to the label on the key.

On Grid 2,

  • the column on the left refers to the colour of the label.
  • the row along the top refers to the initial position of the key from left to right.

Grid 1Grid 2Grid 3
123456
RCAFDBE
GEDBCFA
BFBCAED
CBCDEAF
MAFEBDC
YDEAFCB
123456
RVYUZXW
GZXVWUY
BXWZUYV
CUZYVWX
MYVWXZU
YWUXYVZ
UVWXYZ
A536124
B415362
C162453
D351246
E243615
F624531

Step 2: Pivot key

If exactly one of the keys has a label that is the same colour as the key itself, then the pivot is the key whose value is equal to the label of that key.

Otherwise, the pivot is the key whose value is equal to the value in Grid 3 with-

  • the row given by the sum of the primary coloured labels modulo 6, starting with A = 0.
  • the column given by the sum of the secondary coloured labels modulo 6, starting with U = 0.

Note: the primary colours are red, green, and blue and the secondary colours are cyan, magenta, and yellow.

Step 3: Key Configurations

The correct configuration of key values is a 6-cyclic permutation of the configuration '123456' with the value of the pivot key in the correct position.

A strike will be issued if the configuration of key values after swapping two keys belongs to the list below:

123465213645312546412365512634612435
124635214536314652413526513462613425
125346215463315246415623514362614235
126453216543316254416325516423615324
132564231546321654421563521634621354
134265234516324615423561523146623514
135624235461325614425631524316624153
136542236145326451426531526314625134
142356241653341256431562531426631452
143625243156342651432165532416632415
145236245361345261435162534612634215
146523246135346251436152536412635421
152436251364351264451326541263641253
153642253164352641452163542361642351
154632254136354126453621543216643521
156243256413356241456312546123645231
162345261534361245461532561342651234
163524263154362541462315562431652341
164352264513364125463512563124653142
165432265143365214465132564213654321