On the Subject of S

You’d expect these one-letter modules to have gained some decency after a one-year hiatus of them… Maybe? This one has its own problems…

This module has 11 colored buttons arranged into an S shape, and 3 unpressable LEDs on the right, representing the 3 stages of this module. All 11 colors are unique, but there are 12 possible colors that can appear on the module, with one missing. The buttons will flash in a sequence, and there are 3 stages. Stage 1 has 5 flashes, Stage 2 has 6, and Stage 3 has 7. There is a long pause in between the ends of the sequence. Additionally, the order of the colors change every stage. To solve the module, press the buttons based on increasingly complicated rules. The module can't strike or advance until a sufficient amount of inputs have been made. Striking will set the module back to the first stage, but will not change anything.

Stage 1: Simon Scrambles Substitutions

Good thing this step isn't strike-dependent.

Stage 1 has 5 flashes and 5 presses. For each flash, find them in the table below (the row is needed for when the flash happened, and the column is the color). The resulting color is the color that you need to press.

#	Red	Orange	Yellow	Lime	Green	Jade	Cyan	Azure	Blue	Violet	Magenta	Rose
1st	Cyan	Azure	Blue	Violet	Magenta	Rose	Red	Orange	Yellow	Lime	Green	Jade
2nd	Azure	Blue	Cyan	Green	Jade	Lime	Magenta	Orange	Red	Rose	Violet	Yellow
3rd	Blue	Cyan	Magenta	Green	Yellow	Red	Orange	Violet	Jade	Rose	Azure	Lime
4th	Jade	Magenta	Lime	Blue	Orange	Cyan	Rose	Green	Violet	Yellow	Azure	Red
5th	Red	Blue	Cyan	Jade	Lime	Rose	Azure	Green	Orange	Violet	Yellow	Magenta

If the color that you need to press is missing from the module, press the color that flashed instead. Save the positions of the presses and the missing color for Stages 2 and 3.

Stage 2: S from Bamboozled Again and Edgework Modifications

...well, the R step is original, I guess.

Stage 2 has 6 flashes and 8 presses. In this stage, you will obtain an S-value from modifications of a value. However, before that, you will need the positions of the buttons you pressed in Stage 1. To begin, you must first determine an R-value.

To obtain R, take all of the positions of the flashes in Stage 2 as a list, and then append the positions of the presses in Stage 1. Replace all 10s with As. Then, concatenate the list into one string. This is a number in undecimal (base-11). Convert this to decimal and take the last 2 digits. Finally, if the module "Bamboozled Again" is present, swap the digits. This is R.

Store R into S. S will be modified using each color in the order they flashed. If at any point...

• S exits the range 00-99, take S modulo 100.
• S becomes a single digit, prepend a zero.

Color	Flashed in Stage 1	Pressed in Stage 1	Both Flashed and Pressed in Stage 1	Neither Flashed nor Pressed in Stage 1
Red	Subtract the number from one hundred	Add ten times the first digit	Subtract the first digit	Do nothing
Orange	Replace the first digit with nine minus the second	Replace the first digit with the difference between digits	Replace the second digit with the first	Add the digital root
Yellow	Add the number to fifty	Add nine minus the first digit	Add the second digit	Double the number
Lime	Add the sum of the first digit and the digital root	Add the sum of the second digit and the digital root	Subtract the higher digit	Add the product of the digits
Green	Subtract eighteen minus the sum of the digits	Add the higher digit	Subtract the sum of the digits	Add the sum of the digits
Jade	Add twice the sum of the digits	Add twice the first digit	Subtract twice the first digit	Add twice the digital root
Cyan	Subtract the number from ninety-nine	Add ten times the second digit	Subtract the second digit	Swap the digits
Azure	Replace the second digit with nine minus the first	Replace the second digit with the difference between digits	Replace the first digit with the second	Subtract the digital root
Blue	Subtract the number from fifty	Add nine minus the second digit	Add the first digit	Double the number and add one
Violet	Subtract the sum of the first digit and the digital root	Subtract the sum of the second digit and the digital root	Subtract the lower digit	Subtract the product of the digits
Magenta	Subtract nine minus the difference between digits	Add the lower digit	Subtract the difference between digits	Add eighteen minus the sum of the digits
Rose	Subtract twice the sum of the digits	Add twice the second digit	Subtract twice the second digit	Subtract twice the digital root

In addition to the flashes, S will also be modified using edgework and other modules. Look through the table below, and if the condition applies, apply the color modifications in the order they appear in the same way you handled the flashing colors. If you encounter a condition with a semicolon, apply all colors to the left to the semicolon normally, and then apply the next color if the extra statement is true.

Skip this table if you can spell "SIMON" with your indicators.

Condition	Color Modifications
SND or SIG indicator is present	Red
MSA or NSA indicator is present	Cyan
“Simon’s Sums” or “OmegaForget” is present	The color missing from the S in Stage 1
Serial or PS/2 port is present	Orange; Violet if Stereo RCA port is present
Other distinct one-character modules are present	Jade; Rose if “7” or “h” is present
Another module with the word “Simon” is present	Azure
Serial number contains an S	Rose; Jade if there’s more than one S in the serial number
At most one distinct module present out of “Cruel Boolean Wires” and “Modulo Maze”	The color missing from the S in Stage 2
Serial number contains a 6 or 7	Blue, Cyan; Lime if both are present
The anti-unicorn rule does not apply in “D”	Magenta, Green; Yellow if “D” is present
47 or more modules	The color in position 5 in Stage 2; Lime if there are 71 or more modules
No strikes upon entering Stage 2 for the first time	Yellow

This is your final S-value. Store R and S for the next stage, as well as the missing color.

Use the two digits in S to determine what to press (1st digit, then 2nd digit). A number in square brackets refers to the color in that position. If you're attempting to press the color that is absent, press its complement instead.

0	1	2	3	4
Red [10] Jade [0]	Cyan Blue [4] [2]	[8] Magenta [3] Green	Violet [6] [10] Cyan	[9] [4] Orange Yellow

5	6	7	8	9
Lime [1] Azure [7]	Yellow [2] [5] Jade	[1] Rose Lime [0]	[6] Red Blue [8]	Green [7] Orange [5]

Stage 3: Standard Deviation and S3 from Decay

There appear to be remnants of when you would take the standard deviation of 19 elements, which would actually qualify this module to be "objectively bad". Good thing it's only 5 elements now. Oh, and I presume S3 just stood out to the creator more than S.

Stage 3 has 7 flashes and a unique press sequence. In this stage, you will obtain the standard deviation of 5 items, and then retrieve a submission sequence using that standard deviation. The 5 items are as follows:

1. The sum of the positions and color values of the 1st and 2nd flashes.
2. The sum of the positions and color values of the 3rd and 4th flashes.
3. The sum of the positions and color values of the 5th and 6th flashes.
4. The sum of R and the sum of the position and color value of the 7th flash.
5. The sum of S and the sum of the color values of the missing colors from all 3 stages.

Note: A "color value" refers to the number of colors you need to go clockwise from Red (0) to get to the color (e.g. Jade has a color value of 5).

Once all 5 values have been obtained, follow this process to obtain your standard deviation:

1. Take the mean of the 5 items.
2. Replace each item in the list with their absolute differences between themselves and the mean.
3. Square each item in the list.
4. Take the sum of the items in the list.
5. Divide the sum by 4.
6. The standard deviation is the square root of the quotient.

Take the first 4 digits to obtain A. Then, multiply A by the square root of the sum of 111.1 and S, and truncate decimals to get B.

You are now ready to make the submission sequence S3 using the steps below:

1. Divide A by B, and retrieve the quotient (X) and remainder (Y).
2. Put X as a list element in S3. All list elements are separated by commas.
3. Store B into A and Y into B.
4. Repeat steps 1-3 until Y becomes zero (or if otherwise you're attempting to divide by zero).

5. Interpret S3 as a single string. If the module "Decay" is present, reverse this string. Numbers with more than one digit must also be reversed (e.g. 24→42, 100→001).
6. Append two commas to S3.

S3 will be inputted into the module using positions (in the order they appear in S3; colors do not matter). All commas are to be interpreted as 10s. Pressing the second 10 in a row will submit your answer.

Submitting the correct answer will solve the module.

S3 Construction Example

For convenience, let’s say that A is 3516, S is 05, and that this module is paired with a Decay. B is equal to A * sqrt(S + 111.1) = ~37884. S3 will be constructed as follows:
3516 / 37884 = 0 R 3516
37884 / 3516 = 10 R 2724
3516 / 2724 = 1 R 792
2724 / 792 = 3 R 348
792 / 348 = 2 R 96
348 / 96 = 3 R 60
96 / 60 = 1 R 36
60 / 36 = 1 R 24
36 / 24 = 1 R 12
24 / 12 = 2 R 0

Pre-reversal:
0,10,1,3,2,3,1,1,1,2

Submission Sequence (S3):
2,1,1,1,3,2,3,1,01,0,,

Appendix COLOR: Button Colors

Grayscale colors (White/Gray/Black) will never appear on the module.

If colorblind mode is enabled, the word corresponding to the color will appear between the buttons in positions 0 and 6 on the module.