On the Subject of hexOS

"Hey, I didn't give you permission to use this technology!"
"These guys stole the source code, and couldn't be bothered to put in a keypad?"

The module has a computer with the operating system hexOS.

NOTE: For the entire module, you should never discard leading 0's!

Rhythm Identification (4-bit)

Pressing and immediately releasing it will alternate between playing 2 different rhythms each time it's played. Find both rhythms where black is a chord played and add their values together. Don't carry. (1+1 ≠ 10)

0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111

Perfect Cipher

The monitor also alternates between 2 triplets of flashing tiles. For each tile, take only the color that appeared for most. Decipher them into 2 letters.




A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Logic Gates

# Logic # Logic
AZ AND HS OR
BY NAND IR NOR
CX XAND JQ XOR
DW COMPARISON KP GULLIBILITY
EV A=1 THEN B LO NA THEN NB
FU SUM MN IMPLIES
GT EQUALITY SUM

Using both characters, obtain 2 logic gates from the left table.

Form pairs from 4-bit's 1st & 2nd, 1st & 3rd, 1st & 4th, 2nd & 3rd, 2nd & 4th, and 3rd & 4th digits.

Apply each pair to both gates, writing down each result.

Take (# of +) - (# of -) and drop the negative sign. This is the offset.

AND
LR 0 1 2
0 - - -
1 - 0 0
2 - 0 +
OR
LR 0 1 2
0 - 0 +
1 0 0 +
2 + + +
NAND
LR 0 1 2
0 + + +
1 + 0 0
2 + 0 -
NOR
LR 0 1 2
0 + 0 -
1 0 0 -
2 - - -
XAND
LR 0 1 2
0 - 0 0
1 0 0 0
2 0 0 +
XOR
LR 0 1 2
0 + 0 -
1 0 0 0
2 - 0 +
COMPARISON
LR 0 1 2
0 0 - -
1 + 0 -
2 + + 0
GULLIBILITY
LR 0 1 2
0 - - 0
1 - 0 +
2 0 + +
A=1 THEN B
LR 0 1 2
0 - - +
1 - 0 +
2 - + +
NA THEN NB
LR 0 1 2
0 + - -
1 0 0 0
2 - + +
SUM
LR 0 1 2
0 + - 0
1 - 0 +
2 0 + -
IMPLIES
LR 0 1 2
0 + + +
1 + + 0
2 + 0 -
EQUALITY
LR 0 1 2
0 + - -
1 - + -
2 - - +

Sequence Addition

The screen cycles a 30-digit number, with a pause indicating the end. Write down the entire sequence. Add each individual digit with the offset. Apply the digital root* if any exceed 9.

Sequence Modification

  • If the length of the sequence isn't divisible by 6...
    • Cut the rightmost digits until the original sequence length is divisible by 6, and paste them in a new sequence.
    • Make the new as long as the other one by repeating its own digits.
    • Add both sequences' individual digits. If any digit exceed 9, apply the digital root*.
  • Split the sequence in groups of 6. Add the left half of each group with the right half. Link all sums from left to right into one big number.
  • Repeat Sequence Modification until it is less than 6 digits long, then exclude the leftmost digits until it is 3 digits long.

*Digital Root: Adding up all digits individually until one number is formed. Example: 555 = 5+5+5 = 15 = 1+5 = 6.

Submitting

  • Holding the screen stores the number in the top-right. Releasing the screen submits the earliest unfilled position with the stored number's digit in the same position. Continuing to hold cancels the current submission. Holding and submitting the pause will clear the submission.
    • Hold and release the screen when the leftmost digit of the 3-digit number matches the leftmost digit on the module.
    • Do the same with the middlemost digit, then the rightmost digit.
  • The uplink between the assigned vault and the system will be completed, and the module will be disarmed, making it completely safe to interact with.

NOTE - Due to quantum entanglement, upon a received strike of a hexOS module, every instance of hexOS will slow down their informational distribution.

Disclaimer - While hexOS is a canon concept within Hexyl's world, the attachment of this operating system to explosive devices is a dubious concept at best.

On the Subject of octOS

"This thing is hazardous to even stand near, and you want to handle it with your BARE HANDS?"

All vault uplink modules are built to hold stability through any errors, but if the user inputs the shutdown code "888" before playing the sequence and the bottom-right object spins clockwise, the materials contained within the linked vault will completely destabilize, and the module will be overloaded.

This will make calculating the correct value significantly more difficult, but it will also send off a much greater payout in energy when successfully solved.

NOTE: For the entire module, you should never discard leading 0's!

Rhythm Identification II (4-bit)

Pressing and immediately releasing it will alternate between playing 2 different rhythms each time it's played. Find both rhythms where black is a chord played and concatenate both values together. (23 and 10 = 2310)

00
01
02
03
10
11
12
13
20
21
22
23
30
31
32
33

Perfect Cipher II

On press, the monitor alternates between 2 sets of 3 visual sequences containing 3 patterns in 2 colors. For each sequence, note down the 3 patterns with the colors that flashed least. Obtain a character using these colors. Move across the letter table in accordance to the symbols. The resulting character is the deciphered character. Repeat for the other 5 sequences.

Perfect Cipher II (Continued...)


  I R C L U F O X A J S D M V G P Y B K T E N W H Q Z
1 Right
(C)
1 Left
(C#)
2 Right
(D)
2 Left
(D#)
3 Right
(E)
4 Right
(F)
4 Left
(F#)
5 Right
(G)
5 Left
(G#)
6 Right
(A)
6 Left
(A#)
7 Right
(B)

Find the first instance of the 6-letter key, and note down its number.

Phrases (1-12) # Phrases (13-24) #
a maze with edges like their knives 1 what they will make me 13
someday ill be the shape they want me to be 2 they found me in my lowest days 14
but i dont know how much more
theyll wake away before theyre satisfied
3 breathed life back into my frozen body 15
they have sliced away my flesh 4 promising a more beautiful future 16
shorn of unsightly limbs and organs 5 then i discovered 17
more stitch and scar than human 6 what they really wanted 18
if only marble 7 they pulled me into their vortex 19
grew back so easily 8 and i saw my future reflected in their eyes 20
they have stolen away my spirit 9 a shimmering halo of impossible dreams 21
memories scattered into the slipstream 10 void of my self 22
i have no idea who i used to be 11 it was 23
i can only guess 12 perfect 24

Logic Gates II

Before doing the logic gates, if the 4-bit's first and third, or second and fourth digits match, replace each digit in 4-bit with the NOT equivalent.

Write down the 30-digit number like in hexOS. It is split into 2 sequences, with the screen cycling 3 digits of α, then 3 digits of β. Make a sequence called γ. Nth digit of γ matches the digit in Nth position of α, if N is odd, or β, if N is even.

Go through each digit in γ from left-to-right and follow all conditions in order. The symbol can be replaced more than once.

  1. If the difference of the current α & β digits is 5, replace γ's symbol with =.
  2. If the current and previous α digits match, replace γ's symbol with +.
  3. If the current and previous β digits match, replace γ's symbol with *.
  4. If the current and previous γ symbols match, replace γ's symbol with >.

Use the logic gate with matching symbols to the current γ symbol. The first 2 digits in 4-bit is the pair.

Take the result, call it an operand, and append it as the last digit in 4-bit, removing the first digit. If now the second and last digits of the 4-bit are the same, change the operand to the smallest number not present in 4-bit if NOT was applied on 4-bit before, and biggest otherwise.

Obtain a digit from applying the operand to the α and β digits whose position matches the current γ position. Record only the rightmost digit. Concatenate each digit to a sequence called δ.

NOT
IN OUT
0 4
1 3
2 2
3 1
4 0
IN OUT
# Operand
IN OUT
0 α*β
1 abs(α-β)
2 α+β
3 min(α,β)
4 max(α,β)
IN OUT
AND (0)
LR 0 1 2 3 4
0 0 0 0 0 0
1 0 1 1 1 1
2 0 1 2 2 2
3 0 1 2 3 3
4 0 1 2 3 4
OR (1)
LR 0 1 2 3 4
0 0 1 2 3 4
1 1 1 2 3 4
2 2 2 2 3 4
3 3 3 3 3 4
4 4 4 4 4 4

Logic Gates II (Continued...)


NAND (2)
LR 0 1 2 3 4
0 4 4 4 4 4
1 4 3 3 3 3
2 4 3 2 2 2
3 4 3 2 1 1
4 4 3 2 1 0
NOR (3)
LR 0 1 2 3 4
0 4 3 2 1 0
1 3 3 2 1 0
2 2 2 2 1 0
3 1 1 1 1 0
4 0 0 0 0 0
XAND (4)
LR 0 1 2 3 4
0 0 1 2 2 2
1 1 1 2 2 2
2 2 2 2 2 2
3 2 2 2 3 3
4 2 2 2 3 4
XOR (5)
LR 0 1 2 3 4
0 0 1 2 3 4
1 1 1 2 3 3
2 2 2 2 2 2
3 3 3 2 1 1
4 4 3 2 1 0
COMPARISON (6)
LR 0 1 2 3 4
0 2 1 0 0 0
1 3 2 1 0 0
2 4 3 2 1 0
3 4 4 3 2 1
4 4 4 4 3 2
GULLIBILITY (7)
LR 0 1 2 3 4
0 0 0 0 1 2
1 0 0 1 2 3
2 0 1 2 3 4
3 1 2 3 4 4
4 2 3 4 4 4
A=2 THEN B (8)
LR 0 1 2 3 4
0 0 0 0 0 4
1 0 1 1 3 4
2 0 1 2 3 4
3 0 1 3 3 4
4 0 4 4 4 4
NA THEN NB (9)
LR 0 1 2 3 4
0 4 0 0 0 0
1 3 3 1 1 1
2 2 2 2 2 2
3 1 1 1 3 3
4 0 0 0 0 4
SUM (+)
LR 0 1 2 3 4
0 0 1 2 3 4
1 1 2 3 4 0
2 2 3 4 0 1
3 3 4 0 1 2
4 4 0 1 2 3
PRODUCT (*)
LR 0 1 2 3 4
0 0 0 0 0 0
1 0 1 2 3 4
2 0 2 4 1 3
3 0 3 1 4 2
4 0 4 3 2 1
IMPLIES (>)
LR 0 1 2 3 4
0 4 4 4 4 4
1 3 4 3 4 3
2 2 2 4 4 2
3 1 2 3 4 1
4 0 0 0 0 4
EQUALITY (=)
LR 0 1 2 3 4
0 4 3 2 1 0
1 3 4 1 2 0
2 2 1 4 3 0
3 1 2 3 4 0
4 0 0 0 0 4

Sequence Addition II

  • Add each digit in δ with the number obtained in Perfect Cipher II. Apply Digital Root if any exceed 9.
  • Split δ into groups of 3. Add the 2 left digits with [the right * 10].
    Subtract 100 if any result yields 3 digits.
    Link all sums from left to right into one big number.
  • Sequence Modification II

    • If the last digit is an 8, replace all digits with the sum of that digit and their neighbouring digits. If the sum is a 2 digit number, take the rightmost digit.
    • Otherwise, if the last digit is 0, divide the number by 10. Replace the last digit with an 8 if δ is more than 3 digits long.
    • Otherwise, if the last digit is divisible by 3, replace all 3's, 6's, and 9's with either 7 on positions not divisible by 3, or 0 otherwise.
    • Otherwise, if the last digit is prime, add prime-positioned digits, and subtract non-prime-positioned digits with the last. If outside 0-9, add/subtract 10 accordingly.
    • Otherwise, subtract all digits with the last. If negative, add 10.
    • Repeat Sequence Modification II until δ is 3 digits long.

Submitting II

  • Submit δ the same way as in hexOS. Striking the module will safe-boot it back into hexOS, and all of your progress will go in vain.

NOTE - Due to the nature of octOS' instability, it is unable to slow down the informational distribution upon a received strike.

Disclaimer - octOS is not a canon modification to hexOS. However, the negative side effects of existing nearby a destabilized vault link is very real. Expected side effects include: rapid cooling or heating of nearby surfaces, general magical instability within the area, low/medium-energy spell surges, warped gravity, headaches, and itchiness and/or numbness of the skin. If nearby objects start to dissolve, or if objects start to gain a fabric-like appearance, please restabilise the vault link as soon as possible to prevent possible long-lasting damage.