On the Subject of Knot Wires

Can you knot or can you not?

This module consists of four components, each facing a cardinal direction, connected by eight wires.
The five components are: Button, Screen, LEDs*, Battery Holder and the wires themselves.
*Each of the three LEDs counts as a separate component where colour is concerned.

There are multiple different types of Knot Wires module, each with its own defusal instructions.

Identification

The module type is determined by how the components are connected:

ACORS
TVXYZ

Some module types may require further classification by finding its serial number.
The module serial number consists of six letters, the first three of which are given by the position of the components relative to the button.

Component
LEDsScreenBattery
Relative
Position
90° ClockwiseDLB
180°IKH
90° AnticlockwisePFN

The last three letters of the serial number correspond to whether each component is directly connected to the battery holder:

Component
ButtonLEDsScreen
Battery
Connection
WEM
-/-UQJ

Defusal

Every type of Knot Wires module is defused by interacting with the button.

Holding the button will cause the screen to display a non-repeating sequence of solid colours and coloured numbers ranging from 01 to 99.
Releasing the button before the sequence begins counts as a tap.

Type A:

Hold the button when the last digit of the seconds timer is the index of the first true statement:

  1. Button is white.
  2. No LED has the same colour as any other component.
  3. Battery is red.
  4. No yellow components.
  5. Text on the button shares a character with the module serial number.
  6. The module has a D battery.
  7. At least two LEDs are the same colour.
  8. "ABORT" is written on the button.
  9. A blue component is present.
  10. None of the above statements are true.

Release the button when the digital root of the displayed number is the index of the first true statement:

  1. Battery and Button are the same colour.
  2. Two or more green components are present.
  3. All components share a colour with an LED.
  4. Middle LED is cyan.
  5. Screen faces north.
  6. No other component has the same colour as the battery.
  7. Text on the button shares a character with the bomb serial number.
  8. There are exactly four distinctly coloured components on the module.
  9. None of the above statements are true.

Note: The colour of the display is ignored.

Type C:

The button may be held at any time.
The colours of the three LEDs indicate the three conditions the displayed number must meet when the button is released:

Left
R: Less than 70
G: Not one higher than a multiple of three
B: Sum of digits is less than 13
C: Difference between digits is greater than 1
M: Last digit is greater than 2
Y: At least one even digit
W: Neither digit is 3 or 6
Middle
R: Not one higher or lower than a multiple of seven
G: Sum of digits is not a multiple of 4
B: Difference between digits is not a multiple of 4
C: Not two higher or lower than a multiple of seven
M: Sum of digits is odd
Y: Difference between digits is odd
W: Sum of digits is more than one away from 9
Right
R: At least 30
G: Not one lower than a multiple of three
B: Sum of digits is greater than 5
C: Difference between digits is less than 5
M: Last digit is less than 7
Y: At most one even digit
W: Neither digit is 4 or 5

Note: The LED component is assumed to be facing south in the tables above.
Rotate the component accordingly.

The table of integers below can be used to find valid submissions:

010203040506070809
10111213141516171819
20212223242526272829
30313233343536373839
40414243444546474849
50515253545556575859
60616263646566676869
70717273747576777879
80818283848586878889
90919293949596979899

Type O:

The button may be held at any time.

One of the first five displays is the same each time the sequence is restarted.
The number shown on the repeated display is the starting value and its colour corresponds to the list of modifications to be applied to the starting value in sequence.

RedGreen
  1. If the wires are a primary colour, add 10.
    Otherwise subtract 10.
  2. If the number is greater than 50, subtract 50.
  3. If there are at least three secondary coloured components, subtract this number from 50.
    Otherwise double the number.
  4. Add the number's digital root.
  1. If the button faces east or west, add the first number in the bomb serial number. Otherwise add the last number.
  2. If the number is even, halve it. Otherwise subtract 1.
  3. Subtract the sum of the digits of the number.
  4. If at least two LEDs are the same colour, subtract the second-last digit. Otherwise add the last digit.
BlueCyan
  1. If the first digit is larger than the second, swap the digits.
  2. If the button reads "PRESS" or "PUSH", add triple the number of ports. Otherwise add triple the number of batteries on the bomb.
  3. Take the difference between the current number and the starting value.
  4. If this number is less than the number of modules on the bomb, double the number.
  1. If there is exactly one cyan LED, add the sum of the digits.
  2. Swap the last two digits.
  3. If the button is red, cyan, or white, double the number.
  4. If the battery is red, cyan, or white, subtract the number from 100.
MagentaYellow
  1. Take the last two digits of the square of the number.
  2. If the wires, battery, and button are all different colours, add the difference between the digits of the number. Otherwise add the difference between the digits of the starting value.
  3. If either digit is greater than 5, subtract 11.
    Otherwise add 9.
  4. If there are any magenta components, add the total number of widgets on the bomb.
  1. If the wires share their colour with any other component, add the sum of the serial number digits. Otherwise add the product of the serial number digits.
  2. If the module's battery type can be found on the bomb, add triple the last digit of the number.
  3. Take the sum of the digits of the number.
  4. If the LEDs are opposite the battery, multiply by 4. Otherwise multiply by 6.

If the value obtained at the end of the sequence is...

  1. negative, take its absolute value.
  2. below 10, add 20 to the value.
  3. greater than 40, subtract 20 until the value falls below 41.

The result is the final value, F.

To defuse the module, release the button at the Fth display of the sequence.

Otherwise, the button may be safely released when screen does not display a number.

Type R:

The colour of the wires indicates which of the mazes below is to be navigated.
Rotate the maze such that its orientation matches that of the button:

Red
Green
Blue
Cyan
Magenta
Yellow
White

The base locations of the start and exit are given by the colours of the button and battery, respectively.
If the button and battery are the same colour, the exit colour is white instead of the battery's colour.

R C G W M B Y

Modify the start and exit locations by moving them one space in the directions specified by each true statement:

StartExit
NorthModule has a AAA batteryTwo or more primary coloured LEDs
EastModule serial number contains 'L'Button is labelled "ABORT"
SouthModule has a 9V batteryTwo or more secondary coloured LEDs
WestModule serial number contains 'F'Button is labelled "HOLD"

If the start and exit lie on the same space, release the button only when the display is white to defuse the module.

Otherwise continue to the next page.

Releasing the button when the display is a given colour will move one space in its assigned direction.
Use the list of conditions below to assign a direction to each colour, stopping at the first satisfied condition:

Red/Cyan

  1. If there are two or more white components, the R/C direction is the direction the button is facing.
  2. Otherwise if there are no blue LEDs, the R/C direction is opposite the direction the screen is facing.
  3. Otherwise if the LEDs are opposite the screen, the R/C direction is opposite the direction the battery is facing.
  4. Otherwise the R/C direction is north.

Green/Magenta

  1. If there are two primary coloured batteries, the G/M direction is opposite the R/C direction.
  2. Otherwise if there is one secondary coloured battery, the G/M direction is opposite the direction the button is facing.
  3. Otherwise if there are three or fewer distinctly coloured components, the G/M direction is opposite the direction the battery is facing.
  4. Otherwise the G/M direction is east.

Blue/Yellow

  1. If three or more components have the same colour, the B/Y direction is 90° clockwise from the G/M direction.
  2. Otherwise if any other component has the middle LED's colour, the B/Y direction is 90° clockwise from the R/C direction.
  3. Otherwise if R/C direction is the direction the screen is facing, the B/Y direction is 90° clockwise from the direction the LEDs are facing.
  4. Otherwise the B/Y direction is west.

If a colour is assigned to a direction that already has a colour assigned to it, assign the colour to the direction 90° clockwise from it.

Tapping the button will make a move in the remaining unassigned direction.

Releasing the button when the display is white will undo any moves and return to the start location.

The module is defused once the exit location is reached.

Type S:

0-----
1.----
2..---
3...--
4....-
5.....
6-....
7--...
8---..
9----.
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--..

The button may be held at any time.

The module must be unlocked by releasing the button when the screen shows the correct colour.

This colour is obtained by interpreting the first digit of the bomb serial number as a base-36 digit, taking the digit modulo 6, and indexing into the table below.
The colour to submit matches the colour of the corresponding component.

012345
1st* LED2nd* LED3rd* LEDBatteryButtonWires

Once the module is unlocked, the three LEDs each flash a base-36 digit in Morse code.
Use the battery type to find the value of c as a base-36 character of the bomb serial number. Apply the functions corresponding to the colour of each LED onto its digit, and take the output modulo 36 to obtain a new digit for each LED.

Batteryc
AA1st character
AAA2nd character
D4th character
9V5th character
ColourFunction
RedAdd c
GreenAdd the value of the next* LED
BlueDouble the value and subtract c
CyanSubtract c
MagentaAdd the value of the previous* LED
YellowSubtract from double c
WhiteSubtract from c

*position in anticlockwise order, with wrapping.

Turn each output digit into Morse code and concatenate them, in order, to form a single string.

Take m and n to be the respective smaller and larger of the 3rd and 6th digits of the bomb serial number.

  1. If m + n is larger than the length of the string, skip this step.
    Otherwise if the text on the button reads:
    • PUSH or PRESS- Reverse the last m + n entries of the string.
    • HOLD or ABORT- Reverse the first m + n entries of the string.
  2. If m is zero skip this step. Otherwise invert the mth entry of each group of length n in the string, changing dots to dashes and dashes to dots.
  3. If the length of the string is not a multiple of three, wrap around to the beginning of the string.
  4. Separate the string into groups of three entries each. The respective 1st, 2nd, and 3rd entries of each group correspond to red, green, and blue colour components. The component is active only if there is a dash in its position.
  5. Additively mix the colour components in each group to produce a sequence of colours to submit.

Release the button when the correct colour is displayed to progress the next colour in the sequence. The module is solved once each colour in the sequence is submitted.
Tapping the button submits black.

Submitting an incorrect colour will cause the module to lock back up, requiring the unlock colour to be resubmitted.
Once unlocked, continue to submit the rest of the sequence.

Type T:

The button can be held and released at any time.

Holding the button displays two overlapping sequences, one is a letter in Morse code, the other is one of the words in the table on the next page in tap code.
Neither sequence necessarily transmits from the beginning when the button is first held.

Morse Code:

  • If the only the first digit changes, a dash is transmitted.
  • If only the last digit changes, a dot is transmitted.
  • If both digits change, a break between repeats of the sequence is transmitted.

Tap Code:

  • The amount the digit(s) change from the previously displayed number is a number from 1 to 5, these numbers form the tap code sequence.
  • There are no breaks between repeats of the sequence.

Submission

  1. Start at the displayed word.
  2. Go down the table the number of rows equal to the alphabetic position of the displayed letter, wrapping from bottom to top.
  3. Tap the button when the new word's rule is satisfied by the bomb timer.
    A correct submission will turn off one of the LEDs.
  4. Repeat steps 2 and 3 two more times.
12345
1ABC/KDE
2FGHIJ
3LMNOP
4QRSTU
5VWXYZ
ACID The sum of the seconds digits equals 7.
AZON The tens digit is greater than the ones digit.
BLUE The ones digit is equal to the number of blue components.
COPY The seconds digits are equal to each other.
ECHO The minutes digit is equal to the ones digit.
FIVE The ones digit is 5.
FOUL The ones digit is equal to the number of red and yellow components.
GREY The ones digit is equal to the number of distinctly coloured components.
JOIN The seconds digits have a difference of 1 between them.
LAND The ones digit is equal to the number of cyan and yellow components.
LEFT The ones digit is equal to the first numeric digit of the bomb serial number.
MOVE At least two digits are zero or there is less than one minute remaining.
NEWS The sum of the seconds digits is equal to the number given by the button's direction: N = 3, E = 5, S = 9, W = 11
ONYX The sum of the digits is greater than 16 or less than 5.
PINK The ones digit is equal to the number of magenta components.
PORT The ones digit is equal to the number of ports mod 10.
PUSH The difference between the minutes digit and the ones digit is given by the button's text: PUSH = 1, PRESS = 2, HOLD = 3, ABORT = 4
QUAD All nonzero digits of the last four are distinct.
SLOW The tens digit is zero.
STAR The sum of the digits is a multiple of 5.
THIS There is at most one unique nonzero digit.
TICK The number of odd digits is odd.
WHAT The ones digit is equal to the number of solved modules plus one mod 10.
WHEN The seconds digits have a difference of 4 between them.
WIRE The ones digit is equal to the index of the wire's colour in the list:
R M Y W C B G
1APPLE
2ANGER
3BRAIN
4BURST
5CAJUN
6CLIFF
7DEMON
8DOUGH
9ENJOY
10EXACT
11FIRST
12FRESH
13GLAZE
14GUILT
15HAVOC
16HOTEL
17INDEX
18IONIC
19JERKY
20JUICE
21KANJI
22KIWIS
23LOOSE
24LUNAR
25MERIT
26MUDDY
27NEWLY
28NOTCH
29ORBIT
30OXIDE
31PLANT
32PRISM
33RADIX
34ROBOT
35SPARK
36SUGAR
37TAWNY
38TRICK
39ULTRA
40UNZIP
41VALUE
42VITRO
43WAXES
44WRITE

Type V:

The button may be held at any time.

The button may be released safely before the tenth display is shown.
Once the button is released after the tenth display was shown, the module enters submission mode, and the button may no longer be released at any time.

The first ten colours of the sequence form five pairs that each correspond to a letter of the alphabet using the table below.
The five letters form one of the words in the list on the right after a sequence of three encryptions.

Decipher the word by starting from the button and go anticlockwise around the module, applying the steps corresponding to each component in order.

Take the sum of the alphabetic positions of the first two letters of the bomb serial number modulo 5 and add one to it.
Submit the two colours corresponding the nth character of the deciphered word.
Do not submit any of the first ten displays.

RGBCMYW
RVABCDEF
GAWGHIJK
BBGLMNO
CCHLXPQR
MDIMPST
YEJNQSYU
WFKORTUZ

Screen: Chain Rotation Cipher

  1. Take the number corresponding to the button's text and colour.
    RGBCMYW
    PRESS1234567
    PUSH891011121314
    HOLD15161718192021
    ABORT22232425012
  2. Caesar shift the first letter of the word forward by this number.
  3. Caesar shift each subsequent letter forward by the alphabetic position of the previous decrypted letter.

LEDs: Playfair Cipher

  1. Concatenate the names of the colours of the three LEDs in anticlockwise order and append the letters in the bomb serial number in reading order.
  2. Remove any duplicate letters and any instance of the letter X to construct the key.
  3. Enter the letters of the key into a 5 by 5 grid in reading order, then enter the remaining unused letters of the alphabet, except for X, into the grid in alphabetical order.
  4. Insert an X into the encrypted word at the position indicated by the the sum of the numbers in the bomb serial number modulo 6:
    • 0 - Before the first letter.
    • 5 - After the last letter.
    • Else - Between the nth and (n + 1)th letters.
  5. Separate the word into three pairs of letters:
    • If both letters are X - both letters remain X.
    • If one letter is X - The X is unchanged and the other letter is mapped to its diametric opposite in the grid.
    • If both letters are the same - Both letters are mapped onto their diametric opposite in the grid.
    • If the letters share a row - The letters are mapped onto the letters to their right in the grid, wrapping to the left.
    • If the letters share a column - The letters are mapped onto the letters below them in the grid, wrapping to the top.
    • Otherwise - The letters lie on diagonally opposite corners of a rectangle. The letters are mapped onto the horizontally opposite corners of the rectangle.
  6. Remove the X inserted at step 4.

Battery: Trifid Subtraction Cipher

  1. Take the sum of the first number, last number and alphabetic position of the first letter of the bomb serial number.
  2. The keyword is the nth word from the top in the table above.
  3. Turn each letter of the keyword into the ternary representation of its alphabetic position and enter each into the columns of a 3 by 5 grid of digits.
  4. Turn each letter of the encrypted word into the ternary representation of its alphabetic position and enter each into another 3 by 5 grid of digits in reading order.
  5. Take the elementwise sums of each digit in the two grids modulo 3.
  6. Turn the columns of digits of the new grid back into letters.
ABCDEFGHIJKLM
001002010011012020021022100101102110111
NOPQRSTUVWXYZ
112120121122200201202210211212220221222

Type X:

The button may be held at any time.

The sequence of numbers is reset after every tenth display, which is blank.

Releasing the button when a blank display is shown will advance the module to its submission phase. Take note of the numbers that were shown before it.

Apply a transformation to each of the nine numbers shown based on their colours.

  • If the colour of the number does not match any of the components, the number is unchanged.
  • Otherwise, apply the transformation according to the component that matches the number's colour.
    BatteryThe last two digits of triple the number.
    Left* LEDSubtract the ones digit from 9, leaving the tens digit as it is.
    ButtonTo each digit:
    • If 5 or greater, subtract 5.
    • If less than 5, add 5.
    Middle LEDSubtract the number from 100.
    WiresSwap the digits.
    Right* LEDSubtract the tens digit from 9, leaving the ones digit as it is.

*Assuming the LED component is facing north.

Take the product of all nine transformed numbers.

In the submission phase:

  • The module will cycle through up to 11 different numbers.
  • Tapping or releasing the button when a display is shown will turn it red and eliminate it from the sequence.
  • Some of these numbers appear as a pair of consecutive digits in the product.
    • If there are five or fewer of such numbers, eliminate them from the sequence.
    • Otherwise, eliminate the rest of the numbers.
  • The module is solved once there are no more numbers left to eliminate.
  • The module will reset if any number is wrongly eliminated.

Type Y:

The button may be held at any time.

Releasing the button will cause the module to play two sounds, these sounds correspond to the digits of the number that was shown on the screen when the button was released.
Do not release the button if a coloured screen or multiple of 11 is displayed.

There are ten sounds, each corresponding to one of the digits from 0-9.
Each sound originated from one of the modules in the checkerboard below. Identify the modules whose sounds are associated with digits.

Any LED
is red
Wires are
yellow
or white
Any LED
is wires'
colour
Button is
green or
magenta
Any LED
is button's
colour
Else
Button label shares letter with bomb serial number A MistakeColored
Squares
Graffiti
Numbers
Painting Simon
Shifts
Swan
Two LEDs are the same colourBattleship CreationHeart Quiz
Buzz
Simon
Shouts
Tennis
Bomb has no batteries BoxingDouble
Expert
HogwartsQwirkle SinkWord
Search
Module has AA batteriesBroken
Buttons
Double
Oh
Hypercube RGB MazeStreet
Fighter
Yahtzee
Else Cheap
Checkout
Fast
Math
LaundryRPS
Judging
ScrewZoni

Tapping the button will cause a sequence of five sounds to play corresponding to a five digit number. For each true statement below, transform the number in the way described.

  1. If the used sounds fill a row of the board or leave a row empty- Swap the first and second digits.
  2. If the used sounds fill a column of the board or leave a column empty- Swap the fourth and fifth digits.
  3. If the used sounds form a 2x2 square somewhere on the board- Reverse the digits of the number.
  4. If the used sounds form the corners of a 3x3 square somewhere on the board- Subtract the number from 99999.
  5. If any letter is common to both the bomb and module serial numbers- Swap the second and fourth digits.
  6. If there are more used sounds on black squares than white- Swap the first and third digits.
  7. If there are more used squares on the right half than the left- Swap the third and fifth digits.
  8. If there is a zero in the bomb serial number- Add 11111 to the number.

If the resulting number is less than 1000, add 1000 to it.

Use the first true statement going from left to right/top to bottom to select one row and column from the board, these will be used to obtain three prime numbers:

  1. If the intersection of the row and column is a used sound, the first prime is 2, otherwise it is 3.
  2. Count the number of used sounds in the selected column:
    • 0-1: The second prime is 5.
    • 2-3: The second prime is 7.
    • 4-5: The second prime is 11.
  3. Count the number of used sounds in the selected row:
    • 0-1: The third prime is 13.
    • 2-3: The third prime is 17.
    • 4-5: The third prime is 19.
    • 6: The third prime is 23.

Calculate the remainders of the transformed number when divided by the three primes.
After the sequence of sounds has played, three zeroes will appear on the display. In this state, holding the button will increment one of the digits and releasing it will lock in the digit displayed.
Once all three digits are locked in, the displayed number must produce the same three remainders when divided by the three primes.

Submitting incorrectly will return the module to its original state and generate a new five digit number.

Type Z:

Initially, the button may only be held when the last seconds digit of the bomb timer is the sum of the values of the three LED colours:

RedCyanGreenMagentaBlueYellowWhite
0 1 23

The button may be released at any time.

The first time a number is shown in a particular colour during the sequence, the same number is displayed each time the sequence is restarted.
Once all seven of such numbers have been shown at least once, and the button is released, a 149 second countdown will begin.

Seven inputs must be made before time runs out, in order to find which inputs those are:

  1. Arrange the seven colours in ascending order of their corresponding numbers.
  2. For each colour, in order:
    • Go down its corresponding lists below, stopping at the first conditions that are true.
    • Hold the button when the left list's rule is met.
    • Release the button when the right list's rule is met.

Holding or releasing the button at the wrong time will reset the module back to initial state. The numbers will stay the same.

Red
  • If all three LEDs are the same colour, hold when the seconds digits of the bomb timer match.
  • If two LEDs are the same colour, hold when the difference between the seconds digits of the bomb timer is 1.
  • Otherwise, hold when the difference between the seconds digits of the bomb timer is 2.
  • If no components have the colour of the largest number, release when the display is the largest number's colour.
  • If one component has the colour of the largest number, release when the display is the middle value's colour.
  • Otherwise, release when the display is the smallest value's colour.
Green
  • If the module serial number has more than one vowel, hold when the display is green.
  • If the module serial number does not contain D, K, or N, hold when the display is yellow.
  • Otherwise, hold when the display is red.
  • If there is more than two thirds of the initial bomb time remaining, release after 6 seconds.
  • If there is more than one third of the initial bomb time remaining, release after 3 seconds.
  • Otherwise, release immediately.
Blue
  • If the middle LED is a primary colour, hold when the displayed number is a multiple of 7.
  • If any LED is a primary colour, hold when the displayed number is a multiple of 5.
  • Otherwise, hold when the displayed number is a multiple of 3.
  • If the battery is facing north, release when the display is the colour of the button.
  • If the screen is facing north, release when the display is the colour of the battery.
  • Otherwise, release when the display is not the colour of any other component.
Cyan
  • If the button has "ABORT" written on it, hold when the displayed number is prime.
  • If the button has "PUSH" written on it, hold when the displayed number has exactly two prime factors*.
  • Otherwise, hold when the displayed number has exactly three prime factors*.
*Duplicate factors are counted.
  • If the number of the battery's colour is less than 31, release when the sum of the seconds digits of the bomb timer is 9.
  • If the number of the battery's colour is less than 61, release when the sum of the seconds digits of the bomb timer is 7.
  • Otherwise, release when the sum of the seconds digits of the bomb timer is 5.
Magenta
  • If the module has a D battery, hold when the last digit of the displayed number is equal to the number of red components.
  • If the module has AA batteries, hold when the last digit of the displayed number is equal to the number of blue components.
  • Otherwise, hold when the last digit of the displayed number is equal to the number of white components.
  • If any lit indicator has a letter in common with the module serial number, release when the displayed number has the same last digit as the smallest number.
  • If any unlit indicator has a letter in common with the module serial number, release when the display has the same last digit as the middle number.
  • Otherwise, release when the displayed number has the same last digit as the largest number.
Yellow
  • If there no yellow components, hold when the bomb timer has a 0 in any position.
  • If there are three or fewer secondary coloured components, hold when the bomb timer has a 2 in any position.
  • Otherwise, hold when the bomb timer has a 4 in any position.
  • If the largest number is a primary colour, release when the sum of the displayed number's last two digits is 5 or 15.
  • If the second-largest number is a primary colour, release when the difference between the displayed number's last two digits is 5.
  • Otherwise, release when either digit of the last two digits of the displayed number is the last numeric digit of the bomb serial number.
White
  • If the white number is multiple of 5, hold when the last seconds digit of the bomb timer is the last numeric digit of the bomb serial number.
  • If the white number is a multiple of 3, hold when the last seconds digit of the bomb timer is the first numeric digit of the bomb serial number.
  • Otherwise, hold when the last seconds digit of the bomb timer is the digital root of the numeric digits of the bomb serial number.
  • If one of the two smallest numbers is white, release when the last two digits of the displayed number have a difference of less than 3 from any colour number.
  • If one of the two largest numbers is white, release when the last two digits of the displayed number have a difference of exactly 3 from any colour number.
  • Otherwise, release when the last two digits of the displayed number have a difference of more than 3 from all colour numbers.