On the Subject of Knot Wires

Can you knot or can you not?

Identification

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

A	C	O	R	S
T	V	X	Y	Z

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
		LEDs	Screen	Battery
Relative Position	90° Clockwise	D	L	B
	180°	I	K	H
	90° Anticlockwise	P	F	N

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

		Component
		Button	LEDs	Screen
Battery Connection	—	W	E	M
	-/-	U	Q	J

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:

0. Button is white.
1. No LED has the same colour as any other component.
2. Battery is red.
3. No yellow components.
4. Text on the button shares a character with the module serial number.
5. The module has a D battery.
6. At least two LEDs are the same colour.
7. “ABORT” is written on the button.
8. A blue component is present.
9. 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:

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:

Type O:

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:

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.

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

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:

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:

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.

Type V:

Screen: Chain Rotation Cipher

1. Take the number corresponding to the button’s text and colour.
   

   	R	G	B	C	M	Y	W
   PRESS	1	2	3	4	5	6	7
   PUSH	8	9	10	11	12	13	14
   HOLD	15	16	17	18	19	20	21
   ABORT	22	23	24	25	0	1	2

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.

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.

  Battery	The last two digits of triple the number.
  Left* LED	Subtract the ones digit from 9, leaving the tens digit as it is.
  Button	To each digit: If 5 or greater, subtract 5. If less than 5, add 5.
  Middle LED	Subtract the number from 100.
  Wires	Swap the digits.
  Right* LED	Subtract 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:

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:

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.