On the Subject of The Kill Switch

Heyyy, what’s the rushhh? I’ll strike eventually, don’t worryyy.

Pressing any of the three buttons will solve the module. One of the buttons is the kill switch; when pressed, it will cause a strike some time in the future.*

For each button in reading order, assign values of 𝑥_n using the table below:

𝑥1	𝑥2	𝑥3
Batteries, modulo 3	Indicators, modulo 3	Ports, modulo 3
(Modulo 3: divide by 3, take the remainder. Eg., 11 / 3 = 3 rem 2, so 11 mod 3 = 2.)

Also take the sum of the hexadecimal labels above each button, convert it into ternary and call it D. (See Appendix B451C for more details.)

Find the first rule that applies to find the location of the kill switch:

(Button 1 is the leftmost, Button 3 is the rightmost.)

1. If all three values of 𝑥_n are equal, the kill switch is Button (𝑥₁ + 1).
2. Otherwise, if all three values of 𝑥_n are distinct:
   1. If exactly one of these values occurs in D’s digits, the kill switch is the switch with this value assigned to it.
   2. Otherwise, if exactly one of these values does not occur in D’s digits, the kill switch is Button (that value + 1).
   3. Otherwise, the kill switch is Button (D’s last digit + 1).
3. Otherwise, if the highest value of 𝑥_n is unique, the kill switch is
   Button ((D’s last digit + that value) mod 3, + 1).
4. Otherwise, if the lowest value of 𝑥_n is 0, the kill switch is
   Button ((D’s first digit + D’s last digit) mod 3, + 1).
5. Otherwise, the kill switch is Button (D’s first digit + 1).

*If all of the modules on the bomb are solved before that happens, the module will strike immediately.

Appendix B451C: Hexadecimal and Ternary

The number system we use every day is called decimal (or denary). It uses ten unique symbols, the digits 0-9, to represent numbers using place values. The rightmost digit means units, the digit left of that means tens, and so forth, each place left being ten times more significant than before. Each place represents some amount of a power of ten.

Binary is another commonly seen number system that works largely the same as decimal, but with two digits, 0 & 1, instead of ten. Its place values are the powers of two, so each place left is two times more significant, rather than the ten seen in decimal.

Hexadecimal and ternary follow the same formula — hexadecimal has sixteen unique digits, ternary has three. Hexadecimal uses powers of sixteen, ternary uses powers of three.

For hexadecimal’s sixteen digits, we use 0-9 for the first ten and A-F for the last six. For example, the hex number 9E is equal to (9 × 16) + (14 × 1), which is 158 when written in decimal. The ternary number 210 is equal to (2 × 9) + (1 × 3) + (0 × 1), which is 21 in decimal.