On the Subject of Parity
Back in the old days there were only two types of modules: decent ones and decent ones... wait hold on!
On the module will be a square display showing a letter and a digit, two switches with LEDs connected to them, and a button to the right.
Apart from the letter-number pair shown on the module, each LED has a letter-number pair associated with it, obtained from the serial number. The third and fourth characters are associated with the left LED, while the fifth and sixth characters are associated with the right LED.
Each of these letters has a sequence associated with it found in the table below. These sequences can be compared with each other. If you have to swap elements in the sequence to get to the other an even number of times, they share parity. If it takes an odd number of swaps however, they do not.
| A | B | C | D | E | F | G | H | I | J | K | L |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 3412 | 3421 | 3124 | 2143 | 1432 | 4321 | 2431 | 2134 | 1342 | 4213 | 2413 | 1423 |
| M | N | P | Q | R | S | T | U | V | W | X | Z |
| 2314 | 1234 | 4132 | 3241 | 1243 | 4123 | 4231 | 3214 | 1324 | 4312 | 3142 | 2341 |
For both LEDs, note down the following:
- Whether the sequence of its letter shares parity with the sequence of the displayed letter.
- Whether its number shares odd-even parity with the displayed number.
The states of the LEDs are determined as follows:
- The left LED must be on if these conditions are of the same parity (both apply or neither does).
- The right LED must be on if these conditions are of opposite parities (only one applies).
Set the LEDs to their correct states using the switches and submit by pressing the button on the right. If this is done correctly, the module will solve. Otherwise, a strike will be incurred, and the display will change.