On the Subject of Slowest but Possible Cursed Vaults

Guys, the thermal drill. Go get it.

• The vault has a distinctly-coloured dial in each of its four corners that can point in any of the four cardinal directions.
• Selecting a dial may or may not rotate all other dials. There are 4 gearing ratio states which return to initial configuration and the order does not matter.
• For each arrow/cardinals used, starting from north, add 1 for each 90° in the clockwise direction, i.e. 0 = North, 1 = East, 2 = South, 3 = West.
• There are 4⁴-1 possible combinations to unlock the vault, from 0001 to 3333 (number of clicks of TL,TR,BL,BR) and there will only be 1 correct combination for each stage.
• In all operations, modulo 4 at any point when needed.
• In order to obtain the result states:
  • Split the serial number into three pairs, and interpret them as a base 36 number and convert them into hexadecimal, taking the last two digits of each.
  • If two consecutive pairs of digits are equal, add the other pair to the second of the consecutive pairs and take the last two digits of the sum.
  • Find the table below whose corners match the colours of the dials on the module.
  • For each pair of digits, find the intersection point of the row corresponding to the first digit and the column corresponding to the second digit.
    This point lies in the centre of a 2×2 subgrid containing directional arrows.
  • Refer to the main manual for ruleseeded manual.

This method (all combinations) is currently the only possible method that I am aware of (without using tools), please contact me for new methods.

Preparation of offset tables

• For each dial, compute the difference by subtracting the direction from all dials before and after the rotation. Do this for a total of 4 times for each dial, and do the same for each dial. You should have a total of 16 sets of 4 numbers.
• Remember to reset when going from one dial to the other dial. This information will be unchanged throughout the module.

Preparation of cumulative value tables

For each stage:

• If it is not the first stage, the offset table for each dial should be shifted down according to number of times the dials have been pressed previously.
• Subtract the target configuration by the current initial configuration, this is your target cumulative value.
• (12 combinations) Construct a cumulative value table for each dial, where the dial is pressed 1, 2, and 3 times.
• (rest of combinations) Find the combination such that when added together, the value is equal to the target cumulative value.
• Example will be given in the next page.

Example solution:

Table of directions (this is obtained from the module):

Offset table (this is obtained by subtracting all dials before and after the rotation):

Cumulative table (this is obtained by cumulating the differences):

Given initial configuration = 0233, and target configuration = 0201 (from the serial pair), hence target cumulative values = 0201 - 0233 = 0012.

Solution:

The sum of cumulative values is found 0000 + 0201 + 0000 + 0211, which is equal to 0012. Thus, 0201 (number of TL, TR, BL, BR dial presses, respectively) was found as the answer.

After successfully submitting the stage, the offset table should be shifted by 0, 2, 0, 1 rows respectively, Since the next offset of TR is going to be 0103.