On the Subject of Faster Cursed Vaults

Work smarter, not harder!

If you are not familiar with how the module works, please read the original manual. This manual does not support rule seeds.

In this solving method, directions will be noted down by numbers modulo 4. Adding 1 is the same as rotating a dial 90° clockwise.
For example, if 0 is North, 1 would be East.

Begin by noting down the initial state of dials.

For each dial, rotate it 3 times. Note down the state of the dials at every rotation. After you've noted down all 3 states, reset the module and continue.

Subtract each state of the dials by the initial state of dials. This way, the states will be offset such that the initial state is [0000].

Next, find all 3 target states. Subtract each state by the initial state.

The target states can all be reached by a combination of dial presses. To find the combination required to reach a state from the initial one, find 4 states from the ones you've noted down such that the sum of these states is equal to the target state. More details will be provided in the example on the next page.

After you've found all combinations, go through all of them in order to unlock the vault. Since all combinations are calculated from the initial state, to reach the 2nd and 3rd target states, take the difference of dial presses between consecutive dial combinations to form the required ones.

For example, if you need to press the top left dial 2x to reach the first state and 1x to reach the second state from the initial state, you will need to press the top left dial 3x to reach the 2nd state from the 1st, as 1 - 2 ≡ 3, modulo 4.

Example

The initial state is [0233]. All of the noted down states will be put into a table as follows:

#Top LeftTop RightBottom LeftBottom Right
00233023302330233
11331030131000000
22200003002130211
33113013313200022

After subtracting [0233] from each element in the table, we get a new set of states:

#Top LeftTop RightBottom LeftBottom Right
00000000000000000
11102011233110211
22011020100200022
33320030011310233

Assume that the states we need to reach are [0013], [2023] and [1220]. Subtracting [0233] from all of these gives us our actual target states: [0220], [2230], [1031].

We find the combinations required by selecting 4 states from each column on the table such that they sum to any of the target states.

In this case:
[0220] = [1102] + [0000] + [3311] + [0211];
[2230] = [2011] + [0201] + [0000] + [0022];
[1031] = [0000] + [0300] + [1131] + [0000].

For the 1st combination, this is equivalent to pressing the top left dial 1x, bottom left 1x and bottom right 1x -> (1011).

By the same definition, the 2nd combination is (2202), and the 3rd is (0330). Our initial state is (0000). To reach (1011), we press the dials as described above. To reach (2202) from (1011), we take the difference of these combinations to get (1231) -> top left 1x, top right 2x, bottom left 3x, bottom right 1x. Repeat this for the 3rd combination and unlock the vault to solve the module.

00112233445566778899AABBCCDDEEFF

00
00
11
11
22
22
33
33
44
44
55
55
66
66
77
77
88
88
99
99
AA
AA
BB
BB
CC
CC
DD
DD
EE
EE
FF
FF

00112233445566778899AABBCCDDEEFF
00112233445566778899AABBCCDDEEFF

00
00
11
11
22
22
33
33
44
44
55
55
66
66
77
77
88
88
99
99
AA
AA
BB
BB
CC
CC
DD
DD
EE
EE
FF
FF

00112233445566778899AABBCCDDEEFF
00112233445566778899AABBCCDDEEFF

00
00
11
11
22
22
33
33
44
44
55
55
66
66
77
77
88
88
99
99
AA
AA
BB
BB
CC
CC
DD
DD
EE
EE
FF
FF

00112233445566778899AABBCCDDEEFF
00112233445566778899AABBCCDDEEFF

00
00
11
11
22
22
33
33
44
44
55
55
66
66
77
77
88
88
99
99
AA
AA
BB
BB
CC
CC
DD
DD
EE
EE
FF
FF

00112233445566778899AABBCCDDEEFF
00112233445566778899AABBCCDDEEFF

00
00
11
11
22
22
33
33
44
44
55
55
66
66
77
77
88
88
99
99
AA
AA
BB
BB
CC
CC
DD
DD
EE
EE
FF
FF

00112233445566778899AABBCCDDEEFF
00112233445566778899AABBCCDDEEFF

00
00
11
11
22
22
33
33
44
44
55
55
66
66
77
77
88
88
99
99
AA
AA
BB
BB
CC
CC
DD
DD
EE
EE
FF
FF

00112233445566778899AABBCCDDEEFF
00112233445566778899AABBCCDDEEFF

00
00
11
11
22
22
33
33
44
44
55
55
66
66
77
77
88
88
99
99
AA
AA
BB
BB
CC
CC
DD
DD
EE
EE
FF
FF

00112233445566778899AABBCCDDEEFF
00112233445566778899AABBCCDDEEFF

00
00
11
11
22
22
33
33
44
44
55
55
66
66
77
77
88
88
99
99
AA
AA
BB
BB
CC
CC
DD
DD
EE
EE
FF
FF

00112233445566778899AABBCCDDEEFF
00112233445566778899AABBCCDDEEFF

00
00
11
11
22
22
33
33
44
44
55
55
66
66
77
77
88
88
99
99
AA
AA
BB
BB
CC
CC
DD
DD
EE
EE
FF
FF

00112233445566778899AABBCCDDEEFF
00112233445566778899AABBCCDDEEFF

00
00
11
11
22
22
33
33
44
44
55
55
66
66
77
77
88
88
99
99
AA
AA
BB
BB
CC
CC
DD
DD
EE
EE
FF
FF

00112233445566778899AABBCCDDEEFF
00112233445566778899AABBCCDDEEFF

00
00
11
11
22
22
33
33
44
44
55
55
66
66
77
77
88
88
99
99
AA
AA
BB
BB
CC
CC
DD
DD
EE
EE
FF
FF

00112233445566778899AABBCCDDEEFF
00112233445566778899AABBCCDDEEFF

00
00
11
11
22
22
33
33
44
44
55
55
66
66
77
77
88
88
99
99
AA
AA
BB
BB
CC
CC
DD
DD
EE
EE
FF
FF

00112233445566778899AABBCCDDEEFF
00112233445566778899AABBCCDDEEFF

00
00
11
11
22
22
33
33
44
44
55
55
66
66
77
77
88
88
99
99
AA
AA
BB
BB
CC
CC
DD
DD
EE
EE
FF
FF

00112233445566778899AABBCCDDEEFF
00112233445566778899AABBCCDDEEFF

00
00
11
11
22
22
33
33
44
44
55
55
66
66
77
77
88
88
99
99
AA
AA
BB
BB
CC
CC
DD
DD
EE
EE
FF
FF

00112233445566778899AABBCCDDEEFF
00112233445566778899AABBCCDDEEFF

00
00
11
11
22
22
33
33
44
44
55
55
66
66
77
77
88
88
99
99
AA
AA
BB
BB
CC
CC
DD
DD
EE
EE
FF
FF

00112233445566778899AABBCCDDEEFF
00112233445566778899AABBCCDDEEFF

00
00
11
11
22
22
33
33
44
44
55
55
66
66
77
77
88
88
99
99
AA
AA
BB
BB
CC
CC
DD
DD
EE
EE
FF
FF

00112233445566778899AABBCCDDEEFF
00112233445566778899AABBCCDDEEFF

00
00
11
11
22
22
33
33
44
44
55
55
66
66
77
77
88
88
99
99
AA
AA
BB
BB
CC
CC
DD
DD
EE
EE
FF
FF

00112233445566778899AABBCCDDEEFF
00112233445566778899AABBCCDDEEFF

00
00
11
11
22
22
33
33
44
44
55
55
66
66
77
77
88
88
99
99
AA
AA
BB
BB
CC
CC
DD
DD
EE
EE
FF
FF

00112233445566778899AABBCCDDEEFF
00112233445566778899AABBCCDDEEFF

00
00
11
11
22
22
33
33
44
44
55
55
66
66
77
77
88
88
99
99
AA
AA
BB
BB
CC
CC
DD
DD
EE
EE
FF
FF

00112233445566778899AABBCCDDEEFF
00112233445566778899AABBCCDDEEFF

00
00
11
11
22
22
33
33
44
44
55
55
66
66
77
77
88
88
99
99
AA
AA
BB
BB
CC
CC
DD
DD
EE
EE
FF
FF

00112233445566778899AABBCCDDEEFF
00112233445566778899AABBCCDDEEFF

00
00
11
11
22
22
33
33
44
44
55
55
66
66
77
77
88
88
99
99
AA
AA
BB
BB
CC
CC
DD
DD
EE
EE
FF
FF

00112233445566778899AABBCCDDEEFF
00112233445566778899AABBCCDDEEFF

00
00
11
11
22
22
33
33
44
44
55
55
66
66
77
77
88
88
99
99
AA
AA
BB
BB
CC
CC
DD
DD
EE
EE
FF
FF

00112233445566778899AABBCCDDEEFF
00112233445566778899AABBCCDDEEFF

00
00
11
11
22
22
33
33
44
44
55
55
66
66
77
77
88
88
99
99
AA
AA
BB
BB
CC
CC
DD
DD
EE
EE
FF
FF

00112233445566778899AABBCCDDEEFF
00112233445566778899AABBCCDDEEFF

00
00
11
11
22
22
33
33
44
44
55
55
66
66
77
77
88
88
99
99
AA
AA
BB
BB
CC
CC
DD
DD
EE
EE
FF
FF

00112233445566778899AABBCCDDEEFF