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Forgot you can only use them once.
Formula
C(10, 4) = 10! / (4!(10 - 4)!)
C(10, 4) = 10! / (4! * 6!)
Factorials
10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800
4! = 4 × 3 × 2 × 1 = 24
6! = 6 × 5 × 4 × 3 × 2 × 1 = 720
Values
C(10, 4) = 3,628,800 / (24 * 720)
C(10, 4) = 3,628,800 / 17,280
C(10, 4) = 210
So, there are 210 different combinations when choosing 4 numbers from the set of numbers 0 to 9 without repetition.
Will still take a while.
...well, it's not 24. I'm not exactly Mr. Math, but the point is that it won't take you nearly as long as you think depending on your luck.
That's why I wish they didn't go so hard on the ridiculous side quests needed to sidestep these keypads, because they just encourage standing there and bruteforcing, which is boring even with only 24 combinations, but is so much safer on NRFTW that the only reason to do otherwise is for challenges.
https://savagecore.github.io/pd3-vault-cracker/
You get 2-4 numbers and they can repeat, thus you can have from 14 to 36 codes.
Edit: Oh I see where I went wrong. 14/36/24 is right.
1222 2111
1211 2122
1212 2121
1221 2112
1121 2212
1122 2211
1112 2221
14 for 2-number combinations.
1123
1132
1232
1223
1233
1213
1231
1312
1323
1332
1322
1321
Multiply by 3, 36 for 3-number combinations.
No idea what the calculation is on these, but writing them out by hand got weird.
14 for 2 fingerprints
36 for 3 fingerprints
24 for 4 fingerprints