Abandoned crates

While out digging on the asteroid, miners and xenoarchaeologists may occasionally stumble upon crates buried in the rock. These crates are typically sealed with an old, reliable anti-tamper mechanism and a deca-code lock, a mechanical lock requiring that a 4-digit code be entered to unlock the crate. Deca-code locks have fallen out of favour on more modern installations due to mechanical limitations on the code that restrict the possible combinations to numbers where all four digits are unique, and vulnerabilities where a multitool can be used to determine how close the previously-entered code was to the correct answer, allowing a moderately-skilled codebreaker to bypass the lock.

Cracking the code

The deca-code lock is essentially a mastermind puzzle with 10 different colours of pegs. In fact, it's easier than that, because of the limitation that the same peg can't be used more than once in the code.

If you don't have a multitool, go and fetch one before you start. Randomly guessing numbers has such low odds of hitting the right code that you might as well just leave it.

Firstly, enter any four digits you like, as long as they're all different. "1234"is a good start. Then, use the multitool on the crate - it will give you a short explanation of how many digits in your guess are found in the correct code (and of those, how many were in the correct position).

Try another guess, say "5678" and take more notes. You get 10 guesses, so your first couple of guesses should simply be to eliminate the possible combinations that it can't be. For instance, if you find all four digits in 1234 and 5678, then you know the final code does not contain 9 or 0.

After that, try shifting the numbers along - 3456, for instance. If you get a number showing in the correct position, then that must be one of the numbers that was in an incorrect position in your earlier guesses, but your priority should be finding all four of the correct numbers first and then worrying about the order.

Once you get some clues that certain numbers are definitely present, change the remaining digits about. Usually you'll end up with groups or pairs where you know that one of the numbers is present. Try swapping one of the numbers for one from the other group - if it makes no difference, then you know they're both right or both wrong.

With a little practice, this process becomes relatively simple - you'll probably be able to crack them in less time than it takes to persuade security to let you "borrow" a gun.

Examples

It's easier to show than to tell, so your friendly admonster fired up his test server. We'll run through some step-by-step, with an explanation at each stage.

Example 1

• 1234 - 0 correct digits at correct positions and 0 correct digits at incorrect positions. This is a stroke of luck. 4 digits eliminated immediately.
• 5678 - 1 correct digits at correct positions and 2 correct digits at incorrect positions. Now we're getting somewhere. We also know that the missing digit must be 9 or 0.
• 7890 - 2 correct digits at correct positions and 1 correct digits at incorrect positions. 3 digits in this group too. That means the incorrect digit from 5678 must be 5 or 6, as we know the incorrect one in this group is 9 or 0. 7 and 8 are definitely present.
• 7895 - 1 correct digits at correct positions and 1 correct digits at incorrect positions. We put in the digits we know for sure are present, 7 & 8, and swap out one of the ones we're unsure on for another one we're unsure on. We only changed the last digit, 0, for a 5, and it tells us there's one less correct answer. Now only does this tell us that 5 and 9 are 'not in the code, as the change was to the correct digits it tells us that 0 is the last digit in the correct answer.
• 7860 - 2 correct digits at correct positions and 2 correct digits at incorrect positions. We already know 7 or 8 are in the right place, so 6 isn't. Let's swap them around.
• 6870 - The crate unlocks!

Example 2

• 1234 - 0 correct digits at correct positions and 1 correct digits at incorrect positions. Decent enough start.
• 5678 - 0 correct digits at correct positions and 1 correct digits at incorrect positions. Interesting. So 9 and 0 are both present. Let's see if we can narrow down the other two.
• 3456 - 1 correct digits at correct positions and 0 correct digits at incorrect positions. Doesn't tell us much yet, other than the position of whichever one is in this range. Let's start putting 9 & 0 in.
• 7890 - 0 correct digits at correct positions and 3 correct digits at incorrect positions. Bingo. As the last two guesses had all four numbers, it can't have 1 or 2. That means 3 or 4 are correct (from the first guess), and knowing that means we can eliminate 5 & 6 from the third guess. So the code has 3 or 4, 7 or 8, 9, and 0.
• 3890 - 1 correct digits at correct positions and 2 correct digits at incorrect positions. Swapping the 7 for a 3 puts a correct one in the correct position - we didn't change any positions around, so this means the first digit must be 3. It also tells us that the 8 is incorrect. So the final code is 3, 7, 9 and 0 in a different order.
• 3907 - The crate unlocks!

Example 3

Ran through this as a speedrun, probably not the optimal route. All the italic notes were added after I'd found the answer.

• 1234 - 1 correct digits at correct positions and 1 correct digits at incorrect positions.
• 5678 - 0 correct digits at correct positions and 0 correct digits at incorrect positions. That's handy. Last missing digits are 9 and 0.
• 1290 - 1 correct digits at correct positions and 2 correct digits at incorrect positions. So it's 1 or 2, 3 or 4, 9 and 0.
• 1390 - 1 correct digits at correct positions and 3 correct digits at incorrect positions. All four digits confirmed, let's try the order.
• 1903 - 0 correct digits at correct positions and 4 correct digits at incorrect positions. So the first digit isn't 1. Next.
• 9301 - 1 correct digits at correct positions and 3 correct digits at incorrect positions. Let's see if it's the 3. In retrospect, this was a bad move as 1290 had a correctly positioned digit, so I should have already known that 3 wasn't the 2nd digit. At least this tells us that SOMETHING in this guess is correct.
• 0319 - 0 correct digits at correct positions and 4 correct digits at incorrect positions. Again, confirmed that 3 isn't in the right place.
• 3091 - 0 correct digits at correct positions and 4 correct digits at incorrect positions. The 9 isn't the one that's right, so the last digit must be 0. Let's put the other digits in place - we know what numbers are not in each position from our earlier guesses.
• 9130 - The crate unlocks!

Example 4

Another speedrun.

• 1234 - 0 correct digits at correct positions and 1 correct digits at incorrect positions.
• 5678 - 1 correct digits at correct positions and 2 correct digits at incorrect positions. We can eliminate 9 and 0.
• 3456 - 2 correct digits at correct positions and 1 correct digits at incorrect positions. 5 & 6 are probably correct. Let's confirm that.
• 1256 - 1 correct digits at correct positions and 1 correct digits at incorrect positions. Confirmed. Also eliminated 1 & 2, and we know 3 OR 4, and 7 OR 8 are there.
• 3756 - 1 correct digits at correct positions and 1 correct digits at incorrect positions. This eliminates 3 & 7, as swapping them in for two known wrong answers produces the same result.
• 8456 - 2 correct digits at correct positions and 2 correct digits at incorrect positions. All four digits confirmed, let's try the order - we'll keep 4 in the same place and see what happens.
• 5468 - 2 correct digits at correct positions and 2 correct digits at incorrect positions. Something moved into the right place, and something that was in the wrong place moved into the right place.
• 5486 - 1 correct digits at correct positions and 3 correct digits at incorrect positions. Swapping the last two digits for a little more info, then plug them in where they fit the pattern...
• 6458 - The crate unlocks!

Example 5

Possibly lucky? Got this in less than three minutes from start to finish. Partly through lucky guesswork, but it wouldn't have taken much longer from that point.

• 1234 - 0 correct digits at correct positions and 2 correct digits at incorrect positions.
• 5678 - 1 correct digits at correct positions and 1 correct digits at incorrect positions. No 9 or 0.
• 3456 - 0 correct digits at correct positions and 2 correct digits at incorrect positions.
• 1256 - 0 correct digits at correct positions and 0 correct digits at incorrect positions. Code is 3, 4, 7 & 8. 7 or 8 were in the right place. Keep one there, move the other.
• 4873 - The crate unlocks! Lucky guess? Maybe, but we still had 5 more guesses to try other combinations.