Mimic Logic

Mimic Logic

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Numbers Dungeon Guide for V.1.006
By P4wn4g3
This is a guide for those who would like help with the Numbers dungeon specifically.
   
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Intro
Numbers mode is a fairly easy mode available after defeating Standard, Expert, and Random, in which all chests except the center will give you a number that represents the number of neighboring mimics on all 8 sides of that chest. Often called the Minesweeper dungeon due to it's similarity and shared rules with that game, each room is a 3x3 grid of 9 chests, the first level will start you off with 2 mimics, then the last few floors in that level with have 3 chests. 3 chests will be the number of mimics the rest of the game. In this mode the mimics lie, so if a mimic says 3 in a 2 chest puzzle for example then we know it's lying. Later in the dungeon statement text will replace other number hints randomly. For the statement text, I will assume you are already familiar with solving the hints given here since they tend to be mostly from the Standard dungeon.

General Method

I consider Numbers to be one of the easiest modes. The easiest general method to use is to find a starting point, then solve the rest of the puzzle logically, and finally double check your results either using the puzzle possibilities I've listed below or by looking for other solutions logically. You will need to use a Blue Crystal from time to time since we have a statement chest that throws off our ability to always accurately find each mimic, as well as 2-3 lying mimics that will cause situations where there are multiple solutions. Later on we will get 2 statements that cover up a useful number and the center, which eventually becomes a less useful Expert+ statement talking about gold or whatever. I do recommend buying Blue Crystals whenever you get the chance, it's rare that they are useless and you can use them as a starting point.
Puzzle Possibilities
Since all puzzles in this dungeon include a fixed number of mimics, and since they all provide the same hints, there are a limited number of puzzles in the game we can be presented with. I worked with a friend to make the following visuals via ChatGPT to represent all possible puzzles in the entire numbers dungeon, these DO NOT include rotated or reflected solutions. Examine these and rotate them in your own perspective to compare them to your puzzles, If you compare your current puzzle to these you may be able to quickly find the solution. However, there are a lot of cases where it will be faster to begin solving on your own and comparing your solution to these possibilities. Keep in mind multiple answers when you do this.

It is useful to use common scenarios in your logic to use a proof by contradiction to narrow down the kind of puzzle you have. Proof by contradiction means you assume something to be either correct or incorrect then you solve the remainder of the puzzle. If at any time you find data that contradicts the possibility of the assumption you made, you've successfully proven that situation false in this puzzle therefore the opposite of your initial assumption MUST be true. Note that you need to be specific with your initial assumption, you can't simply flip everything in the puzzle. If you assumed a 3 was true and proof by contradiction found a contradiction, the 3 and only the 3 will have been proven false. This is the main methodology in the dungeon which is why it can take some time to solve these puzzles and why it's in a harder tier. The process is quite easy to follow.

2 chest puzzle possibilities
Yes there are only 6 possibilities in the earlier levels.

Note there are some obvious standouts in these configurations, such as 0 0 0. 0 0 0 in a row guarantees the middle chest to be true. The the center north/east/south/west can only be a zero if it's two neighbors are zero. This remains true for the entire dungeon. We also have two cases where there is a 1 1 1, and these are the only times where the middle chest will be false. 1 2 1 will be symmetrical along the middle and mean the middle left/right or top/bottom are the mimics. This leaves 0 1 1 as another easy case to confirm with 2 more possibilities. Finally we are left with the possibility of a mimic in two opposing corners, meaning the other two corners will both be zero.

3 chest puzzle possibilities

This is a more complicated case with 16 possible puzzles. Note we can still easily account for 0 0 0. 2 3 2 replaces the prior 1 2 1 pattern. Note that a 3 on one edge will always indicate the opposite edge is free of mimics, so we would make that assumption to test if that lines up with the other parts of the puzzle. This test accounts for 6 of the puzzles, including the 2 3 2 puzzle. That means that it will need to be tested against all 6 of these solutions to make sure there aren't possibly multiple solutions, and note that the 3 could be lying, so comparing only a 3 on an edge to these images won't help you too much. We will want to solve for at least 4 correct numbers before we can quickly identify the puzzle from the image. 0 in a corner is in several other puzzles, 4 total not counting what we have covered already. 3 in the corner accounts for exactly one puzzle and the layout will always need to match the example here. This leaves 4 more cases. The cases where there are twos at the north middle, east/west middle, and south middle are similar and easy to test by starting with the 1/2/1 in the corner (Combo 12) and moving to 1 2 in the corners across from each other (combo 10). The final two have no mimic in the middle and instead have a true statement, with a two next to that statement. Two 2s mean that it is Combo 13. A single 2 means it's combo 15.
2 Mimic Strategy
First I recommend you look at the table(s) above and memorize some common scenarios. Identifying those is essentially the strategy for finding starting points in Numbers.

Second, look at the alphabetical statements and determine if they are providing useful information. Use Standard/Expert dungeon strategies to solve those, identify a group of mimics, or determine that the info is useless.

Since there are 5 main categories for the 2 mimic table I'll just list those. These will get you through any 2 mimic floor.

Starting Points and Tests
  • If two opposing edges have 1,2,1, the middle will be true and the two mimics are the edge boxes between the 1s (Combo 8). Otherwise move to the next bullet.

  • As soon as you find a mimic that isn't next to a particular 2, that 2 must also be a mimic.

  • Identify any triple zero along an edge. If this case doesn't apply skip to the next. If you have one, you're down to one of two puzzles. Either the mimics are the opposite corner and the opposite center giving a middle edge 1, center true, and a middle edge 2 (Combo 1), or both opposite corners are mimics with 2 middle row 1s on the edge and a true statement in the middle (Combo 2).

  • Identify any 0 in the corner, this accounts for 3 possibilities after the above. If there are no corner zeroes, move on to the next tip. Otherwise you'll always have the corner 0 between two edge 1s, with a true statement in the middle. From there we can look to see if we have 0,1,(not 1) along either edge moving away from the 0.

    1. If both corners in-line with the zero (across not diagonal) are a number other than 1, they are the two mimics. (Combo 5)

    2. If one of the corners in-line with the zero is a 1 and the second corner isn't a 1, the second corner is a mimic and the other mimic is the edge-box surrounded by 1,2,true,1,1 (See combo 4).
      Finally if we have both lines moving away from the 0 as 0,1,1, the 2 mimics are the edge boxes bordering the 2 in the diagonally opposite corner of the 0 (Combo 6).

  • The last possibilities here involve having 1,1,1 along an edge.

    1. If the two corners will make another edge of 1,2,2 opposite one another, we will have our mimics sandwiched between the 2s as a center false statement and an incorrect edge along the 2s. (Combo 7)

    2. Otherwise, we will have 1,1,1 across and 1,1,1 down sharing a corner 1. This means our center is false, and the last mimic is diagonally opposite the shared corner 1. (Combo 3)
3 Mimic Strategy
Again I recommend you look at the table(s) above and memorize some common scenarios. Identifying those is essentially the strategy for finding starting points in Numbers.

Second, look at the alphabetical statements and determine if they are providing useful information. Use Standard/Expert dungeon strategies to solve those, identify a group of mimics, or determine that the info is useless.

These get more complicated. Note that it's common for mimics here to get you identifying the correct puzzle pattern, but at an incorrect orientation. See the triple zero below for an example, many of these instances aren't quite so easy to identify.

Starting Points and Tests
  • Look for triple 0 along an edge. This always means the puzzle can be assumed to be Combo 1, use a proof by contradiction to make sure that we don't have 3 mimics posing as 0 or something similar. Even if that is the case, one of the two lines of zeroes will be mimics and the other will be true. Make sure the middle statement is true and the 2s on the sides of the middle statement are there. If you have two lines of zeroes, you'll want to use a blue crystal and open all chest on the side it identifies as safe.

  • 2,3,2 on opposite edges will nearly always mean the middle row between these is a row of mimics (Combo 16). Unfortunately, those can also be 3,3,3 creating a perfectly symmetrical box of 2 in each corner and 3 in each edge, meaning it's blue crystal time. You need to get the blue crystal to identify one safe edge, you can open the four 2s in the corner before doing this.

  • Look for a 3 in a corner (Combo 14). That's 3 in the corner, 3 in the spotlight. Assume it's true and mark the 3 adjacent boxes as mimics. Inspect the rest of the puzzle, make sure nothing is rendered impossible for your assumption otherwise the 3 is lying. Note that if you have more than one 3 in a corner, all corner 3s are false because there can only ever be one and none of the other corners will have a 3. This would automatically mean you have puzzle Combo 7, Combo 8, Combo 9, Combo 10, or Combo 12.

  • As soon as you find a mimic that isn't next to a particular 3, that 3 must also be a mimic.

  • Look for a lone 0 along an edge. If one or more exist, it's one of the mimics. This automatically means the puzzle can't be combo 8, Combo 9, or Combo 12. If you're lucky enough to have 2 zeros along an edge, you're down to Combo 2, Combo 4, Combo 6, Combo 14 (above), Combo 15 (above), Combo 16. Those last 3 are other starting points, the rest will take more logic to solve so keep going from here if you haven't solved yet.

  • Look for 0 in a corner. If it has a neighboring 3 assume it to be false, there are no cases where a corner 0 can be next to a center 3. If an edge goes 0-#-2, either the 0 or the 2 must be a mimic (so you definitely have a mimic in a corner and can rule out any solution that doesn't have a mimic in the corner). Otherwise assume it to be true with all truthful neighbors. There are 4 puzzle possibilities that stem from this, either Combo 2, Combo 4, Combo 7, and Combo 9. Some of these are listed above.

    1. If we have Combo 7 or Combo 4 we will have center edge neighboring the 0 of 1 and 2. Note that both combo 4 and combo 7 share 2 mimics opposite the 0,1. For combo 7 this means we will have a corner 1 diagonally opposite the 0, with a 2 next to it. Be aware that if you have a 0,1 opposite each other or even 2 zeroes and two ones in corners, you will end up with 2 solutions which will require blue crystals. For Combo 4 we will end up with a 2 in the diagonal corner opposite the 0, and a 0,1,1 along an edge. In this puzzle a 0,1 across from a 0,1 might make it so you need to use a blue crystal, but I think you can solve this one regardless due to the corner 2. You need to be careful when you get 2 alphabetical statements, you may need to test this from another angle and if you find another solution, use a blue crystal.

    2. If you otherwise end up with a corner 0 with 2 neighboring 1s, you have either Combo 2 or Combo 5. These puzzles share 3 non mimics as a row from the 0 of 0,1,1, and two mimics, one opposite diagonally from the 0 and one between that mimic and the safe corner 1. These two puzzles are so similar that they can be identical and leave us with no way of solving without using blue crystals. Open all known safe boxes first. If we have 2 rows of 0,1,1 off the corner 0 and we have a row/column next to the 0,1,1 of 0,3,3 we will have multiple solutions and will need to use a blue crystal, however the center and 0 should be safe as are the 0's neighbors. Similarly if we have 0,1,1 in both corners we will know the two corner 1s are safe and the center is safe. Blue crystals for the rest.

  • Look for a 3 along an edge. If it's true, the opposite 3 chests must be true. Mark these four as truthful and if you find only logical inconsistencies as answers then the 3 (and only the 3) must be false. Do note there are quite a few possibilities for a 3 in an edge, not including the 2,3,2 case you must disprove Combo 3, Combo 5 (see the previous bullet), Combo 6, Combo 8, and Combo 11. Each can be flipped 8 ways, leaving 40 possibilities. A case where the 3 is false leaves us with a similar number of unknowns, we will have Combo 1, Combo 2, Combo 3, Combo 4, Combo 5, Combo 6, Combo 7, Combo 10, Combo 11, Combo 13, Combo 14, Combo 15, and Combo 16 so I hope you've applies all the above methods to whittle these down.

  • Outliers: 1,1,1 along an edge implies Combo 3 or Combo 8. 1,2,1 along an edge implies Combo 6, or Combo 15. 1,2,2 along an edge implies Combo 11 or combo 14. Finally we have various arrangements of only 1,2 along an edge (not counting previously mentioned possibilities) which include Combo 10, Combo 12, and Combo 13. For all of these you can attempt to identify one or two other numbers to compare your puzzle with but you'll need a starting point to help narrow things down.

  • If all else fails, use a blue crystal to get you started. The following screenshot had a very large number of possibilities and no starting point. I used a Blue Crystal and determined since there were no zeroes or threes possible in the puzzle that I could identify puzzles with a corner 1 and no 0 or 3 to test, which left me with Combo 10, Combo 12, Combo 13, and Combo 15, the latter 3 of which aren't possible.
2 Mimic Examples
Example 1


The very first thing to notice in this puzzle is that it's giving us a 0 0 0 scenario. If we assume those are truthful we are then assuming all 6 upper chests are truthful. Now let's try to employ proof by contradiction assuming all 6 of these chests are false. We can only have 2 false chests so we have proven that these 6 chests MUST be true.


According to our image above there are only two possibilities here and it is extremely easy to figure it out from there. If you are applying logic though, let's assume 0 is true. That means the other two are false. 0 now neighbors a mimic and is a third mimic, so this is impossible and zero is false. Next we move to 1, which can only be true if it's remaining neighbor is false. 2 is our remaining mimic by elimination.



Example 2

This puzzle is a little more complex. I'm going to start by assuming it's combo 6, since at a glance it's not triple zero or triple 1. The easiest way to do this is to assume a corner 2 is true and its two non-diagonal neighbors will be mimics. Since it's a two mimic puzzle, all other chests must be true.

Center and northeast are true, but the 2 in the east is wrong as is the 0 in southeast. This means 2 with 2 mimics at north and west is wrong. Our next likely configuration is Combo 4. We do have a 1,1 across from a 2,1 so we can assume those as true and orient our configuration. According to Combo 4 the mimics will be northwest and west. Everything else is true and this aligns exactly with Combo 4. The puzzle is solved.

3 Mimic Examples
Example 1
The first thing to note in this puzzle is the 0 in the north. The only way this is possible is if its corner neighbors are also zero, therefore it's a lying mimic. Next we have a 3 in east, which if true means it and the 3 opposite edge boxes are true.


We have 4 numbers here so we can look at our 16 possibilities to see if this is a match for any yet. Here we find Combo 6 is the only matching possibility for the assumption that 3 is correct, so let's fill in the rest according to that orientation. We see that this is correct according to Combo 6 and there isn't any overlap with other puzzle possibilites.



Example 2

Here we have a more complicated example. We can immediately mark the 0 at the top as a mimic, but what can we do after this?


The southeast corner looks similar to one of our examples, but it's rotated and mirrored so it's easier to start by solving some of the boxes here. Looking at northwest and west we see that even though these two share a minimum of at least 2 neighboring mimics between them, there is a 1 between them so we know there is at least one mimic between them. This means the southwest statement must be false.


From here it is still easier to use logic to solve the puzzle since our orientation is still bad. We need to determine the final mimic between the west and northwest chests and there is really only one situation which makes sense, the 1 must be lying. Now we can double-check this against Combo 4 and see we have a match. We can also see Combo 7 is an invalid answer to the puzzle. Note that this is a situation where solving is much easier than comparing to the picture. If I had included rotated and mirrored images here we would have 128 pictures to compare against, so it's easier to just compare 16 of them. If you want to save the file and rotate/mirror it yourself, that's a legitimate way to compare these as well but it will likely still be slower than solving a situation like this logically.


Example 3


Here we have an obvious mimic for the top 0 so I went ahead and marked it. The next few patterns we have aren't immediately obvious even though we have zeroes in the corners, partly because the neighbor of the southwest zero is an alphabetical statement. So let's focus on the southeast 0. Assuming it's true, all neighbors are safe.


The rest of the puzzle doesn't make any sense because it will lead to too few or too many mimics. Southeast is a mimic.


We might be able to solve using the diagrams at this point, but it seems faster to do it ourselves. Notice that we have a 1 between the two 2 mimics, meaning it's our third mimic. At this point all we need to do is verify the rest of the info is inline with the puzzle, which it is, so we can solve.


In this case it was straightforward to use logic to solve the puzzle and not reference the puzzle possibilities at all due to the placement of the clues.



Beware Multiple Solutions
These situations don't normally occur until you have 2 dialog boxes which can have multiple correct configurations. They are unlikely but they do happen, so when you have situations when a group of 4 numbers has multiple puzzles associated with it, make sure you test out both solutions and use blue crystals on the questionable boxes. My original examples for this section had errors in it, Onion_Bubs was kind enough to provide some working examples.

Example 1


In this puzzle, we have determined the 0 in the west to be false from the start. The zero in the southeast is true, and due to this the 3 in the southwest must be false. If the 3 were true and the 0 were false we would have too many mimics. So now we can solve the northwest box as true since we have accounted for all red boxes. We mark all solutions with X or O and open all. This leaves us with 2 boxes that can't be solved without using an item. Notice the two solutions that Onion_Bubs has put to the left are Combo 4 and Combo 7, where the circles are intended to be truthful to that particular scenario.

Example 2


In this puzzle we have another lone zero on a middle edge at the bottom, automatically making it a mimic. This means the box north of it stating there is a mimic among the black boxes is automatically true. This means the 3 in the southeast has to be false, we have found 2 mimics already so the zero in the northwest must be true as well as its neighbors, and since the west 1 is correct this means the southwest 1 is as well. The north 1 points at the two remaining boxes as having a mimic between them. Note that just because the 3 western boxes are true doesn't mean the 3 in the east can't be a mimic if it only has 2 neighboring mimics. We need to use an item to finish this puzzle out, the diagrams show that this puzzle currently has a solution of Combo 2 or of Combo 5.

Example 3


This third puzzle shows us a more complicated scenario. If we start by looking at the zeroes, it's important to note that only one 0 can exist in a corner, so if one is correct the other is wrong. Also impossible is having two 3s on an edge on the north and west, at least one if not both are lying. Since at least one is lying, the 0 in the northwest corner is lying. We have also confirmed the east blue box as safe. It's a safe assumption at this point to say that our southeast zero, next to a confirmed true chest and a 1, is going to be safe. We can open chests so far to confirm our steps. Next we have our middle statement about a mimic in a blue box, meaning either one of the corners or potentially both have mimics, but since both of the 3s are either one or the other lying, this means one blue box and one 3 is a liar, and this leaves us only with Combo 5 as a pattern. In this situation, there are two different orientations of Combo 5 that can be true for this puzzle, meaning we must use an item to figure out which orientation we are working with so we can open all remaining safe boxes. Onion_Bubs provided a diagram of the orientations to the left.

Example 4


This last example shows some progress made on a puzzle. See if you can follow the logic and determine what the possible solutions are and why.
Remember how there can't be multiple corner 0 boxes.
Here we have middle directly accusing northwest, so one of them is a mimic.
We also have a conflict between middle and north.
Northwest and north are on a team opposing middle.
Note that 0 and 3 can't occur next to each other in any puzzle variation. They can be diagonal if the middle box were to say 3, but that never happens. Therefore either the northwest 0 is lying or the 3 is.
Lastly we have a 0 next to two 1s. A few of our corner 0 cases include these possibilities, and if this zero is true then the middle statement has to be true to disprove the other zero. We mark the northwest 0 as false and the southeast and it's neighbors true.
From the teams assigned earlier, north is also a mimic. The 1 next to it is obviously truthful.
This leaves us with a 3, and a 1. Which one is the mimic? Can you figure it out?
Solutions are either the 3 or 1 are liars, meaning we have Combo 2 or Combo 5.
Outro and Credits
Following the format of the Confuse guide by Onion_Bubs, thank you to Oni_The_Demon and overmind for their fantastic guides for general Mimic Logic gameplay. The two of them have pretty comprehensively covered the other game modes so I recommend you check out their guides if you haven't done so already.

https://gtm.steamproxy.vip/sharedfiles/filedetails/?id=3173467113
https://gtm.steamproxy.vip/sharedfiles/filedetails/?id=3169013240
Next, thanks to everyone who responded to the thread that inspired this guide, including Onion_Bubs, Oga, qbicfeet, and my friend asmeurer who used ChatGPT to generate the puzzle answers.

Thanks for reading my guide. Please let me know if there are any rules I have missed or any situations that you're unsure about, as well as any other feedback you might have about this guide. If you have a more helpful way of solving situations than I do, especially for 3 mimic puzzles with only 1s and 2s, let me know in the comments.
15 Comments
Onion_Bubs 18 May, 2024 @ 8:21pm 
Looks good for the most part. Just a couple of corrections I'd make.

Under example 1, I'm not sure what you mean about accounting for all red boxes. In theory, a blue chest claiming there's more red mimics than blue mimics could still be a mimic if there's 1 red mimic, because then there would also be 1 blue mimic so it would be lying. The reason it can't be the third mimic in that example is because it's too far away from the truthful 1 in the east position.

Under example 3, the middle box doesn't just say there's a blue mimic, it specifically says there's 1 blue mimic. That plus the two blue chests in east and southeast both being safe means exactly one of the corner 1s is a mimic and the other is safe.
P4wn4g3  [author] 18 May, 2024 @ 7:50pm 
Yeah, I wasn't 100% sure that my logic on those accounted for every possibility, does it look good to you? Should I reword something?
Onion_Bubs 18 May, 2024 @ 7:30am 
Glad they were helpful!

When you have two 0s in opposite corners in a 3-mimic puzzle, it's true that they can't both be telling the truth. There is one way they could both be mimics, and that's if the center chest is the third mimic. So if you've got two 0s in opposite corners and you've worked out that one of them is definitely a mimic and the center chest is definitely safe, the other 0 will also be safe.

In a 2-mimic puzzle, they can't both be mimics, and the only way they could both be truthful is if the other two corners are the mimics. So the vast majority of the time, once you've worked out what one of them is, you immediately know what the other one is too.
P4wn4g3  [author] 18 May, 2024 @ 2:01am 
Thanks. I've added these, let me know if you find anything else worth adding here.
Onion_Bubs 16 May, 2024 @ 7:04pm 
Sure, you can use those screenshots!
P4wn4g3  [author] 14 May, 2024 @ 9:03pm 
Thanks, I've been out on vacation. Can I use these in the guide?
Onion_Bubs 2 May, 2024 @ 4:27am 
Last one. [ibb.co] This would be another combo #2/#5 situation except, thanks to the center chest, I know it has to be combo #5. Only problem is, as the diagrams I added show, there are two valid orientations for combo #5.

In this case, it was the second one.
Onion_Bubs 2 May, 2024 @ 3:56am 
Had the combo #2/#5 situation happen again [ibb.co] so I included diagrams like on the combo #4/#7 one. Last time it was combo #2, this time it was combo #5.
Onion_Bubs 1 May, 2024 @ 7:25pm 
Got another one. [ibb.co] I've included the (flipped and rotated) diagrams of combo #4 and combo #7 and circled the numbers that match up with the puzzle to show how both of those solutions are valid.
Onion_Bubs 1 May, 2024 @ 4:55pm 
It was actually combo #2 in the end. Just because the edge opposite a 3 is all safe doesn't mean the 3 itself is safe - it could be a mimic with 2 other mimics around it.