# It's a LITS! And a... um...?

I've combined two of my favourite puzzle types - a LITS grid-deduction puzzle and a, er... a, um... you know, I could have sworn I wrote it down here somewhere!

Click on the image for a resolution where the small words held within it are readable. A wordless version of the grid for solving the LITS puzzle can be found here.

The rules for the LITS puzzle are as standard, with two additional constraints:

Rules of LITS (adapted from Grandmaster Puzzles):

• Shade exactly four connected cells in each outlined region, to form an L, I, T, or S tetromino (rotations and/or reflections permitted).
• All shaded cells are connected with each other.
• No 2×2 group of cells can be entirely shaded.
• When two tetrominoes in adjacent regions share an edge, they must not be of the same type (L, I, T, or S), regardless of rotations or reflections.
• Additionally: Each type of tetromino (L, I, T, or S) must be used exactly four times.
• And: The five empty cells already coloured black for visual purposes should be considered confirmed unshaded and cannot be shaded as part of a tetromino.

Use the output of the solved LITS to deduce the final answer to the puzzle, which should be a single thematic word...

What is this word?

• Still trying the LITS, LITS noob here, but prety sure what the other puzzle is... Sep 14, 2021 at 11:37
• Wait, for clarification, we should do the black spots as unshaded or should we just call them decoration and are not part of the puzzle? Sep 14, 2021 at 11:39
• @Anonymus25 Either! Both! I struggled to work out how best to say that (see chaotic early edit history!) The black spaces are purely for decoration but within a LITS that basically means they function as unshaded cells at the end. The important thing is: they are not shaded and cannot be part of a tetromino. Hope that makes sense! :)
– Stiv
Sep 14, 2021 at 11:41
• @Stiv, so they're like holes which are not part of the grid? Sep 15, 2021 at 5:03
• Somebody had fun filling in all the not-clue words, particularly on the right side of the board. Just there to mess with the hippopotomonstrosesquippedaliophobes? Sep 15, 2021 at 21:08

The topical word is:

LIST, which is, of course, an anagram of LITS.

The LITS solution is:

Here, coloured cells are part of the solution. Identical shapes are coloured with the same colour to make illegal adjacency stand out.

I don't have a systematic approach, I'm afraid. I started with the two obwious shapes, then worked from the top right corner. Anonymous 25's first steps describe that quite well. The S shape in the lower left corner had to be connected to the right, because all sensible connections upwards were hampered by having to use the same shape in adjacent cells.

The rest was constantly re-painting cells in the middle with MS Paint's bucket tool until I had a solution where each of the shapes was used four times. I didn't bother to mark cells that would make a 2×2 "lump", so I ran into creating these a lot. Looking at the other quite systematic approaches, I probably just got lucky. :)

The next step:

The second puzzle is a Connect Wall. The shapes of the LITS regions even spell out CONNECT WALL.

Or rather, these are four separate Connect Walls, one for each shape. I didn't see that and threw all words into one Great Connect Wall of China. Very intimidating. Sconibulus didn't make this mistake and could find many of the groups. I'm working from that output here.

First level:

L
Island: Desert, Treasure, Easter, Traffic
Jump: Rope, Ship, Suit, Jet
Shot: Screen, Sling, Snap, Moon
Standing: Crop, Order, Stones, Guard

I
League: Ivy, Rugby, Premier, Major
Virus: Anti, Retro, Corona, Computer
Hamster: Ball, Wheel, Cult, Cage

T
Race: Rat, Drag, Master, Sack
Lose: Weight, Count, Heart, Control
Sound: Asleep, Pollution, Barrier, Bite
Running: Costs, Water, Joke, Shoes

S
Bag: Sleeping, Body, Tea, Punch

Second level

Long: Island, Jump, Shot, Standing
Idea: League, Virus, Hamster, Factory
Track: Race, Lose, Sound, Running

Third and last level:

List: Long, Idea, Track, Shopping

Remarks:

I reckon the "idea list" is not a list of ideas, but an idealistic person. The clue for the second level Stiv (the puzzle's creator) mentions in comments below is that the first letters of the category match the corresponding letter shapes L, I, T and S.

• You have the correct final answer :) Re your walls: rot13(Y = nyy pbeerpg; V = bar jbeq sebz lbhe 'snpgbel' tebhc arrqf gb or fjnccrq jvgu n jbeq sebz lbhe zvffvat tebhc, juvpu zvtug znxr vg rnfvre gb fcbg gung pbaarpgvba; G = bar bs 'ehaavat' arrqf fjnccvat jvgu bar bs jung lbh'ir pnyyrq 'yvtug', ohg vfa'g...; F = nyy pbeerpg. Frpbaq yriry: 'Fcrrq' vf vapbeerpg, ohg vs lbh fhff gung bar lbh zvtug fhff gur bgure (uvag). Abgr gung va rirel tebhc gur jbeqf nyjnlf nyy pbzr orsber be nyy pbzr nsgre gur yvax jbeq, gurer'f ab zvk naq zngpuvat.)
– Stiv
Sep 15, 2021 at 8:16
• Thanks, for the additional hints, @Stiv. I've already seen the factory overhead. I'm now creating the Wikipedia page for Blue Öyster Wheel. Sep 15, 2021 at 8:29
• All first level connections now correct. The second-level one you're missing is the most obscure by far. There's a built-in clue that might help you narrow down its first letter at least - can you spot it?
– Stiv
Sep 15, 2021 at 11:03
• Well done, all now correct :) Now I need to have a think about how to award this checkmark...
– Stiv
Sep 15, 2021 at 12:05
• Ah, it was Hamster. Initially I thought Cargo, haha Sep 15, 2021 at 13:04

Partial answer, stuck near the last step.

LITS solution:

The 'background' tetormino must be in the bottom left to connect the S piece to the rest of the puzzle. Because the background is unshaded, the piece connecting to the T piece in the top left must be an S piece. The 'o' section in the upper left must be an L piece containing the bottom left corner. The background connector cannot connect to that L piece, as it would have to be an L itself, or make a square with the S piece bottom left. This means the 'o' square must be shaded across all three bottom squares to connect the left and right sides. The piece immediately to it's right must then be an I along the left side of its region, this lets us finish the 'o' L and place a T to its right. Moving back to the left, we know the rectangle there contains either an S or T piece, occupying the bottom left, and both center squares, this means the territory encircling it must have its piece in the top half. This means the connection to the bottom-left S must be to its right. The territory below the T we'd just placed must now connect left, but it can't reach straight left, or the 'background' piece would force a square. Therefor the 'background' piece must be an 'L' to reach the available connection point at the bottom of the territory, and so the territory must contain an S, to prevent an L-L connection. Now the only available connection to the right side of the puzzle is the tuning fork A, which must have 3 shaded squares across the upper connection. If we look at the bottom right, we have 2 L territories that can only contain I or L pieces, and a 2x3 rectangle. The bottom left square of the rectangle must be empty, as if it we full, the left territory must be an I, making the rectangle an L, and then neither I nor L can fit in the right territory. This means that the bottom-right of the rectangle is filled, which forces the right territory to be an L. If the left territory is also an L, it will require a fifth L to connect, either from the tuning fork a to its left, which is illegal anyway, or through an S in the rectangle to an L above. Therefor the left territory is an I, and the rectangle a T. Since the connection of the territory above must now be to the left, that piece must be an I, and the piece below an L. All that's left now is the top left, which can be either an L or an I, and an S or a T. Fortunately, we've used all our Ls and Ts, so they must be I and S respectively.

Diagram (apologies for messiness):

Pulling the words out, we get these lists:

 L        I        T         S
Crop     Worker   Rat       Detention
Screen   Ivy      Asleep    Ridge
Rope     Farming  Drag      Hanging
Desert   Anti     Heart     Sleeping
Treasure Retro    Pollution Body
Suit     Rugby    Costs     Moses
Ship     Floor    Weight    Wright
Order    Ball     Count     Currency
Traffic  Corona   Barrier   Horse
Sling    Cult     Joke      Tea
Easter   Wheel    Master    Visitor
Snap     Premier  Water     Leisure
Jet      Computer Sack      Picnic
Guard    Cage     Control   Dead

These look a little like they might be Connect Walls... and I've maybe got these categories?

L

Island: Desert, Treasure, Easter, Traffic
Jump: Rope, Ship, Suit, Jet
Shot: Screen, Sling, Snap, Moon
??: Crop, Order, Stones, Guard

I

League: Ivy, Rugby, Premier, Major
Virus: Anti, Retro, Corona, Computer
??: Worker, Farming, Floor, Cult

T

Race: Rat, Drag, Heart, Sack
Under: Weight, Water, Bite, Control
Sound: Asleep, Pollution, Barrier, Master
??: Costs, Count, Joke, Shoes

S

Bag: Sleeping, Body, Tea, Punch
??: Ridge, Wright, Currency, Horse

• I got the same grid as you, but capitulated before the wall, because I failed sort the words by shape. :( To fill in some gaps: L is rot13(fgnaqvat); I is rot13(snpgbel); T is rot13(ehaavat) and S is rot13(pneg), but you must swap rot13(pheerapl & ybnqf). Sep 14, 2021 at 20:31
• Great work so far :) The solid block of explanation is quite hard work to follow without intermediate diagrams, but the key logical step involving the O's connectivity is there. Interesting you worked entirely L to R rather than picking off the easier parts on the R first! A lot of your wall work is correct, but you should apply the comments from @MOehm above and then reconsider other categories too (there are a few further errors...).
– Stiv
Sep 15, 2021 at 6:02

Partial answer for the LITS, I believed I have encountered an error.

The first thing to do is fill in all trivial deductions, which is that the S and T area must be the S and T tetromino respectively. (Notice I am using puzz.link, so the black areas are made into unshaded cells.) And then, there are some unshaded cells to prevent 2×2 areas.

The big aha moment (putting it early to not waste time):

The bottom left S tetromino area needs to connect to other areas. This is when we realise that it must connect through the huge area. So, we can mark a lot of unshaded cells this way:

And now,

Connectivity logic, "this must be shaded, otherwise Problems" logic, no 2×2 logic, and reachability logic gets us here:

Some more logic:

The top left rectangle must play nice with the O shaped area. (It's sort of an O, right? This will be a teensy bit important for the other puzzle genre.) Similar logic down below with the other rectangular area. Doing that along with some other stuff nearby gets us here:

A very nice little step here:

The N shape near the upper left O shaped area I mentioned before must be either an I or L tetro. Being an I causes 2×2 problems on the right side with the Y-ish area underneath.

And now I think I have reached a contradiction.

Unless I'm mistaken, I believe all of the above logic is legal. But that causes problems in the top left area. Here is how I got there. First, I deduced that the N area has to be an L. I was going to say that I have found all Ls, but that causes problems here:

And this is the problem:

Now there is no way for that area to connect with the other areas it's supposed to without making an L. Please, if you are reading this, please, help to correct my mistake, or is there really no solution at all?

For the other genre:

It's a Connect Wall, of course! My feelings say that we need to take the shaded words and put them in a connect wall. Unfortunately, the LITS is broken, so this is impossible.

EDIT: I would fix this today, but it's getting late where I'm from, so probably about 12 to 13 more hours I'll fix this

Edit again: thanks to everyone who helped find the answer, keeping this as a mark on this site :)

• A promising start, but your last two images contain several logical errors. Go back a couple of steps and make sure everything you're doing is logically sound and not based on any guesswork. I guarantee you it's solvable :) PS Probably not worth posting a partial answer to seek help on a grid-deduction puzzle - you could always use the chatroom...
– Stiv
Sep 14, 2021 at 12:51
• Alright, but it's getting late, probably tommorow, can you please edit it to just the progress so far so it looks nicer? Sep 14, 2021 at 13:05

OP here (hi!). I have awarded the green checkmark to @MOehm's answer for being the most complete (the LITS solved state is presented, the hidden connecting wall is identified, and the final one-word answer has been found). I also highly commend the answer by @Sconibulus for verbalising a logical path through the LITS grid deduction process and being first to identify many of the connecting wall connections.

However, what this question still lacks is a step-by-step explanation of the LITS solution process with diagrams to make it easier to follow. I now present this here for future reference (along with a explanations of a few Easter Eggs that have not so far been uncovered...).

## LITS solution:

Step 1:

Two shapes must be wholly shaded from the start. We then notice that the tetromino in the large 'background' shape MUST be placed in a position where it links the stranded S-piece to the rest of the letter mass. We can thus rule out the majority of these background cells, noting at the same time that the T-piece in the top-right corner must be linked through the rightmost C-area, and only an S-piece will permit this.

There are also a number of other cells that MUST be shaded due to the constraints of their areas, regardless of what shape they end up being.

Step 2:

Focus on the L-area in the bottom-right...

It is impossible for the tetromino in this area to extend any further upwards. If it did, regardless of the shape forced in the neighbouring rectangle-area, it becomes impossible to place a tetromino in the other adjacent L-area:

As a result, this L-area must contain an L-shape and not border the tetromino in the other L-area (which would be forced to be a second illegally-touching L).

Step 3:

A key deduction. Look at the adjacent O and N-areas in the top-left quadrant...

Do the tetrominoes in these 2 shapes need to abut each other - or is there a way for the O-area to be linked to the W-area at the same time as the stranded S-piece?

A little thought (noting that the O-area MUST contain an L-tetromino) shows that this hypothetical O-S-W linkage is impossible without forming a 2x2 shaded area or two identical tetrominoes touching. (For an exhaustive exploration of all possibilities, see the image below...)

As a result, the tetrominos in the O and N areas must abut...

Furthermore, the N-area cannot contain a second L-piece, and so must contain an I-piece. This forces the placement of two adjacent tetrominoes.

Also, while we're thinking about the N-areas in general, note that if the E-area connected to its adjacent N-area with an L-piece, this would force a second illegally-touching L-piece in the N-area; we can deduce the states of a couple more cells in the E-area as a result...

Step 4:

Focussing now on the rectangle in the top-left quadrant...

The tetromino in this area must connect with the L-piece in the adjacent O-area. As a result, the centre-right cell within this shape MUST be shaded (since if, alternatively, the bottom-right cell were shaded this would force two illegally-touching L-pieces). This forces some cells in the adjacent C-area:

This now leaves only one option for connecting the stranded S-piece to the rest of the tetromino mass - via an L-shape in the background-area, and an S-shape in the W-area:

Step 5:

Focus next on the A-area...

The cell above the black space MUST be shaded, for connectivity. A few other spaces in the shape can be ruled out due to being unreachable or forcing two touching identical tetrominoes.

Importantly, we still need to place 3 I-pieces and there are now only 3 shapes remaining which could contain one! The I-pieces in the remaining C- and L-areas are fixed; the remaining I-piece must occupy one side of the remaining N-area.

This final I-piece can then be placed by noting that the E-area must connect to the N-area:

And finally, there is only one way to place the tetromino in the A-area (using an L-shape) and the last unresolved rectangle must contain an S-piece since we have used our full complement of T-shapes:

## Easter Eggs:

I had a lot of fun choosing 'spare' words to include in the grid. Most were chosen pretty much at random, using words that commonly have multiple connections; however, some were specifically chosen to conceal messages or just for fun...

Just for fun:

1. As spotted by @DarrelHoffman in comments, I chose to fill the 5 background-area squares that are impossible to connect to any other area with ridiculously long words.

2. There's also a concealed reference to the 2004 Will Ferrell movie, Anchorman lurking in the top row of the grid.

3. In several instances I laid red herring words that looked like they might be related to each other, in vague attempts to trap solvers trying to shortcut the logic of the LITS. Notably, the rectangle between the two L-areas contains three character names from Doctor Who (one of which was required for the connecting wall, the others not so much). Elsewhere you might spot partial names of Marvel's Avengers, Oscar-winning movies and more...

A concealed instruction:

Just in case anyone was in any doubt that the second stage of the puzzle required the construction of 4 separate connecting walls grouped by common tetromino shapes, I laid a hidden instruction within the puzzle...

If anybody happened to notice that there were a lot of animal names in the grid and then listed them, they would notice that their initials read in order spelled out 'ONE WALL PER LITS SHAPE'.

Alternatively, if anybody noticed that the words beneath the centre of the T-area spelled out 'SECRET MESSAGE: READ ANIMAL START LETTERS. OVER.' this would direct them towards this!

My thanks to all who attempted this puzzle :)