How to Solve LITS Puzzles

LITS was invented by Inaba Naoki, and was first published in the Japanese magazine Nikoli in 2004. The name comes from four of the tetromino shapes. The O (square) tetromino is not included, because the rules forbid shading any 2×2 areas.

Rules
Basic Techniques to Solve
Solving the Puzzle

Rules

Shade four cells in each region to place exactly one L, I, T, or S-tetromino there.

Shaded cells must form an orthogonally contiguous area.
Each tetromino may be rotated or reflected.
Orthogonally adjacent tetrominoes must be different types. Pieces of the same type are permitted to touch diagonally.
Shaded cells may not cover any 2×2 area.

Shapes may be rotated or reflected.

Adjacent shapes must be different.

Identical pieces may touch diagonally.

Shaded cells may not cover a 2×2 area.

Basic Techniques to Solve

Look at small regions first.
Eliminate corner cells created by shading.
Watch for potential isolations.
Shrink large regions by imagining shapes and connections.

Start Small

The key to a LITS puzzle involves small areas that limit possible piece types. Later in these tips, we’ll examine how we create those restricted areas while solving. To start, though, first look at the smallest regions in the grid, usually composed of 4-6 cells. Imagine each tetromino shape and how it might fit. Some regions might only hold one type of piece, while others can contain several. What you’re looking for are cells that must be filled, regardless of the possible pieces. Shade all cells where piece options overlap.

In this tiny LITS puzzle, the highlighted region can only fit two possible shapes, each in one orientation.
When we imagine both placements, we see that three cells overlap.
Regardless of the solution for this region, these three cells are shaded.

Eliminate Corners

As you shade cells, you will frequently discover three-cell corners. Here, you can create further restrictions by marking out the fourth, because the rules forbid any 2×2 areas. Of course, every L, S, or T tetromino forms one or more of these corners, so if you place one, you can always eliminate cells.

A large portion of solving LITS involves preventing 2×2 areas.
S-tetrominoes have 2 corners.
So do T-shapes.

Avoid Isolation

Remember that all shaded cells must form a single orthogonally-connected area in the solution. So watch the areas of the grid where marked-out cells leave shaded pieces with only one path out. If that option is a single cell, it must be part of the adjacent tetromino. Sometimes, this path may require you to choose between more than one cell. In that case, examine other nearby cells along with it. What shapes can you eliminate? Does using that cell force an identical shape, or create a 2×2 covered area? Even if you can’t deduce which cell works immediately, you might discover overlapping cells you can shade in the region, or other cells you can eliminate if that region is large.

Unshaded cells surround this S-piece, We need to find an escape on an orthogonal path.

The next shape must use one of these two cells. It can’t use both, because of the 2×2 rule.

We know the I doesn’t fit, and S isn’t allowed. L is possible, as long as it doesn’t touch the right side.

That gives us four placement options. L (purple & red), or T (gold & green). Notice where they all overlap.

We found one shaded cell, because all four options used it. We can eliminate the cell that no option used.

Shrink Large Regions

Large regions seem intimidating at first, because they often look like they can potentially hold any type of piece. What you want to do here is chip away at all that space by working on smaller regions surrounding it, Using the 2×2 and identical shape restrictions, you can make the space smaller and smaller until it’s easier to solve. Watch out for:

Identical Shapes: If a portion of the unsolved region is adjacent to a known piece, think about those adjacent cells. Can another type of piece fit there? If some cells can only be shaded by being part of an identical tetromino to the adjacent one, you can eliminate them from the region.
2×2 Areas: Okay, what if non-identical shapes fit those adjacent cells? Does using them create a 2×2 area no matter what piece you try? If so, eliminate them.
Isolated cluster: This one’s a little sneakier. Let’s say we just eliminated a cell in our unknown region. Maybe we had a corner in an adjacent region, or perhaps we eliminated all possible pieces that would use it. Does marking it out isolate some cells so they can no longer fit a piece? If so, we can mark them out, as well.

This small puzzle contains a large region that could fit anything. Let’s see how we can shrink it.

These cells could only be filled by an identical L-tetromino, so we eliminate them.

The I-tetromino which could use this cell creates a 2×2 area with the next cell up. So we eliminate this cell.

An S or T piece here creates a 2×2 area. An I piece forces the L to escape in the next region with an L or T piece, neither of which is legal.

In fact, any placement that avoids shading this red cell causes the same problem. So it must be shaded.

So after all of that shrinking, we now know this region contains these two shaded cells as part of an S or T shape placement.

Solving the Puzzle

I know I bounced around through several different puzzles in the technique examples. If you’d like, you can use them to practice! Here are all the examples used:

For now, though, let’s walk through our original puzzle from the top of the page.

So Many W’s

Here we go, our original puzzle to solve.
5-cell “W” regions like this give us a lot of information. They can only hold an S piece in two possible positions.
Three cells overlapped, so they must all be part of the S-piece. This creates a corner, so we can eliminate a cell.

We can quickly apply this logic to all the other 5-cell W’s.
We can solve this region and eliminate two cells. The upper one can’t be part of the S-tetromino in that region.
Now we can solve this region. Then, we eliminate this cell, which forces an L-shape.

We know this 6-cell zig-zag has to hold an S. This cell can’t be part of it. That eliminates the cell to its left and solves the region.
We just cut off the three beige cells, so we can eliminate them. The red cell can’t be part of the S, so we remove it, which solves the region.
We have to mark out another cell, since it can’t be part of an S piece. We’ve also got several regions with four cells left, which solves them.

Regional Conflict

We’ve solved these two areas by eliminating cells. Next, we’ll focus on the lower right area of the grid.
This region holds either an I or L piece. Three cells overlap, so they must be shaded.
This region can only fit L-shapes. They can’t use this cell without creating a 2×2 area.

That leaves two options, both of which eliminate the beige cell. We can shade the overlap.
Notice the known L cells only touch our unknowns diagonally. We can’t eliminate L in that region yet.
We can’t use this cell – the resulting L or I would create a 2×2 area with the S above it.

Now, we can’t fit an I, and any S would touch another S. As you can see, either T placement creates a 2×2 area.
There is only one valid L placement. Now we know the unknown cells must be an I-tetromino.
After completing the I-piece, we eliminate a cell. Now we can complete the L-shape.

One Final Region

We’re down to one last area. Obviously, we can eliminate these cells, because the I would create a 2×2 area. But there’s a better place to look.
This S isn’t connected to other shaded cells. We must use one of these three cells to place a piece. Any shape using two of them creates a 2×2 area, so I isn’t an option.
A tetromino starting here would have to reach the L to the left. L and S are both invalid, as is the I. A T would also create a 2xx2 area, so nothing works.

We still can’t reach the L without creating a 2xx2 area. Nor can we wrap around the S to reach the T below.
That leaves only this cell, which must be shaded. It can’t be part of an S or T, so the final shape is an L.
After placing the final tetromino, we’ve solved the puzzle!

Rules