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.
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.
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.
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.
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.
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:
Shade cells in each region equal to the number given. If a region has no number, it may have any number of shaded cells, including zero. The remaining unshaded cells must form a single orthogonally contiguous area.
When they’re not in your boot, snakes are often found sunning themselves in some peaceful place. In this grid, you can see the head and the tip of the snake’s tail. Can you safely uncover the rest of its body?
The German puzzle Miss Lupun (an anagram of “plus minus”) was the inspiration for today’s puzzle – Math Ladders. Simply change the number at the top of the building into the number at the bottom using the mathematical operations in the circles between floors. Use only the digits 0-9 in four separate columns.
I really liked the concept behind Index Sums puzzles. Do a little mild arithmetic based on the values of rows and columns, and shade the appropriate cells to reach the given totals. I use a chalkboard for the look in several other puzzle types, so why not a whiteboard here?
Similar to a nonogram, Tile Paint puzzles reveal a picture. Each region must be fully shaded, or empty. Numbers indicate the total of shaded cells in their row or column.