LITS
Play LITS — and see why "no square piece" is not a rule at all: the square IS a 2x2 block, which LITS already forbids everywhere.
Click a cell to shade it. Shade exactly four connected cells in every outlined region; all shaded cells on the board must form one joined-up group; no 2×2 block of shaded cells anywhere; and two tetrominoes of the same shape may not touch side by side. Everything runs in your browser; nothing is uploaded.
"No square piece" is not a rule
LITS is named for the four tetrominoes it allows, and the usual way to say so is that the square is banned. But the square piece is a 2×2 block, and LITS already forbids every 2×2 block of shaded cells. The ban says nothing the other rule had not already said.
Enumerated rather than asserted — there are exactly 5 connected four-cell shapes up to rotation and reflection, and exactly one contains a 2×2:
One shape out of five, and it is the block itself rather than a shape that happens to contain one. The four letters in the puzzle's name are simply what the no-2×2 rule leaves behind — a solver who has understood that rule has nothing further to learn from "no square".
So what is the rest of that rule doing?
If banning the square were the whole of it, the no-2×2 rule would be redundant with itself. It is not: a 2×2 can also be built from two cells of one perfectly legal piece and two of another, straddling a region border. Counting every valid shading at three strengths of the rule separates the two effects:
| Board | Regions | No 2×2 rule | Square banned only | Full rule | Share removed by the square |
|---|---|---|---|---|---|
| 6 × 6 | 5 | 212,270 | 93,425 | 13,717 | 60% |
| 6 × 6 | 6 | 65,099 | 19,835 | 380 | 70% |
| 5 × 5 | 4 | 11,299 | 4,806 | 568 | 61% |
Of everything the rule removes, banning the square accounts for 60–70%, and the straddling 2×2s do the rest. So the answer to how much banning the square cuts the search is: most of it, but never all of it — and it was not a separate rule to begin with.
An earlier version of that table said the opposite. An earlier capped run put the seam share at 69% at 6x6 with six regions. Uncapped it is 30%. Several layouts had hit the 2,000-solution cap, so the largest counts were the ones truncated, and the ratio inverted. The lesson is worth more than the number: a count that stops at a cap is not a count, and capping hurts most exactly where the totals are biggest — which is where a ratio is decided. (69% became 30%.)
Why this board has no single right answer
A printed LITS has exactly one solution. Random region layouts do not. Of 1,364 layouts tested at these sizes, 1,117 had at least one valid shading and 0 had exactly one.
Printed LITS puzzles have exactly one solution. None of the 1,364 random layouts tested here did, so the boards on this page are layouts known to be solvable and the game is to find any shading that obeys all four rules. That is a limit of random layouts, not a claim that unique ones are rare by nature.
How to use
- Pick a board and press New board.
- Click a cell to shade it.
- Shade exactly four connected cells in every outlined region.
- All shaded cells on the board must form one joined-up group, with no 2x2 block anywhere.
- Two tetrominoes of the same shape may not touch side by side.
Frequently asked questions
What are the rules of LITS?
Shade exactly four connected cells in every region, so each region holds a tetromino. All the shaded cells on the board must form one connected group. No 2x2 block of shaded cells is allowed anywhere. And two tetrominoes of the same shape, counting rotations and reflections as the same, may not touch orthogonally.
Why is the square tetromino not allowed?
It is not banned separately — it cannot exist under the rules already given. The square piece IS a 2x2 block, and LITS forbids every 2x2 block of shaded cells. Of the five connected four-cell shapes, exactly one contains a 2x2 and that one is the square, so the four letters in the name are simply what the no-2x2 rule leaves behind.
How much does banning the square cut the search?
Counting every valid shading with the rule at three strengths, banning the square accounts for 60 to 70 percent of the solutions the no-2x2 rule removes. The other 30 to 40 percent are removed by 2x2 blocks that straddle two perfectly legal pieces across a region border — which is the part of the rule that is doing genuinely new work.
Do the boards here have one answer?
No, and that is deliberate. Printed LITS puzzles have exactly one solution, but random region layouts do not: of 1,364 layouts tested, 1,117 had at least one valid shading and none had exactly one. The boards here are layouts known to be solvable, so any shading obeying all four rules counts.
What counts as the same shape?
Rotations and reflections. An S and its mirror image Z are both S for the purposes of the touching rule, and an L rotated a quarter turn is still an L. That is why there are five distinct tetrominoes rather than seven.
What does LITS stand for?
The four tetrominoes that can appear: L, I, T and S. The fifth, O, is the square, which the no-2x2 rule rules out.
Does this send anything anywhere?
No. Boards are generated and checked entirely in your browser, and nothing is uploaded.
🔒 This tool runs entirely in your browser. Nothing you enter is uploaded, logged, or stored.