The rules
Every row and every column has numbers along the edge. Each number is the length of a block: a run of filled cells.
- Blocks appear in the order of the numbers. Beside the rows, the first block is the one nearest the start of the row (on the left). Above the columns, the first block is the top one.
- There is at least one empty cell between two blocks.
- 0 means the whole line is empty.
Every puzzle has exactly one solution. You can reach it by reasoning about one row or one column at a time, without guessing.
How to play here
- Click a cell to cycle between empty, filled and X. X is a note for yourself: “not filled”. Right-click marks X right away.
- Keyboard: arrows to move, Space or F to fill, X to mark, Delete to erase.
- The clue of a completed row or column is struck through.
- Thick lines split the grid into groups of five, so counting is easy.
Difficulty levels
| Level | Typical size | What decides it |
|---|---|---|
| Easy | 10×10 | Fewer than 55 deduction steps |
| Medium | 15×15 | 55 to 99 steps |
| Hard | 20×20 | 100 to 159 steps, or one or two full line checks |
| Expert | 25×25 | 160 steps or more, or three or more full line checks |
The level is set by what the computer solver needed: how many deduction steps (one row or column at a time), and which techniques.
Techniques
Counting
If a line already has every filled cell its numbers require, the rest are empty. And the reverse: if the number of undecided cells equals exactly what is still missing, fill them all.
Overlap
In a 10-cell line with a block of 7: wherever the block starts, cells 4 to 7 are always part of it. Work out where the block sits when pushed to the start of the line and where it sits when pushed to the end, and fill the part they share.
Pushing blocks
The same idea, using what is already known in the line. Push every block as far as it will go in one direction without contradicting filled cells and X marks, then in the other direction. A cell that a given block covers in both positions is filled. A cell no block can reach is empty.
Full line check
When pushing blocks isn’t enough: go through every legal arrangement of the blocks in the line. A cell that gets the same value in all of them is fixed.
Tips
- Start with the lines that have large numbers. That’s where the overlap is biggest.
- After every change to a line, check the lines that cross it.
- Mark X on every empty cell you’re sure of. It makes pushing blocks quicker.