Pick a line (a row or column) with a clue containing only one number, n, whose value is more than half the line length, then imagine you have a block of solids of length n which you can place in the line and slide about. Imagine pushing the block as far as it goes into one end of the line, then imagine pushing it similarly into the other end, e.g. for a 10-cell line with the rule ‘6’:

										6, pushed left
										6, pushed right

Because the block is longer than half the line's length, there is an overlap in the middle. There is no way for either of these cells to be dots, so you can shade them in as solids:

6

Sometimes you already know the state of some of the cells, because you determined them from the lines perpendicular to the line you're working on currently. This might allow you to solve more of the current line than what you would have been able to if it was empty:

										6, before
										6, pushed left
										6, pushed right
										6, after

You can determine which cells can only have dots in them when a gap of adjacent blank cells is too small for a solid block:

4, before

4, after

or when all solids are accounted for:

								2, before
								2, after

These tactics can also be adapted and applied to lines with more than one solid block. In general, you imagine each as a sliding block, all of them on the line together, but free to slide around. They are always separated by at least one dot, never overlap, and never change their order. You should try to find all the possible ways for them to fit into the line without contradicting what's there already. If there are some cells that cannot be both solids and dots despite all the different arrangements, you can fill them in.

Normally, the rule for a particular line is insufficient to solve it completely. However, the cells you determine on the line you're working with are also cells on other lines, perpendicular to that one. This is extra information about those other lines that you didn't have when you last tried to solve them — try again, and you might get even more information, which might help to solve some parts of other lines, and so on. Eventually, the whole grid is complete.

Lines consisting of more and larger blocks are more likely to yield more information. Conversely, lines with only a few small blocks might yield nothing initially, so it's important to choose the other lines first.

A simple way to choose a productive line is to look for one with a single, large block — if its length is greater than half the line length, it will yield something, and longer blocks will yield more.

More generally, you can use the following approach to find out exactly how many solid cells of each block will be immediately revealed on a fresh line. A line of 20 cells with a rule ‘7.2.1.4’ is given as an example:

7.2.1.4

Follow these steps:

These are the widths of the known regions of solids:

7.2.1.4

The blocks of a coloured puzzle can have different colours, usually shown either by colouring the block's length, or by placing a code by the length (such as ‘R’ for ‘red’). Colours make the rules for solving slightly different, because two adjacent blocks of different colours may touch without any intervening dot.

This means, when counting to find an extreme position of a block, you must not account for at least one dot between two blocks of different colours. Also, even when you have found all the cells of a block, you might not be able to fill in dots either side of it, because the adjacent blocks could be of different colours.