Using colours

Notes keep what each cell can still hold. Colours keep something else: what you are thinking. A painted cell changes neither the grid nor the answer. It keeps an idea in view while you look elsewhere.

How to paint

Colours are a way of organising your thinking, not help with solving: they reveal no numbers and don't change what is possible in the grid. A solve with colours is still a solve without help.

Following a number

The simplest use is to choose a number and paint every cell where it can still go. Among notes with several numbers, one number on its own is hard to follow. Painted, you can see at a glance how it spreads across the grid and where it has few places.

Here every cell that can still hold the 6 is painted. In row 1, box 2 and column 6, only two possibilities are left.

Keeping a pattern

When you find a pattern you haven't used yet, it is worth marking it. After thinking about another part of the grid, it is easy to forget a naked pair seen two minutes earlier. Painted, it is still there.

A naked pair in row 6, with the 4 and the 8, painted so it doesn't get lost.

It helps to use few colours and give each one a single meaning: for example, blue to follow a number and green to mark a pair. There is no rule for what each colour means, as long as it doesn't change halfway. A grid with six colours says as much as a grid with none. Once a pattern has given what it can, remove the colour.

Two sides of a choice

Colours also allow a line of reasoning that would otherwise be hard to follow. If a number can only be in two cells of a unit, exactly one of them must hold it. Give each cell a colour and look for another unit that includes one of them and where the same number also has only two possibilities. The second cell of that unit takes the opposite colour. Carry on like this, from link to link. In the end, either all the blue ones are true or all the orange ones are. This idea is called simple colouring.

  1. Let's follow the 6. In row 1 it can only be in two cells. One turns blue, the other orange: the 6 is in one of them, we don't know which.
  2. In box 2, the 6 can only be in the blue cell or the one in row 2, column 6. Each rules out the other, so this one takes the opposite colour: orange.
  3. In column 6, the 6 can only be in that orange cell or the one in row 5. This one takes the opposite colour: blue.
  4. The cell in row 5, column 8 sees one cell of each colour: the orange one along column 8, the blue one along row 5. Whichever colour is true, there is a 6 it can see. It can't hold the 6.
  5. Without the 6, only the 1 is left: it is a naked single.

Simple colouring is an advanced technique. It is a good example of what colours make possible, and something to try when you get stuck on a Hard puzzle.

Your turn

Next time you play and find a pattern you can't use yet, paint it. You will find you come back to it without effort.