How to solve Color Link (Numberlink)

Find the way for every line

Every square carries a line, so a square with no dot joins in two directions and a dot in just one. Everything below follows from that.

Master No.2 is 11×11 with 9 colours. Out of 121 squares, only 16 have a line at once, the ones drawn in the picture. From here on, the question is which line goes round which side.

Start from the corners

A corner square has only two neighbours. A line through an empty corner has to use both, so corners are always the first place to look. If one of those neighbours is a dot, that dot's line is settled too.

In Easy No.11 the top-left corner has no dot, and its neighbour at row 1, column 2 is a red dot. So red's line goes into the corner and comes down to row 2, column 1.

Dots with one exit

A dot takes exactly one line. If walls and other colours' dots leave it only one square to go to, its line goes there.

In Normal No.2 the yellow dot at row 6, column 1 has a pink dot above, a brown dot below and the wall on its left. Its only exit is row 6, column 2 on the right.

In Normal No.28, the square at row 1, column 5 has dots on all three sides. A line through it would have to join two of them, and only the two blue dots can be joined. So the yellow dot at row 1, column 6 can only go down, and green goes down along the wall.

A colour with only one route

A colour hemmed in by walls and other colours' dots sometimes has just one possible route. A line cannot go through a dot, so a dot works just like a wall.

Take red in the same puzzle. The red dot at row 1, column 2 has blue dots to its right and below, so it can only go left into the corner. From there it comes down, and at row 2, column 1 the right is a blue dot again. At row 3, column 1 it could continue down to row 4, column 1, but that square is a dead end walled by dots. So it turns right to reach the red dot at row 3, column 3. That is 6 squares, and the only route red has.

Leave no square a line can't reach

Every square must carry a line, so a shape that leaves a square no line can reach is wrong. When both dots of a colour sit on one wall, the line often runs straight along it (87 of the 114 such pairs in the free puzzles).

The purple dots of Normal No.16 are at the two ends of the bottom wall. Bulge the line up by one square (dashed): the square at row 7, column 3 is then walled in by purple above and on both sides, and no line can reach it. A stretch shut in by a line and the wall can only be filled if it holds both dots of a colour. With no dots in it, the shape cannot be right. In this puzzle the purple line runs straight along the bottom row.

Don't cut another colour off

A line with both ends on walls divides the board. If a colour's two dots end up on opposite sides of it, that colour can never be joined. Before taking the shortest way, check which dots end up on each side.

The purple dots of Master No.2 are at row 9, column 1 on the left wall and row 11, column 6 on the bottom wall. Any line between them parts the board into a lower-left side and the rest. The light blue dot at row 11, column 2 sits on the bottom wall between the purple dots, so it is on the lower-left side whatever route purple takes. To join light blue, the other light blue dot at row 5, column 4 must be on that side too. So purple passes above row 5, column 4, however long that makes it.

The shortest route is 8 squares and there are 6 of them, but every one passes below row 5, column 4, so none will do. In the answer the purple line is 30 squares long.

When stuck, try one fork

When nothing more is certain, look for a line end with only two ways forward. Follow one of them in your head. If it runs into a dead end, it is wrong, and the other is the way.

Hard No.8 stops at the position in the picture once the corners and the certain squares are done. The blue line has reached row 3, column 2, and the next step is a fork: up or down. Try down.

Then the light blue dot at row 4, column 3 is blocked on its left and can only go right. The square at row 2, column 2 loses both left and down, so the red line above comes through it heading right. Finally the green dot at row 3, column 3 can only go right too, into row 3, column 4, and that is a dead end: every square beside it belongs to another colour.

So blue goes up. In this puzzle that one fork is enough: everything left follows one square at a time, to the end.

And if you really can't go on, the game's hint will show you one line.

A whole 5×5, start to finish

Here is Easy No.29, from the empty board to the end, using nothing but the ideas above.

1. The two dots on the bottom row go up

   Look at the green dot at row 5, column 1 and the yellow dot at row 5, column 2. Their other neighbours are dots of other colours and the wall, so each can only go up.

2. The three empty corners are forced turns

   The top-left, top-right and bottom-right corners have no dot, so a line must turn through each, using both of its neighbours. Both neighbours of the top-right corner are red dots, so red is done. The other two pieces have no colour yet, so they are drawn in grey.

3. Red fixes the path beside it

   With red finished, the square at row 1, column 3 cannot go right, so it takes its other two ways, left and down. In the same way row 2, column 4 goes left and down, and row 3, column 5 goes left and down. The grey piece now runs in one length from the top left to the bottom right.

4. Green carries on up

   The green line at row 4, column 1 cannot enter row 4, column 2 on its right, which is yellow, so it goes up to row 3, column 1. Nothing more is settled for certain now.

5. Work out the grey piece's colour

   The grey piece's left end is at row 2, column 1. Suppose it joins the blue dot beside it (dashed). The whole grey piece would then be blue. But the only dots past its other end, at row 5, column 4, are yellow and green, so a blue line would dead-end there. So it does not join blue: row 2, column 1 goes down to row 3, column 1, and the grey piece is green.

6. Blue goes down

   Blue can't go left now, so the blue dot at row 2, column 2 can only go down to row 3, column 2. The green line now runs in one length from the left column through row 1, column 3 to the bottom right.

7. The rest falls into place

   From here it is one square at a time. Yellow at row 4, column 4 goes left. Blue at row 3, column 3 goes left and blue is joined. Green at row 5, column 3 goes right and meets the line that was grey, joining green. Yellow joins at row 4, column 2, and every square is filled.

Look over the finished board: green is one long line of 15 squares, going all the way round, with the short blue and yellow lines inside it.