Strategy for large boards

A 14×14 board uses the same techniques as a 5×5. What changes is how much there is to look at. With twelve or more colors and close to two hundred cells, the hard part is knowing where to look next, and most stalls come from scanning at random. The habits below keep a large solve moving, and the worked example at the end shows them on a smaller board you can follow move by move.

Start at the border and corners

The edge of the board is where cells lose neighbors, so it's where squeezes and forced moves show up first. Go around all four corners before anything else. A corner has only two neighbors, so if one of them is a dot or a path tip, that color has to run through the corner.

Then walk the outer ring. Large boards often have one or two long paths that hug the border for a whole side or more, because a dot near the edge with neighbors already taken has nowhere else to go. Once a border path starts, follow it as far as it's forced. Each cell it takes turns the next ring in into a new edge.

Finish short pairs first

Look for pairs whose dots are two or three cells apart, especially inside clusters of other dots. These usually have only one sensible route, and once they're done they become walls that create squeezes around them. A finished pair also removes a color from everything you have to keep in mind.

Don't assume a short pair takes the shortest route. Before you draw it, check the cells it leaves behind. If joining two nearby dots directly would strand an empty cell, that pair has to bend to pick the cell up.

Split the board into regions

Every long path you finish is a wall. When a wall runs most of the way across the board, stop and list which colors have ends on each side of it. Any color with one end on each side has to pass through the gap in the wall.

Count the gap. If a gap is two cells wide and exactly two colors need to get through it, each of them takes one of those cells, and you often know which one by which side its ends are on. If more colors need to cross than the gap has cells, a move you made earlier was wrong. This is the bottleneck idea used at the scale of the whole board, and it's the main way big boards become several small ones.

A scanning order that works

Scan in the same order every time, so nothing gets skipped:

1. Corners, then the cells along each edge.
2. Dots that touch other dots or a finished path, since these have the fewest exits.
3. Empty cells next to the move you just made. A new forced move usually appears beside the last one.
4. Gaps between regions, and which colors still need to cross them.

Only when a full pass finds nothing do you move on to thinking ahead.

Keep momentum

When a move is forced, follow its chain until it stops: the tip you just extended, then the cells next to it, then the next tip. Jumping to the other side of the board in the middle of a chain is how forced moves get missed. Big boards reward finishing one area, even a dull one, before you start another.

As you go, note the tips that have exactly two choices. Those are the candidates for thinking ahead later, and on a big board they're hard to find again.

When to think ahead

Thinking ahead is slow, so save it for when the scan is empty. Pick a tip with exactly two options. Prefer the option that would seal off part of the board or run along an edge, because that's the one that fails fastest when it's wrong. Play it in your head, follow only the forced moves it causes, and stop as soon as something breaks: a stranded cell, a color cut off from its partner, a tip boxed in. If nothing breaks within a few moves, try the other option instead of going deeper.

Worked example

This 8×8 has eight colors, small enough to follow but big enough that random scanning gets lost.

Corners and short pairs

The top-left corner has two neighbors, and one of them is Blue's dot at row 2, column 1. Blue has to run up through the corner and along the top. At row 1, column 2 it can't go down, since that's Orange's dot, so it continues to row 1, column 3.

The cell at row 3, column 1 now has two usable neighbors: Orange's dot below it and the empty cell to its right. Orange runs up into it, right one, and meets its partner at row 2, column 2. That's a short pair finished in four cells.

Blue at row 1, column 3 can't turn down. Row 2, column 3 is boxed in by Orange and two Green dots, so Blue would have nowhere to go. Blue continues right, and at row 1, column 4 Green's dot below forces it on to row 1, column 5. That leaves row 2, column 3 with only Green's two dots as neighbors, so Green joins through it.

The first real choice

Blue at row 1, column 5 can go right or down. Nothing is forced, so this is where thinking ahead comes in, and the right-hand option is the edge-hugging one to test first.

If Blue turns right, it has to run along the whole top edge and down the right side. Row 2, column 5 is then squeezed between Red's dot and the empty cell below, so Red has to drop through it and down column 5, and on its way left to its partner at row 4, column 2 it runs along row 5. That walls Brown in above row 5, cut off from its partner at row 7, column 2. So Blue turns down column 5, and Brown, now with one open side, steps down to row 4, column 4.

A wall splits the board

Now the top-right corner. Row 1, column 6 has only two usable neighbors, and one is Red's dot, so Red runs up through it, along to the corner, and down the right edge. Purple, left with one open side, drops down and joins its partner. Blue continues down column 5 and left to its partner at row 6, column 4. Pink and Brown follow their only exits.

Blue now forms a wall from the top edge down to row 6. List the colors on each side. Red has one end at row 4, column 2 on the left and its tip on the right edge. Pink has its dot at row 7, column 3 on the left and its tip at row 7, column 5 on the right. Both have to get through the gap under Blue's dot, which is two cells wide: row 7, column 4 and row 8, column 4.

Two colors need to cross and the gap has two cells, so each color takes one. Row 7, column 4 sits between Pink's dot and Pink's tip, and Red could only reach it from below with no way out. So Pink joins straight through it, and Red takes the bottom row. From here everything is forced. Red runs down the left side from row 4, column 2 and along the bottom edge, Brown closes up beside it, Pink joins through row 7, Gray steps down one, and Red's two ends meet in the bottom-right corner.

Notice how much of the solve was the border. Red alone covers most of the outer ring, and the only real decision came at the top edge. On a 12×12 or 14×14 the same pattern repeats several times: corners, a long border path, a wall, a gap count, and an occasional two-way choice tested along an edge.

When a large board still won't give, the puzzle collection has walkthroughs that show each step, and the solver handles boards up to 20×20 if you'd rather check your position against the answer.