Most broken Kakurasu puzzles come from one of six mistakes, and the biggest is committing to a combination before the puzzle forces it. The others are smaller slips: looking at only one direction, mixing up row and column numbers, losing track of what’s already shaded, leaving finished lines open, and using the wrong total when counting empty squares. Each one is below, with how to spot it.
If you’re new, the rules and how to solve pages explain the ideas these mistakes go wrong on.
1. Picking a combination before it’s forced
When a line’s target can be made more than one way, it’s tempting to pick the one that looks neatest and carry on. The puzzle then breaks a few moves later, far from where the mistake was made, which makes it hard to find.
Here is the 5×5 puzzle from the how to solve page. Row 2 needs 6, which could be 1 + 2 + 3, 2 + 4 or 1 + 5. Say you pick 1 + 2 + 3, because it uses the three small squares. Every move after that is honest:
- Column 1 needs 10 and now has row 2. Both ways of making 10 that include row 2 (1 + 2 + 3 + 4 and 2 + 3 + 5) also use row 3, so row 3 is shaded.
- Row 3 needs 3 and now has square 1, so it needs 2 more: square 2 is shaded and squares 3, 4 and 5 are out.
- Column 2 needs 7. It has rows 2 and 3, which make 5, so it needs exactly 2 more. Row 2 is already used, and rows 1, 4 and 5 can’t make 2. The column can’t be finished.
How to avoid it: only shade a square when every remaining combination agrees on it. If two combinations still fit, leave the line and work on its crossing lines until one of them is ruled out.
2. Checking only one direction
Every square counts towards a row and a column. A move can look fine in the line you’re working on and be impossible in the other. In the same puzzle, column 5 needs 3, and row 3 on its own makes 3. But row 3 needs 3 too, and its fifth square is worth 5 to it, which is too much.
How to avoid it: before you shade a square, glance at the target of the line running the other way. It takes a second and catches most mistakes before they happen.
3. Mixing up row and column numbers
A square counts its column number towards its row, and its row number towards its column. The square in row 2, column 4 is worth 4 to row 2 but only 2 to column 4. Adding the wrong one is easy when you’re moving fast, especially near the diagonal where the two numbers are close.
How to avoid it: when you add up a row, read the numbers along the top; when you add up a column, read the numbers down the side. The row and column under your finger are highlighted on PeerPuzzles, which helps.
4. Losing track of what’s already shaded
Once a line has shaded squares, the target that matters is what’s left. A 5-square row that needs 9 could be 2 + 3 + 4 from scratch. But if square 5 is already shaded, only 4 is left, which is square 4 or squares 1 and 3, so square 2 is out. Still thinking in 9s, you’d miss that and might even shade 2 + 3 + 4 on top of square 5.
How to avoid it: every time you shade a square, subtract it from both of its lines’ targets and work with what’s left.
5. Leaving a finished line open
When a line reaches its target exactly, every other square in it must be empty. It’s easy to move on without crossing them out, but those crosses are what the crossing lines need. An uncrossed square looks open to the column running through it, so you lose a deduction there.
How to avoid it: when a target is met (it turns grey on PeerPuzzles), cross out the rest of the line straight away.
6. Using the wrong total when counting empty squares
Counting the empty squares only works with the right largest target for the grid: the sum of all the square numbers in a line.
| Grid | Largest target |
|---|---|
| 5×5 | 15 |
| 7×7 | 28 |
| 9×9 | 45 |
Use 15 on a 7×7 grid and every empty-square count comes out 13 too small.
How to avoid it: check the grid size before you start counting empty squares. The largest target is the grid size times one more than itself, halved: 7 × 8 ÷ 2 = 28.
How to recover from a mistake
- A red target means its line has overshot. Undo until it’s back to normal, then look again at the last square you added to that line.
- A line with no way left usually means an earlier guess. Undo back to before anything you weren’t sure of; on PeerPuzzles, Undo takes back a whole drag at a time.
- Stuck with no mistake? You’ve probably missed a deduction rather than broken the puzzle. Work through when you get stuck.