The fastest way to get better at Kakurasu is to do the obvious work quickly: sweep out the squares that can’t fit, learn the handful of targets that give themselves away, and use two quick checks (odd and even, and counting the empty squares) before reaching for long lists of combinations. Here are nine tips, each a minute to learn.
These build on the techniques in how to solve Kakurasu. If you haven’t played before, start with the rules.
Solving tips
1. Do an opening sweep
Before thinking about any combinations, cross out every square worth more than its row’s target or its column’s target. A column needing 1 loses every row but the first; a column needing 2 loses every row from 3 down. It’s too big to fit applied to the whole grid at once. Across our puzzles it typically clears about a fifth of a 5×5 board, and about a tenth of a 7×7 or 9×9.
2. Learn the targets that give something away
In a 5×5 grid, only targets 5 to 10 tell you nothing on an empty line. Every other target settles at least two squares straight away:
- 1, 2, 13, 14, 15 settle the whole line (one combination each).
- 3 crosses out squares 4 and 5. 4 crosses out squares 2 and 5.
- 11 shades squares 2 and 5. 12 shades squares 4 and 5.
Scan for these first, every puzzle.
3. Learn half the table: the mirror
A target and its mirror (the largest target minus it) have matching combinations: one’s shaded squares are the other’s empty squares. In a 5×5 grid, 4 can be 4 or 1 + 3, so 11 is everything except those: 1 + 2 + 3 + 5 or 2 + 4 + 5. Learn the combinations up to half the largest target and you know them all. This is the same idea as counting the empty squares.
4. Check odd and even
Even squares add up to an even number, so a target is odd exactly when an odd number of odd squares (1, 3, 5…) is shaded. So when a line still needs an odd amount and only one odd square is left open, that square must be shaded.
It works the other way too: if the line still needs an even amount and only one odd square is left open, that square is out.
5. Keep a running remainder
Don’t hold the full target in your head. Subtract each shaded square as it appears and work with what’s left. “Needs 3 more, from squares 1, 3 and 4” is far easier to see through than “needs 10, has squares 2 and 5”.
6. Look back along the crossing line
Every square you settle is in two lines. After each move, check the line running the other way through it before moving on: that’s where the next deduction usually is. It’s the heart of letting crossing lines cut the combinations.
7. Mark the empty squares too
Crossing out squares you know are empty isn’t busywork. Each cross removes combinations from two lines, and most deductions in the middle of a puzzle come from crosses, not shading.
Tips for playing on PeerPuzzles
8. Let the targets check your work
A target turns grey when its line adds up exactly and red when it overshoots. Red means take something out; grey means stop adding to that line. The row and column you’re touching are highlighted, so you always know which two targets a square counts towards.
9. Use the faster controls
- Drag along a row or column to shade (or clear) a run of squares in one go.
- Right-click crosses out a square on a computer; on a phone, switch to Cross. On a keyboard, X switches between Shade and Cross.
- Undo (or Ctrl/Cmd + Z) takes back a whole drag at once.
- Start at 5×5, then move up. Your best time for each size is kept, so you can see yourself improve.