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Kakurasu for Beginners: Start Here

New to Kakurasu? Learn the three rules, solve a few 5×5 puzzles using only the targets that give themselves away, then add the techniques one at a time. This page puts the guides in that order, with a six-row warm-up to check yourself before you move up a size.

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Your path, in order

  1. Learn the rules. The Kakurasu rules page takes a few minutes, with a small puzzle solved step by step. The one idea to take away: a shaded square counts its column number towards its row, and its row number towards its column.
  2. Solve your first 5×5 using the giveaway targets. Look for rows and columns needing 1, 2, 3, 4, 11, 12, 13, 14 or 15. Each of those settles at least two squares on its own. Fill those in first, then see what the crossing lines allow.
  3. Learn three techniques. From how to solve Kakurasu, start with too big to fit, count the empty squares and find what every combination shares. Add them one at a time, a puzzle or two each.
  4. Do the warm-up below. Six single rows, each with one quick deduction. Each one practises an idea from the guides above.
  5. Pick up speed. The Kakurasu tips page adds the opening sweep, the mirror and an odd-and-even check.
  6. When a puzzle goes wrong, read the six common mistakes. The big one is shading a combination before the puzzle forces it.
  7. Move up a size when you’re ready (see below).

Warm-up: six rows to read at a glance

For each row, work out which squares the target settles, then open the answer. Every answer comes from a single line; no crossing lines needed.

1. Target 14

Warm-up 1: A 5-square row with target 14 A 5-square row with target 14. Every square is open. What does the target tell you? 1 2 3 4 5 14
Show the answer
Warm-up 1 answer The squares the target settles: square 1 crossed out, square 2 shaded, square 3 shaded, square 4 shaded, square 5 shaded. 1 2 3 4 5 14

The largest target in a 5-square row is 15, so the empty squares add up to 15 − 14 = 1. Only square 1 is empty; the rest are shaded.

2. Target 3

Warm-up 2: A 5-square row with target 3 A 5-square row with target 3. Every square is open. What does the target tell you? 1 2 3 4 5 3
Show the answer
Warm-up 2 answer The squares the target settles: square 1 still open, square 2 still open, square 3 still open, square 4 crossed out, square 5 crossed out. 1 2 3 4 5 3

Squares 4 and 5 are each worth more than 3, so both are out. The target is either square 3 or squares 1 and 2, so the first three stay open.

3. Target 12

Warm-up 3: A 5-square row with target 12 A 5-square row with target 12. Every square is open. What does the target tell you? 1 2 3 4 5 12
Show the answer
Warm-up 3 answer The squares the target settles: square 1 still open, square 2 still open, square 3 still open, square 4 shaded, square 5 shaded. 1 2 3 4 5 12

Without square 5, the rest add up to at most 10; without square 4, at most 11. Neither reaches 12, so squares 4 and 5 are both shaded.

4. Target 8, with square 5 already shaded

Warm-up 4: A 5-square row with target 8 and square 5 shaded A 5-square row with target 8 and square 5 shaded. What does the target tell you? 1 2 3 4 5 8
Show the answer
Warm-up 4 answer The squares the target settles: square 1 still open, square 2 still open, square 3 still open, square 4 crossed out, square 5 shaded. 1 2 3 4 5 8

Only 8 − 5 = 3 is left. Square 4 is worth more than that, so it’s out. The 3 is either square 3 or squares 1 and 2.

5. Target 6, with square 4 already shaded

Warm-up 5: A 5-square row with target 6 and square 4 shaded A 5-square row with target 6 and square 4 shaded. What does the target tell you? 1 2 3 4 5 6
Show the answer
Warm-up 5 answer The squares the target settles: square 1 crossed out, square 2 shaded, square 3 crossed out, square 4 shaded, square 5 crossed out. 1 2 3 4 5 6

Only 6 − 4 = 2 is left, and the only way to make 2 is square 2 on its own. Square 2 is shaded and squares 1, 3 and 5 are out. The row is finished.

6. Target 26, in a 7-square row

Warm-up 6: A 7-square row with target 26 A 7-square row with target 26. Every square is open. What does the target tell you? 1 2 3 4 5 6 7 26
Show the answer
Warm-up 6 answer The squares the target settles: square 1 shaded, square 2 crossed out, square 3 shaded, square 4 shaded, square 5 shaded, square 6 shaded, square 7 shaded. 1 2 3 4 5 6 7 26

In a 7-square row the largest target is 28, so the empty squares add up to 28 − 26 = 2. That can only be square 2, so square 2 is empty and every other square is shaded.

When to move up a size

You’re ready for 7×7 when you can finish a 5×5 without guessing, you spot the giveaway targets without looking them up, and you work with what’s left of each target as a habit.

Expect the step up to feel bigger than it looks. The largest targets grow, and the number of ways to make a middle target grows much faster:

Grid Largest target Most combinations for one target
5×5 15 3
7×7 28 8
9×9 45 23

On a 7×7 you can still list combinations for the small and large targets, but not comfortably for the middle ones. That’s where too big to fit, can’t do without it and letting crossing lines cut the combinations take over: they settle squares without listing anything.

Next steps

Questions

Do I need to be good at maths?

Only at adding whole numbers. No line in a 5×5 adds up to more than 15, and once you work with what’s left of each target, the sums get smaller as you go.

Why is a 9×9 so much harder than a 5×5?

Because the number of ways to make each target grows fast. In a 5×5 no target has more than 3 combinations; in a 7×7 some have 8, and in a 9×9 up to 23. Listing them stops being practical, so bigger grids lean on the techniques that skip the listing.

Should I time myself?

Only if you enjoy it. Accuracy matters more than speed while you learn. PeerPuzzles keeps your best time for each size, so you can see yourself improve without trying to.