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EverydayKakuro

Hard Kakuro

Play it here, or print it and work in pen. Deduction gets you a long way and then stops once — and the way past is to follow one digit and see what it does.

Tricky · 9×9 · 39 squares

Time 0:00

Down 8
Down 11
Down 3
Down 19
Down 10Across 10
Down 12
Down 4
Down 13Across 30
Across 11
Down 16
Down 17Across 12
Across 17
Across 15
Down 26
Down 3
Down 16
Down 10
Down 11Across 19
Across 13
Down 16Across 8
Down 13Across 11
Across 30
Across 6
Across 9
Across 17

Other ways to play this level

Every puzzle here comes from a library of 60 at this level, each one checked to have a single answer. Generating a brand new one takes a few seconds, because that check is a search rather than a lookup.

Deduction stalls once. You pick the square with the fewest candidates left, follow one of them, and it either completes the grid or contradicts itself — and either way you then know. One guess, no guess inside it.

The point where reasoning runs out

On a hard grid there comes a moment when every run has been narrowed as far as it can go, every elimination has been made, and nothing places. This is not a mistake and the puzzle is not broken. It is the defining feature of this level.

What gets you past it is picking the square with the fewest candidates left — usually two — writing one of them in, and following the consequences. Either the grid completes, in which case you were right, or it contradicts itself, in which case the other candidate was the answer. Either way you now know.

Solvers call this bifurcation. Some players consider it inelegant and prefer puzzles that never need it, which is a fair position and exactly why the easy and medium pages exist. What it is not is guessing in the ordinary sense: you are not hoping, you are testing, and the test always resolves.

How to branch without ruining the grid

Choose the square with two candidates, not three, and prefer one that sits in short runs. A branch in a corner where the runs are two and three squares long resolves in a handful of steps; a branch in the middle of two long runs can take you halfway across the grid before anything contradicts.

Mark it. In pencil, a small circle round the digit you assumed and a note of the alternative is enough. On screen the difficulty is the same and the answer is the same: know which digits followed from the assumption, because if it fails you have to take all of them back and not one more.

And follow it properly. The commonest way this goes wrong is stopping halfway, deciding it "looks fine", and carrying on. It has to run to a completed grid or to an actual contradiction — two of the same digit in a run, or a run that cannot make its clue.

Only one branch, and that is checked

A puzzle on this page needs exactly one of these. Once you have followed a single digit to its conclusion, the rest of the grid falls to ordinary reasoning — you never have to make an assumption while already inside one.

That is measured, not estimated. The grader runs the full deductive solver, and when it stalls it takes the most constrained square and tries each candidate in turn. If one round of that finishes the job, the puzzle belongs here; if a branch is still stuck and needs a second assumption inside the first, the puzzle goes to the expert page instead.

Nine-by-nine grids, around forty squares to fill. Expect half an hour and a rubber.

Common questions

Do hard Kakuro puzzles require guessing?
They require one branch: pick the square with two candidates, follow one, and it either completes the grid or contradicts. That is a test rather than a guess, because the outcome tells you the answer either way.
Which square should I branch on?
The one with the fewest candidates, preferably sitting in short runs. A branch among two-square and three-square runs resolves quickly; one in the middle of long runs can run half the grid before it settles.
What if my branch neither completes nor contradicts?
Then it has not been followed far enough. It must reach a finished grid or a real contradiction — a repeated digit in a run, or a run that cannot reach its clue.

Check this before you rely on it. This tool is provided free and without warranty, and its results are not professional advice.

Hard Kakuro — printable sheet

  • Puzzle 1 — Tricky, 9×9, 39 squares
    Down 8
    Down 11
    Down 3
    Down 19
    Down 10Across 10
    Down 12
    Down 4
    Down 13Across 30
    Across 11
    Down 16
    Down 17Across 12
    Across 17
    Across 15
    Down 26
    Down 3
    Down 16
    Down 10
    Down 11Across 19
    Across 13
    Down 16Across 8
    Down 13Across 11
    Across 30
    Across 6
    Across 9
    Across 17
  • Puzzle 2 — Tricky, 9×9, 43 squares
    Down 27
    Down 13
    Down 7
    Down 9
    Across 17
    Down 3
    Down 16Across 5
    Down 9Across 34
    Down 13Across 5
    Across 8
    Down 29
    Down 13
    Across 13
    Down 21
    Down 15
    Across 6
    Across 15
    Across 3
    Down 12Across 16
    Down 9
    Down 8
    Down 17Across 30
    Down 13
    Across 38
    Across 28
    Across 16
  • Puzzle 3 — Tricky, 9×9, 43 squares
    Down 40
    Down 6
    Down 7
    Down 15
    Down 31
    Down 7
    Down 15Across 18
    Down 6Across 12
    Across 43
    Across 10
    Down 24
    Across 7
    Down 8
    Across 5
    Down 3
    Across 11
    Down 13Across 17
    Down 11Across 5
    Across 26
    Down 15Across 9
    Across 12
    Across 10
    Across 4
    Across 12
  • Puzzle 4 — Tricky, 9×9, 41 squares
    Down 15
    Down 4
    Down 6
    Down 19
    Down 6
    Down 21Across 10
    Across 14
    Down 22Across 18
    Down 4Across 7
    Across 16
    Down 14Across 7
    Across 9
    Down 14Across 10
    Down 12
    Down 4
    Across 15
    Down 17Across 13
    Across 5
    Down 8
    Down 13Across 12
    Down 8
    Down 10Across 7
    Across 37
    Across 6
    Across 11

Answers

  • Puzzle 1 — Tricky, 9×9, 39 squares (answer)
    Down 8
    Down 11
    Down 3
    Down 19
    Down 10Across 10
    2
    7
    1
    Down 12
    Down 4
    Down 13Across 30
    5
    9
    6
    4
    2
    3
    1
    Across 11
    4
    6
    1
    Down 16
    Down 17Across 12
    9
    3
    Across 17
    9
    8
    Across 15
    6
    9
    Down 26
    Down 3
    Down 16
    Down 10
    Down 11Across 19
    3
    8
    7
    1
    Across 13
    9
    4
    Down 16Across 8
    1
    7
    Down 13Across 11
    9
    2
    Across 30
    7
    6
    9
    8
    Across 6
    4
    2
    Across 9
    7
    2
    Across 17
    9
    8
  • Puzzle 2 — Tricky, 9×9, 43 squares (answer)
    Down 27
    Down 13
    Down 7
    Down 9
    Across 17
    9
    8
    Down 3
    Down 16Across 5
    4
    1
    Down 9Across 34
    7
    5
    2
    9
    3
    8
    Down 13Across 5
    2
    3
    Across 8
    1
    7
    Down 29
    Down 13
    Across 13
    4
    1
    8
    Down 21
    Down 15
    Across 6
    2
    4
    Across 15
    9
    6
    Across 3
    1
    2
    Down 12Across 16
    7
    9
    Down 9
    Down 8
    Down 17Across 30
    6
    9
    7
    8
    Down 13
    Across 38
    1
    2
    8
    9
    4
    5
    3
    6
    Across 28
    8
    6
    9
    5
    Across 16
    9
    7
  • Puzzle 3 — Tricky, 9×9, 43 squares (answer)
    Down 40
    Down 6
    Down 7
    Down 15
    Down 31
    Down 7
    Down 15Across 18
    7
    1
    4
    6
    Down 6Across 12
    9
    3
    Across 43
    8
    6
    5
    3
    9
    1
    7
    4
    Across 10
    7
    3
    Down 24
    Across 7
    5
    2
    Down 8
    Across 5
    4
    1
    Down 3
    Across 11
    5
    6
    Down 13Across 17
    9
    7
    1
    Down 11Across 5
    3
    2
    Across 26
    7
    8
    9
    2
    Down 15Across 9
    5
    4
    Across 12
    6
    2
    4
    Across 10
    7
    2
    1
    Across 4
    1
    3
    Across 12
    8
    4
  • Puzzle 4 — Tricky, 9×9, 41 squares (answer)
    Down 15
    Down 4
    Down 6
    Down 19
    Down 6
    Down 21Across 10
    6
    3
    1
    Across 14
    9
    5
    Down 22Across 18
    3
    9
    1
    5
    Down 4Across 7
    6
    1
    Across 16
    9
    7
    Down 14Across 7
    3
    4
    Across 9
    7
    2
    Down 14Across 10
    9
    1
    Down 12
    Down 4
    Across 15
    6
    9
    Down 17Across 13
    8
    5
    Across 5
    2
    3
    Down 8
    Down 13Across 12
    8
    4
    Down 8
    Down 10Across 7
    6
    1
    Across 37
    7
    8
    9
    2
    6
    4
    1
    Across 6
    1
    5
    Across 11
    2
    6
    3