What is elimination in Kakuro?

Proving a digit cannot sit in a particular square, rather than proving one must. It places nothing directly; it removes a candidate elsewhere, and that removal is what forces the next square.

Should I write candidates into the squares?

At this level, yes, once the straightforward moves stop. Eliminations are very hard to spot without pencilled candidates, which is why these grids print with room to write in.

How is medium different from easy here?

An easy puzzle can be finished entirely by pinning digits down. A medium one stalls at least once until you rule a digit out of a square. Both are pure deduction — neither ever needs a guess.

Medium Kakuro

Play it here, and turn the pencil marks on. This is the level where the obvious moves run out and progress comes from proving a digit cannot go somewhere.

Steady · 9×9 · 43 squares

Time 0:00

	Down 3	Down 11				Down 7	Down 9
Across 10	Row 2, column 2	Row 2, column 3	Down 15	Down 10	Across 3	Row 2, column 7	Row 2, column 8	Down 17
Across 12	Row 3, column 2	Row 3, column 3	Row 3, column 4	Row 3, column 5	Down 14Across 20	Row 3, column 7	Row 3, column 8	Row 3, column 9
	Down 5	Down 25Across 19	Row 4, column 4	Row 4, column 5	Row 4, column 6	Down 20Across 10	Row 4, column 8	Row 4, column 9
Across 4	Row 5, column 2	Row 5, column 3		Across 5	Row 5, column 6	Row 5, column 7	Down 16
Across 12	Row 6, column 2	Row 6, column 3	Down 23	Across 11	Row 6, column 6	Row 6, column 7	Row 6, column 8	Down 4
	Down 3Across 17	Row 7, column 3	Row 7, column 4	Down 17	Across 14	Row 7, column 7	Row 7, column 8	Row 7, column 9
Across 22	Row 8, column 2	Row 8, column 3	Row 8, column 4	Row 8, column 5	Across 6	Row 8, column 7	Row 8, column 8	Row 8, column 9
Across 18	Row 9, column 2	Row 9, column 3	Row 9, column 4	Row 9, column 5	Across 16	Row 9, column 7	Row 9, column 8

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.

Grid size for a new puzzle

Somewhere at least one square is cleared by ruling a digit out rather than pinning one down: the combination fits the run, but not with that digit in that square. Still pure deduction, start to finish.

Ruling out, and why it is the step up

At some point in a medium grid every run has been narrowed as far as its own clue allows and nothing more will place. The move that restarts it is different in kind: instead of asking what must go in a square, you ask what cannot.

Here is the shape of it. A run of three clued twenty can be written as three, eight and nine, or four, seven and nine, or five, six and nine, among others. Suppose one of its squares crosses a run that has already ruled out everything above six. That square cannot take the nine — and since every writing of twenty in three squares contains a nine, the nine has to be in one of the other two.

You have placed nothing. What you have done is remove a possibility somewhere else, and it is that removal that turns some other square into a certainty. This is the first idea in Kakuro that is genuinely about elimination, and being comfortable with it is the difference between finishing medium puzzles and abandoning them.

When to stop looking for the easy moves

Later than you think. A medium puzzle opens with a run of straightforward placements and only needs the new idea once those are exhausted. Reaching for an elimination while simple moves remain is slower, not cleverer.

The signal that you have run out is a full sweep of the grid — every short run, then every nearly-complete run — that places nothing at all. At that point writing candidates into the squares is worth the time it costs, because an elimination is very difficult to see without them.

That is why these print with generous squares. A grid sized for one printed digit has no room for four small ones, and a medium Kakuro you cannot annotate is a medium Kakuro you will not finish.

The rhythm of a medium grid

Simple moves until stuck, one elimination, simple moves again. The grid has changed after a removal and squares that were open a moment ago may now be forced, so going straight back to the easy sweep is almost always right.

That loop is exactly what the grader on this site runs to decide which level a puzzle belongs to. A puzzle lands on this page when the loop needs at least one elimination and never needs a guess.

If the loop stalls with no elimination available anywhere, the puzzle is a level above this one. It is not broken and it does not want guessing — it wants the technique on the hard page.

Common questions

What is elimination in Kakuro?: Proving a digit cannot sit in a particular square, rather than proving one must. It places nothing directly; it removes a candidate elsewhere, and that removal is what forces the next square.
Should I write candidates into the squares?: At this level, yes, once the straightforward moves stop. Eliminations are very hard to spot without pencilled candidates, which is why these grids print with room to write in.
How is medium different from easy here?: An easy puzzle can be finished entirely by pinning digits down. A medium one stalls at least once until you rule a digit out of a square. Both are pure deduction — neither ever needs a guess.

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

	Down 7	Down 27			Down 16	Down 7
Across 10			Down 16	Down 3Across 8
Across 31							Down 8	Down 17
	Down 17Across 16				Down 6	Down 25Across 9
Across 13				Across 26
Across 15			Down 9	Down 3Across 3			Down 21
	Down 12	Down 13Across 7			Down 7Across 17			Down 6
Across 42
Across 10				Across 13

	Down 7	Down 27			Down 16	Down 7
Across 10	2	8	Down 16	Down 3Across 8	7	1
Across 31	5	3	7	1	9	6	Down 8	Down 17
	Down 17Across 16	5	9	2	Down 6	Down 25Across 9	1	8
Across 13	9	4		Across 26	4	6	7	9
Across 15	8	7	Down 9	Down 3Across 3	2	1	Down 21
	Down 12	Down 13Across 7	5	2	Down 7Across 17	8	9	Down 6
Across 42	9	6	4	1	2	7	8	5
Across 10	3	7		Across 13	5	3	4	1

Medium Kakuro

Ruling out, and why it is the step up

When to stop looking for the easy moves

The rhythm of a medium grid

Common questions

Medium Kakuro — printable sheet

Answers

		Down 19	Down 7		Down 15	Down 10
	Down 6Across 9			Down 15Across 10			Down 28
Across 34								Down 16
Across 7			Down 16Across 15			Across 16
	Across 9			Down 12		Across 12
		Across 6			Down 11	Across 8
	Down 5	Down 3Across 21				Down 3	Down 9	Down 15
Across 6				Across 25
Across 3					Across 9

	Down 17	Down 7					Down 13	Down 3
Across 10			Down 19		Down 17	Down 9Across 9
Across 23				Down 8Across 17
		Across 19					Down 32	Down 17
	Down 19	Down 7Across 15				Down 6Across 17
Across 12					Down 8Across 16
Across 6			Down 13	Down 12Across 17				Down 15
Across 18						Across 16
		Across 17				Across 10