Rules
The board is a Sudoku with the clues replaced by sums. No cell starts with a digit. You fill each row, each column, and each box with the digits once.
- One of each digit. Every row, every column, and every box holds each digit once. A 4×4 uses 1 to 4 and 2×2 boxes. A 6×6 uses 1 to 6 and boxes that are two rows tall and three columns wide. A 9×9 uses 1 to 9 and 3×3 boxes.
- Cages add up. Dashed cages cover the grid. The number in the top-left corner is what those cells add up to, and a digit does not repeat inside the cage.
- Edge to edge. Cages meet edge to edge. They do not overlap. A cage is two or three cells. On a 9×9 it can be four.
- Nothing filled in. No cell starts with a digit. The sums are the clues. The puzzle is finished when every house has each digit once and every cage hits its sum. A house is a row, a column, or a box.
The dashed 6 bends around a corner: 3+2+1. The 7 beside it is a straight pair: 4+3. A finished grid is drawn in teal.
- Cage sum
- Your digit
- Pencil notes
Tap a cell. Its row, column, box, and cage are tinted. Type a digit or use the keypad. Erase, Backspace, Delete, or 0 clears it. Arrow keys move. Notes (the Notes button, or N) are pencil marks. Shift with a digit toggles one note without turning Notes on. You write the notes yourself.
When you place a digit, that digit leaves the notes in the rest of its row, column, and box. It does not leave the rest of the cage by itself. Strike those yourself. The line under the keypad lists the sets still legal for the selected cage.
A row, a column, or a box adds up to 10 on a 4×4, 21 on a 6×6, and 45 on a 9×9. You will not need that on an easy grid. It is the same total the later sections use.
One-way cages
A cage with one set of digits comes first, then the Sudoku cell it clears, then a digit that every remaining set still uses.
One way to fill a cage
Start with a cage that can be made in only one way. Strike the digits that set cannot use. Hint does one cell at a time. Do this for every one-way cage before you look for a single.
On a 4×4, 3 in two cells is 1 and 2, 4 is 1 and 3, 6 is 2 and 4, and 7 is 3 and 4. Every three-cell cage on a 4×4 is one way too. On a 6×6 the one-way pairs are 3, 4, 10, and 11, and the one-way triples are 6, 7, 14, and 15. On a 9×9 the one-way pairs are 3, 4, 16, and 17, and the one-way triples are 6, 7, 23, and 24. Those 9×9 pairs and triples are the same sums as on a Kakuro. The table stays here.
| Size | Two cells | Three cells |
|---|---|---|
| 4×4 | 3 = 1+2, 4 = 1+3, 6 = 2+4, 7 = 3+4 | 6 = 1+2+3, 7 = 1+2+4, 8 = 1+3+4, 9 = 2+3+4 |
| 6×6 | 3 = 1+2, 4 = 1+3, 10 = 4+6, 11 = 5+6 | 6 = 1+2+3, 7 = 1+2+4, 14 = 3+5+6, 15 = 4+5+6 |
| 9×9 | 3 = 1+2, 4 = 1+3, 16 = 7+9, 17 = 8+9 | 6 = 1+2+3, 7 = 1+2+4, 23 = 6+8+9, 24 = 7+8+9 |
A 9×9 cage can be four cells, and most cages are two or three. The one-way fours are rare: 10 is 1+2+3+4, 11 is 1+2+3+5, 29 is 5+7+8+9, and 30 is 6+7+8+9.
A 5 in two cells is not one way. On a 4×4 it is 1+4 or 2+3. The line under the keypad says “5 in two cells · 1+4 · 2+3”. Leave that cage until a house decides it. When one digit of a one-way pair is already written, the partner is the other digit.
This 3-cell cage sums to 6, so it can only be 1, 2 and 3. The 4 comes off the ringed cell. The same strike comes off the other two cells on the next two hints. The keypad line is “6 in three cells · 1+2+3”.
After those three strikes, the high pair is next. A 7 in two cells is only 3 and 4, so 1 and 2 come off the ringed cell. The partner loses them on the following hint. This is not the second look at a blank board.
The 1 is already written, so the partner in a sum of 4 is 3. The cage sentence comes before “this cell can only be 3”, so the move is still the cage. The 1 stays violet. The new 3 takes the ring.
The same look then strikes the other one-way cages on this 4×4: the sum-6 pair, the sum-4 pair, the other sum-6 pair, and the bottom sum-6 triple. The first single on that walk is a hidden single.
The Sudoku singles
Once the one-way cages have crossed digits out, a Sudoku single finishes the cell. The Sudoku guide already teaches each one. On this site a hidden single is an easy Killer step. On a plain Sudoku it is a medium step.
The three-cell 8 can only be 1, 3, and 4, so those cells cannot be 2. The 2 of row 1 has one home, the ringed cell. See hidden singles.
The ringed cell can only be 3. See naked singles.
Column 3 is only missing 4. The cell’s own cage sums to 5, which is 1+4 or 2+3, so the cage does not place the digit. The column does. A full house loses to the cage when that cage still has one set, because the cage sentence is checked first. See full houses.
In every set
Sometimes a cage still has two sets, and both of them use the same digit. If only one cell of the cage can hold that digit, write it.
This is an easy sentence. The easy grids here finish without it. Some medium grids use it. On a 6×6, 8 in three cells is 1+3+4 or 1+2+5. Both use 1. Within 1 to 6, and within 1 to 9, those are the two sets. A larger range of digits would allow more.
Every combination of this cage includes 1, and only the ringed cell can take it. The other two cells of the 8 cannot be 1. The grid around it is a medium one. The sentence itself is the easy kind.
An easy grid finishes with one-way cages and these singles. A medium grid is where the cage still has several sets.
Lists and totals
List the sets that still fit, take a digit off a cell no set uses, confine a digit to one line inside the cage, and use a house total when cages cover almost the whole house.
A few sets
When no cage is one way, list the sets that still fit. A digit that none of them use comes off the cell. This does not write a digit by itself.
The partner cell loses the same digits on the next hint. Every medium grid needs this list. One 6×6 medium grid opens on it, because nothing on that grid is one way. The list does not finish that grid. The same board later needs the column total.
5 in two cells is 1+4 or 2+3, so 5 and 6 cannot sit on the ringed cell. The keypad line is “5 in two cells · 1+4 · 2+3”. The next hint strikes 5 and 6 on the partner.
One line inside the cage
Look at one digit across every set the cage can still be. If that digit always lands in the same row, the same column, or the same box, it comes off the rest of that line.
Almost every medium grid names this. The picture is a 6×6 that does not need a house total. The cage is one way, 10 = 4+6, and both cells already sit in column 1, so 4 cannot appear lower in that column. The Sudoku pointing line is a different step. It lives with the hard pencil marks, further down.
In every way to fill this cage, 4 lands in column 1, so 4 comes off the rest of that column. This hint strikes the 4 on the ringed cell, which had no pencil mark of its own yet. The cells further down lose 4 by the same rule, each on its own later hint.
The house total
A row, a column, or a box has a fixed total: 10, 21, or 45. When the cages that sit fully inside it add up to less than that, the cells that poke in from outside cages make up the difference.
Three shapes:
- One outside cell, and the rest of the house is covered by cages that stay inside. That cell is the total minus the inside sums.
- The cages that meet the house cover it and stick exactly one cell out. That outside cell is those cage sums minus the total.
- Two cells share the difference. They are a pair. Strike the digits that cannot be part of that pair. This does not write a digit yet.
Some medium grids need this, especially 9×9 medium. A 6×6 medium grid usually stops at the list and the one-line strike. The 6×6 pictures below are the kind that goes on. An outie does not show up on a 6×6. It shows up on 9×9 medium, and again on hard. On a 4×4 the row adds up to 10, and the easy grids finish before that sentence is needed, because a three-cell cage is already one way.
Row 3 must add up to 21. The two cages that stay inside it are both 7, so 21 − 14 = 7. The outside cells are the ends of the row. They add to 7, and the pairs for 7 on a 6×6 are 1+6, 2+5, and 3+4. The left cell is noted 3, 4, 5, 6, so it cannot be 1 or 2, and the ringed cell cannot be 6 or 5. This hint strikes 5 and 6 there. The other cell of the pair is the left end.
Column 6 must add up to 21. The cages fully inside it add up to 18, a 12 and a 6, so the cell poking in at the bottom is 3. A box works the same way. The outie picture is the 9×9.
Box 1 must add up to 45. The cages fully inside it add up to 34, so the two cells of the crossing cage that sit inside the box add to 11. That cage sums to 18, and exactly one cell sticks out, so the ringed cell is 18 − 11 = 7. The 1 already on the board is part of the state this step needs. The other pencil marks are there so the step is forced. The arithmetic is the lesson.
Medium adds the longer lists and, on some grids, the house total. A 6×6 medium grid usually stops before the total. Hard is where two houses are added at once.
Two houses
Add the total across two houses that share a side. If the grid still stalls, the Sudoku pencil patterns are next.
Two houses at once
Add the same total across two houses that touch: two rows in a row, two columns in a row, or two boxes that share a side. Two boxes that touch only at a corner do not count. On a 9×9 the pair of houses adds up to 90.
The arithmetic is the same as the one-house total: inside cages, one cell left, or two cells that share a remainder. Every 9×9 hard grid here uses this step. It is not on a 4×4 or a 6×6, because those sizes have no hard setting. The how-to under the board also names a cage that has to place part of its sum inside one house. That sentence is not one of the pictures here.
Columns 1 and 2 must add up to 90. These two cells, the ringed one and the cell two rows below it in column 3, add up to 5, so 5, 6, 7, 8, and 9 come off the ringed cell. The pairs left for 5 are 1+4 and 2+3. This hint edits only the ringed cell. The other cell is the partner in the sentence.
Boxes 7 and 8 must add up to 90. The cages fully inside them add up to 88, so the ringed cell is 2. It is the inside cell of a sum-8 pair that crosses out of the two boxes. This is a later state than the picture above. The notes are not the same.
Not every hard grid uses both shapes. The shape with one cell left inside is the more common of the two. The shape with one cell sticking out is common too.
Pencil marks from Sudoku
A few hard grids still stall after the two-house total. The next steps are the ordinary Sudoku pencil patterns. The Sudoku guide already draws them.
- Two cells in a house that can only be the same two digits take those digits off the rest of the house. See naked pairs. One hard grid reads: “Row 8 has two cells that can only be 3 and 5, so remove 3 and 5 from the rest of that house.” The returned move struck 5 from one cell, because 3 was not penciled there.
- A hidden pair is the same find from the other side, and it lives in that Sudoku section. There is no separate anchor. One example reads: “4 and 9 in row 4 fit only these two cells, so remove the other digits there.”
- If a digit’s notes inside one box all sit in the same row or column, it comes off the rest of that line. See pointing. That is Sudoku pointing. Section 3 was the cage.
- Claiming is the line the other way around. A hard grid here can be finished without it.
This ladder does not use a naked triple or a hidden triple. The Sudoku page goes on to triples after the pair. Notes on this site are manual. Pencil marks are yours to write, and the Killer board will not fill them in for you.
Some hard grids never name a pencil pattern. Two-house totals are the step that makes a grid hard. The pencil patterns are extra, on some of them.
Hard adds the two-house total and, on some grids, these Sudoku pencil patterns. Nothing in the ladder asks you to guess.
What if
There is no trial step. You do not write a digit to see whether the grid breaks, and Hint will not ask you to.
The three-cell 6 is only 1+2+3. A 4 there is not in any set. Written 4 plus the two empty cells at 1 each is 6, which is not over the sum, so the cell does not turn red on the play board. The red here is the mark for “erase this”. The keypad line says “no combination fits”. Check says keep going. Hint says nothing is forced, and it does not take the 4 away.
If a digit is wrong and the rules do not catch it yet, Check stays quiet and Hint has nothing to say. Erase the digit. Go back to the cages. The red figures in the next section are the failures Check does catch.
Common mistakes
Check turns a cell red when a digit repeats, when a cage is already over its sum, or when a full cage misses its sum. Empty cells on an unfinished grid are incomplete, not wrong. Notes are not errors.
Two 1s in row 1, in different cages and different 2×2 boxes. The repeat is the row. Check cites those two cells.
Two 2s in the sum-11 cage. On a 6×6 a box is two rows by three columns, so these cells are in different boxes, and they share neither a row nor a column. The repeat is the mistake. The 2 at the left of the cage happens to be the digit that belongs there. The wrong 2 is the lower one. Check flags the cage. The row and the column stay quiet.
The cage sums to 4. A written 4 plus one empty cell is already over. Check cites the 4. The empty partner is not washed.
The cage sums to 5. 1+2 is 3. The digits do not repeat, and neither digit alone exceeds the sum. Check cites both cells of the cage.
What to play next
Easy finishes with one-way cages and singles. Medium adds the longer lists and, on some grids, a house total. Hard adds the two-house total and, on some grids, Sudoku pencil patterns.
- EasyOne-way cagesStart with the one-way cages: 3, 4, 6, and 7 in two cells, and 6, 7, 8, and 9 in three. Then the Sudoku singles. The daily size is the 6×6 easy grid, where the one-way pairs are 3, 4, 10, and 11.Play Easy →
- MediumLists, then a totalWhen the one-way cages stop, list the sets and strike a digit no filling uses. If a digit of the cage is confined to one line, take it off the rest of that line. A house total (21 on a 6×6, 45 on a 9×9) is for the grid where a row or a box is almost covered by cages. A 6×6 medium grid usually stops before that.Play Medium →
- HardTwo housesAdd the same totals across two touching rows, two touching columns, or two boxes that share a side. The pair adds up to 90. Then the Sudoku pencil patterns, on the grids that still stall. No guess.Play Hard →
4×4 is easy. 6×6 is easy and medium. 9×9 is medium and hard. Try 6×6 easy and 9×9 medium. The daily puzzle is a 6×6 easy grid: today’s Killer Sudoku opens the same size and setting as 6×6 easy.
Print a Killer Sudoku pack. A 4×4 or 6×6 sheet holds four puzzles. A 9×9 sheet holds two. Large print is one grid.
- GuideSudokuRows, columns and boxes, from singles to triples.
- GuideKakuroOne-way sums first, then short runs and longer lists.
- GuideHashiCount bridges, never cross, connect every island.
- GuideBinairoSpot pairs, fill the gaps, balance every line.
- GuideNonogramsOverlap long clues, cross the gaps, and read the crossing line.
- GuideLight UpLight every cell. Start beside the 4s and 0s.
- GuideSlitherlinkDraw one loop. Start from the 0s and the 3s.
- GuideStar BattleOne or two stars in every row, column and region.
- GuideMasyuTurn on black pearls, go straight through white ones.
- GuideNurikabeGrow each island to its number and keep one sea.