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What goes at the end of the diagonal?
Level 5 · Outside clues and specials
How to solve little killer sudoku
A clue outside the grid gives the sum of the diagonal it points along.
Little killer sudoku puts small clues with arrows outside the grid. Each clue is the sum of every cell on the diagonal the arrow points along.
A diagonal's cells never share a row or column, so digits can repeat on it as long as the matching cells sit in different boxes. Cells of the diagonal inside one box still can't match.
How setters write it
The same rule, worded the ways you’ll see it on puzzles.
- Clues outside the grid give the sum of the indicated diagonal.
- Little killer sums. Digits may repeat.
Worth memorizing
- Digits can repeat on a little killer diagonal, unless another rule stops them.
- Short diagonals near corners are the easy starting points.
Solving tips
Start with short diagonals
Near the corners, a diagonal may cover only two or three cells. A clue of 3 on a two-cell diagonal must be 1 and 2, in either order.
Repeats need different boxes
Two diagonal cells can hold the same digit only if they sit in different boxes. The part of a diagonal inside one box works like a killer cage with no repeats.
Use the extreme sums
Three diagonal cells inside one box add to 6 at least and 24 at most. A clue of 6 on such a diagonal forces 1, 2 and 3, and 24 forces 7, 8 and 9.
Bound the long diagonals
The longest diagonal crosses three boxes with three cells in each. Each group of three adds to 6 to 24, so the full diagonal adds to 18 to 72.
A worked example: three clues near a corner
We name cells by row and column, so row 1, column 3 is r1c3. Three clues point up and to the right near the top-left corner. A 7 covers r3c1, r2c2 and r1c3. A 9 covers r2c1 and r1c2. A 35 covers r4c1, r3c2, r2c3 and r1c4.
- The 7 diagonal sits inside the top-left box, so its three digits all differ. Three different digits make 7 only as 1 + 2 + 4.
- The 9 diagonal is in the same box, so it can't use 1, 2 or 4. The two-cell options for 9 are 1 + 8, 2 + 7, 3 + 6 and 4 + 5. Only 3 + 6 avoids 1, 2 and 4, so r2c1 and r1c2 are 3 and 6.
- The box's other four cells (r1c1, r2c3, r3c2 and r3c3) hold 5, 7, 8 and 9. Two of them, r2c3 and r3c2, lie on the 35 diagonal. They add to at most 8 + 9 = 17.
- The 35 diagonal's other cells are r1c4 and r4c1, each at most 9. So the diagonal adds to at most 17 + 9 + 9 = 35. The clue is 35, so every part is at its maximum. r1c4 is 9, r4c1 is 9, and r2c3 and r3c2 are 8 and 9.
- That diagonal holds three 9s, and it's legal. Each 9 sits in a different row, column and box. The box's last two cells, r1c1 and r3c3, hold 5 and 7.
Practice
Reference table
| Cells on diagonal | Cells in each box along it | Smallest sum | Largest sum |
|---|---|---|---|
| 9 | 3, 3, 3 | 18 | 72 |
| 8 | 2, 1, 2, 1, 2 | 11 | 69 |
| 7 | 1, 2, 1, 2, 1 | 9 | 61 |
| 6 | 3, 3 | 12 | 48 |
| 5 | 2, 1, 2 | 7 | 43 |
| 4 | 1, 2, 1 | 5 | 35 |
| 3 | 3 | 6 | 24 |
| 2 | 2 | 3 | 17 |
| 1 | 1 | 1 | 9 |
Going deeper
Split each diagonal into box pieces
A diagonal's cells never share a row or column, so the only thing stopping a repeat is a box. Split every diagonal into its box pieces. Each piece acts like a small killer cage with no repeats, and different pieces can share digits.
The split isn't always even. An eight-cell diagonal next to the main one crosses five boxes in pieces of 2, 1, 2, 1 and 2 cells. The one-cell pieces can be any digit, which is why that diagonal's range is so wide.
The corner-to-corner diagonal is the neatest case. It crosses three boxes with three cells in each, so each piece is a three-cell cage. A clue of 18 fixes every piece as 1, 2 and 3, and a clue of 72 fixes every piece as 7, 8 and 9.
Clues near the ends of the range
Compare each clue with the table's smallest and largest sum for its length. A clue at the exact minimum or maximum fixes every piece, like the 35 in the example.
A clue 1 above the minimum means every piece holds its smallest set except one, which is raised by 1. A three-cell piece raised by 1 is 1 + 2 + 4 in place of 1 + 2 + 3. These tight clues pin 1s, 2s, 8s and 9s into specific boxes early.
Short diagonals and the 45 rule
In each corner, three short diagonals of 1, 2 and 3 cells lie inside the corner box. Together they cover six of its nine cells. If all three are clued, the other three cells of the box add to 45 minus the three clues.
The same idea works on longer diagonals. Subtract the pieces you know, and the rest of the clue becomes a smaller sum over the cells you don't.
Common mistakes
Treating the diagonal like one cage
Digits can repeat on a little killer diagonal across boxes. Using no-repeat cage combinations for the whole diagonal throws away real answers.
Forgetting the box pieces
Cells of the diagonal inside one box still can't repeat. A clue of 4 on a two-cell diagonal inside one box must be 1 + 3, since 2 + 2 repeats inside the box.
Following the wrong diagonal
Near a corner, a clue can sit next to more than one diagonal. Follow the small arrow and count every cell to the far edge of the grid.
In mixed-rule puzzles
Little killer clues often sit beside killer cages or sandwich clues. When a cage and a diagonal share cells, subtract the known part of one sum from the other to pin a cell. Sandwich logic needs 1s and 9s, and tight diagonal clues often place them. When a puzzle also uses the diagonal rule of X sudoku (1 to 9 on each long diagonal), those long diagonals always total 45, so the useful little killer clues sit on the shorter ones.
What the video shows
- An outside clue gives the sum of the diagonal it points along.
- 1 + 5 + 6 = 12. Digits may repeat on the diagonal if the rest of the grid allows.
Questions solvers ask
What is little killer sudoku?
A sudoku with clues outside the grid. Each clue gives the sum of the diagonal its arrow points along.
Can numbers repeat in little killer sudoku?
Yes, on a diagonal, as long as the matching digits are in different boxes. Normal sudoku rules still apply.
How is little killer different from killer sudoku?
Killer sudoku uses cages drawn inside the grid, and cage digits never repeat. Little killer uses diagonal sums from outside clues, and those digits can repeat.
Which way does a little killer clue point?
The small arrow next to the clue shows the direction. The sum covers every cell along that diagonal to the far edge of the grid.
What is the largest little killer clue?
On a 9x9 grid, the corner-to-corner diagonal can total at most 72, which is 7 + 8 + 9 in each of its three boxes. Shorter diagonals have lower limits, listed in the table on this page.
Does a little killer diagonal wrap around the grid?
No. The diagonal runs from the clue's edge straight to the far edge of the grid and stops there.
Why can digits repeat on a little killer diagonal but not in a killer cage?
Killer cages have their own no-repeat rule. A little killer diagonal has none, so only normal sudoku rules apply, and on a diagonal those stop repeats only inside a box.
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