Killer Sudoku (Sum Sudoku) Puzzle

Killer Sudoku is a sudoku whose clues are sums, and it is also called Sum Sudoku. Every row, every column and every box holds each digit once, and dashed cages tell you what their digits add up to. No digit is given. You can play a 4×4, a 6×6 or a 9×9 grid, and every puzzle here has exactly one solution that you can reach by logic, with no guessing.

Rules

A 9×9 grid takes the digits 1 to 9 and is split into nine 3×3 boxes with thick lines. A 6×6 grid takes 1 to 6, with six boxes two rows tall and three columns wide. A 4×4 grid takes 1 to 4, with four 2×2 boxes.

Each digit appears exactly once in every row, exactly once in every column and exactly once in every box.

The grid is divided into cages, outlined with dashed lines set inside the cells. The top-left corner of each cage shows a sum. The digits in a cage are all different, and they add up to that sum. Cages cover every cell and do not overlap, and the cells in a cage join edge to edge. A cage is two or three cells. On a 9×9, a cage can be four.

No cell starts with a digit. The sums are the only clues.

The puzzle is solved when every row, column and box has each digit once and every cage adds up to its sum.

Controls

Tap a cell to select it. Its row, column, box and cage are tinted, and every cell holding the same digit is shaded a little darker, so you can see at a glance where a digit already sits. Tap a digit on the keypad under the board, or type it. Erase, Backspace, Delete or 0 clears the cell, and the arrow keys move around the grid. The small number on each keypad key counts how many of that digit are still to place, and a digit that is on the board in full is dimmed.

Notes are small pencil marks for the digits a cell could still be. Turn on Notes with the button or the N key, then each digit you tap or type switches that mark on or off. Shift with a digit adds or removes a note without turning Notes on. When you place a digit, that digit’s notes disappear from the rest of its row, column and box, in the same undo step.

The line under the keypad lists the combinations still legal for the selected cage. A 17 in two cells on a 9×9 reads “17 in two cells · 8+9”. Digits you have already written in that cage stay in the list, and a cage that can no longer be made reads “no combination fits”.

A digit that repeats in a row, column, box or cage, a cage whose digits already add past its sum, and a full cage that misses its sum are marked red as soon as they appear. A row, column or box that holds each digit once, and a cage that hits its sum, turn soft teal. Press Hint for one step the rules already force, with a sentence saying why. Press Check when you want the board checked against the rules. Undo and Redo step through your moves, and Reset clears the grid.

Techniques

Easy grids need combinations and singles:

• One way to fill a cage: a two-cell sum of 3 is 1 and 2, and a two-cell sum of 17 on a 9×9 is 8 and 9. When only one combination is left, those digits belong to the cage, and the row, column and box decide the order.
• Singles: a cell with one digit left takes it. The last empty cell of a row, column or box is the simplest case. A digit with only one place left in a row, column, box or cage goes there too.

Medium grids also need a wider look at the cages:

• Compare the fillings: list the combinations a cage can still be. A digit that none of them use comes off every cell of that cage.
• One line inside a cage: if a digit can only sit in one row or one column of its cage, it can’t be anywhere else in that row or column.
• House totals: a row, column or box adds up to 10 on a 4×4, 21 on a 6×6 and 45 on a 9×9. When one cell of the house belongs to a cage that also leaves the house, and every other cell sits in a cage that stays inside it, that cell is the house total minus those inside sums. When the cages that meet the house cover every cell of it and stick exactly one cell out past the edge, that outside cell is those cage sums minus the house total.

Hard grids add the same totals across two houses at once, a cage that has to place part of its sum inside one house, and the pencil-mark steps from a hard Sudoku. Two cells in a house that can only be the same two digits take those digits off the rest of the house. If a digit’s notes inside one box all sit in the same row or column, it can’t be anywhere else in that row or column.

Beginner tips

Start with the cages the line under the keypad can fill only one way. On a 4×4, 3 is 1 and 2, and 7 is 3 and 4. Place one of the pair, and the row and column often place the other.

Use the house total when a row is almost covered by cages. On a 4×4 the row adds up to 10, so two cages of 3 and 6 leave a 1.

If you are new to Killer Sudoku, start with a 4×4. The daily puzzle is a 6×6 easy grid, and the 9×9 grids are medium and hard.