How to play Sum Sudoku

Play Sum Sudoku

The rules

The grid is a 9×9 square split into nine 3×3 boxes. Fill every cell with a digit from 1 to 9 so that each digit appears exactly once in:

• every row;
• every column;
• every 3×3 box.

Dashed lines split the grid into cages. The small number in the corner of a cage is its sum: the digits in the cage add up to it, and no digit repeats inside a cage.

Easy puzzles may start with a few digits filled in. From medium up, the grid starts empty. Every puzzle has exactly one solution, and logic alone is enough to reach it. You never have to guess.

How to play here

• Select a cell: click it, or use the arrow keys.
• Enter a digit: keys 1–9, or the number pad below the grid.
• Notes (small candidates): press N or the Notes button. In notes mode, a digit you type is recorded as a small candidate. Shift + digit also writes a note.
• Erase: Delete, Backspace or 0.
• Undo and redo: Ctrl+Z and Ctrl+Y (on a Mac: ⌘Z and ⌘⇧Z).
• Hint: each press of Hint tells you more: first where to look, then which technique works there, and finally the digit itself. If there is a mistake on the board, the hint shows you where.

A digit that repeats in a row, column, box or cage is marked with stripes and a wavy underline. When a cage’s digits add up to more than its sum, or a full cage misses it, the sum turns red with a wavy underline.

Difficulty levels

The level is set by the hardest technique the puzzle requires, not by the number of cages:

Techniques

Singles

A cell with only one possible digit takes it. A digit that fits in only one cell of a row, column or box goes there.

Cage sums

Only a few sets of different digits reach a cage’s sum. A 2-cell cage of 3 must be 1 and 2; a 2-cell cage of 17 must be 8 and 9. Keep only the digits those sets allow.

Pointing

If, inside a box, a digit can only go in one row or column, remove it from the rest of that line. It works the other way round too.

Cage pointing

If every possible set for a cage contains a digit, the cage must hold it. If the cells that can hold it all lie in one row, column or box, remove that digit from the rest of that unit.

Naked and hidden pairs

Two cells of a unit with the same two candidates take those two digits: remove them from the rest of the unit. Two digits that fit only the same two cells reserve them: remove every other candidate from those cells.

The rule of 45

The digits 1 to 9 add up to 45, so every row, column and box adds up to 45. Add up the cages that lie fully inside a unit. If only one cell of the unit is left over, it is 45 minus that total. If the cages stick out of the unit by one cell, that cell is the extra above 45.

The rule of 45 on several units

Two neighbouring rows add up to 90, three to 135. The same goes for columns and for boxes side by side. Use the same counting on the larger area.

Tips

1. Start with the cages that have only one digit set: small sums (3, 4) and large ones (16, 17 in two cells; 6, 7, 23, 24 in three).
2. Look for rows, columns and boxes almost covered by whole cages: the rule of 45 then gives a cell straight away.
3. Write the possible digits of a cage as notes. They often show a pair or a pointing step.