How to play.

The goal

Every row, every column and each of the nine 3×3 boxes holds each digit from 1 to 9 exactly once. Some digits are given; you work out the rest – no maths involved.

Only the 4 is missing in this row – so it goes in the empty cell.

How to start

1. Nearly full lines. Look for a row, column or box with only a few empty cells. Which digits are missing?
2. Only one digit fits. Pick an empty cell and rule out every digit already in its row, column or box. If only one is left, that's it.
3. Only one place. Pick a digit, say 7, and a box where it's still missing. Often there's just one cell left where it's allowed.
4. Notes. If several digits could fit, write them into the cell as small notes. When you place a digit, it disappears from the notes around it.

You never have to guess: every puzzle here has exactly one solution, and Easy and Medium can be solved with these steps alone.

The goal

The grid is 4×4 to 9×9. Every row and every column holds each number from 1 up to the grid size exactly once – on a 6×6, that's 1 to 6. There are no boxes; instead the grid is split into cages with a thick outline.

The cages

The corner of each cage shows a target and an operation. The numbers in the cage have to make the target with it:

• 7+34added up: 3 + 4 = 7
• 12×34multiplied: 3 × 4 = 12
• 1−12difference: 2 − 1 = 1
• 2÷42divided: 4 ÷ 2 = 2

With − and ÷ a cage always has two cells, and you always take the larger number first – which one sits where doesn't matter. A number may appear twice in a cage, as long as not in the same row or column. A cell without an operation is given.

An example

How to start

1. Cages with few options. “3+” in two cells can only be 1 and 2; “12×” on a 4×4 only 3 and 4. Row and column tell you which goes where.
2. Rule things out. A number that's already in a row can't appear there again – just like in Sudoku.
3. Notes. Write the possible numbers into the cells as small notes and cross them off step by step.
4. The row total. Every row adds up to the same: 1 + 2 + … up to the size, so 21 on a 6×6. Handy for long plus cages.

Easy uses only +, Medium + and −, from Hard on all four operations. Start with 4×4 or 5×5.

Playing here

• Fill in: tap a cell (or move with the arrow keys), then pick a number on the pad or keyboard. The same number again clears it.
• Notes (N or ✎) switches to small pencil marks; Undo (Z) takes back the last step.
• Three modes: Relaxed checks every number right away; Show mistakes marks duplicate numbers (and wrong cages) red; Like on paper marks nothing – you check at the end. The less help, the more Groschen.
• Stuck? Check (1 Groschen) tells you if a number is right, Reveal (3 Groschen) shows the right one.