Arctic SudokuHow to solve
A step-by-step method for both games. Each step links to the technique it uses.
Sudoku – the method
1. Scan digit by digit
Start with the digit that's already placed most often. See which boxes are missing it, and cross out the rows and columns where it already stands. If only one free cell is left in the box, that's its place (a hidden single). Go through 1–9 and repeat.
Techniques: Hidden single
- Basis
- Removed / placed
2. Look for nearly full units
A row, column or box with 7–8 digits quickly reveals what's missing.
Techniques: Naked single
- Removed / placed
3. Repeat until you're stuck
Repeat steps 1–2 until you're stuck. On Extra easy and Easy this alone gets you to the end.
Techniques: Hidden single
- Basis
- Removed / placed
4. Write notes
Fill in every possible digit (candidates) – first in boxes or rows with few empty cells, on hard boards across the whole board. A cell with only one candidate is a naked single.
Techniques: Naked single
- Basis
- Removed / placed
5. Remove candidates with patterns
Locked candidates (a digit that can only go in one row of a box), pairs and triples (two cells with the same two candidates). Each removal can create new singles – go back to step 1.
Techniques: Pointing (locked candidates), Claiming, Naked pair, Hidden pair, Naked triple, Hidden triple
- Basis
- Removed / placed
6. Hard and Expert: two-place digits
Look for digits with only two possible places in a row, column or box. They're the building blocks of X-Wing, skyscraper, colouring and the chains (see Techniques).
Techniques: X-Wing, Skyscraper, Simple colouring, X-Chain
- Basis
- Removed / placed
7. Never guess
Every board in the app can be solved with logic, and mistakes cost.
Killer Sudoku – the method
1. Start with one-combination cages
Start with the cages that only have one combination (table below), for example 3 in two cells = 1+2 and 24 in three cells = 7+8+9. Write the combination as notes.
Techniques: Cage combinations
- Removed / placed
2. Use high and low sums
A cage of 16 in two cells is 7+9; a cage of 5 in two cells is 1+4 or 2+3 – so 5–9 can never go there.
Techniques: Cage combinations, Minimum and maximum sums
- Removed / placed
3. The 45 rule
Every row, column and box sums to 45 (two rows 90, three rows 135). Add up the cages lying entirely inside a box; what's missing to 45 is the sum of the remaining cells. If one cage sticks slightly out of the box, the difference gives the digit in the cell that sticks out (innies and outies).
Techniques: Rule of 45 (one cell), Rule of 45 (several cells), Innies and outies
- Basis
- Removed / placed
4. Combine with normal Sudoku rules
If a digit must be in a cage that lies entirely in one row, it can't be anywhere else in that row. A cage can't contain the same digit twice.
Techniques: Locked candidates in cages
- Basis
- Removed / placed
5. Recheck the combinations
Check the combinations again every time a digit is placed – often several combinations drop out.
Techniques: Combinations across cages
- Basis
- Removed / placed
6. Hard and Expert
Look at groups of cages that together cover an area, the smallest and largest possible sum in a cage, and cages that share cells with the same row or box (see Techniques).
Techniques: Cage splitting, Minimum and maximum sums, Combinations across cages, Chains with cage links
- Basis
- Second colour
- Removed / placed
Cage sums with only one combination
These sums can only be made one way. Write the digits as notes straight away.
| Cells | Sum = digits |
|---|---|
| 2 cells |
|
| 3 cells |
|
| 4 cells |
|
| 5 cells |
|
Smart tips
- Use notes instead of guessing when you're unsure. Only 2 mistakes are allowed.
- Save your hints until you're completely stuck – a clean solve counts most in the statistics.
- When you're stuck, go through one technique at a time, simplest first, instead of staring at the whole board.
- Take a break – surprisingly often, that's what lets you see the next step.
- Move up a level when you solve several boards in a row without mistakes, and down one if you keep using both hints.