Arctic SudokuTechniques
Every technique the app uses, in the order it uses them when solving. Each is a pattern that lets you place a digit or remove a candidate.
Basic (Extra easy and up)
Hidden single
A digit has only one possible place in a box, row or column.
Naked single
A cell has only one possible candidate left.
Cage combinationsKiller
Some cage sums can only be made from one set of digits.
Rule of 45 (one cell)Killer
Every row, column and box sums to 45, so a single cell left outside the cages can be calculated.
Medium (Medium and up)
Pointing (locked candidates)
If a digit in a box can only go in one row or column, it can be removed from the rest of that row or column.
Claiming
If a digit in a row or column can only go inside one box, it can be removed from the rest of that box.
Naked pair
Two cells in a unit with the same two candidates – those digits can be removed from the rest of the unit.
Hidden pair
Two digits that can only go in the same two cells of a unit – all other candidates in those cells can be removed.
Naked triple
Three cells in a unit whose candidates together are only three digits – those digits can be removed from the rest of the unit.
Hidden triple
Three digits that can only go in the same three cells of a unit – other candidates in those cells can be removed.
Locked candidates in cagesKiller
If a cage must contain a digit and lies within one row, column or box, that digit can be removed from the rest of that unit.
Rule of 45 (several cells)Killer
The 45 rule also gives the total of two to four cells left outside the cages.
Hard (Hard and up)
X-Wing
A digit that fits only in the same two columns in two rows (or the reverse) can be removed from those columns everywhere else.
Swordfish
Like X-Wing, but with three rows and three columns.
Y-Wing (XY-Wing)
Three cells with two candidates each – a pivot and two wings – remove a digit from cells that see both wings.
XYZ-Wing
Like Y-Wing, but the pivot has three candidates, so only cells that see all three cells are affected.
W-Wing
Two identical two-candidate cells joined by a strong link remove their other digit from cells that see both.
Skyscraper
Two columns (or rows) where a digit has only two places, with one end of each in the same row – the other two ends remove the digit from cells that see both.
2-String Kite
A digit with two places in a row and two in a column, linked through a box, removes the digit where the loose ends meet.
Simple colouring
Follow a digit through units where it has only two places, colouring the cells in two alternating colours – one colour is the truth.
Innies and outiesKiller
When cages cover a box (or rows or columns) plus a few cells outside, the difference from 45 gives those cells.
Expert (Expert)
Jellyfish
Like X-Wing and Swordfish, but with four rows and four columns.
X-Chain
A chain of one digit that alternates strong and weak links – one of its ends is the digit.
XY-Chain
A chain of two-candidate cells – whichever way it goes, one end holds the same digit.
AIC (alternating inference chain)
A chain that alternates strong and weak links between candidates, also across different digits.
Combinations across cagesKiller
Cages in the same row, column or box can't use the same digits, which rules out combinations.
Cage splittingKiller
Split a cage that crosses boxes and use the 45 rule to find the sum of each part.
Minimum and maximum sumsKiller
The other cells of a cage can only be so large or small, which limits each cell.
Chains with cage linksKiller
A cage that must hold a digit in one of two cells works as a strong link in a chain.
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 |
|
Combination finder
Choose the number of cells and the sum, and mark digits that must or can't be in the cage. Digits in a cage are always different.
Possible sums for 3 cells: 6–24
8 possible combinations
- 1 + 5 + 9
- 1 + 6 + 8
- 2 + 4 + 9
- 2 + 5 + 8
- 2 + 6 + 7
- 3 + 4 + 8
- 3 + 5 + 7
- 4 + 5 + 6