Proven Sudoku
Remote Pairs
Also called Remote Pair chain, Bivalue pair chain.
New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.
What it means
A string of squares that all hold the same two numbers, each one linked to the next. Colours flip down the string. So the two ends hold different numbers, and anything seeing both ends can hold neither.
The exact rule, for stronger players
The rule, stated exactly: A chain of four or more cells all bivalue with the identical candidate pair {x,y}, where consecutive cells see each other. If two cells an odd number of steps apart both see a cell, both x and y are eliminated from it.
What it removes: Remove x and y from cells seeing both ends of an odd-length span.
Why it works: Identical pairs alternate: adjacent cells in the chain must take opposite digits. Cells an odd distance apart therefore hold different digits, so between them they hold both x and y, and anything seeing both is excluded from both.
Worked examples
These come from real Proven Sudoku boards. Nobody drew them by hand to make the pattern look neat. Each one is checked first, so the board is one you could really meet, the pattern is really there, and every digit it rules out is really wrong.
Learn these first
- Naked PairTwo squares in the same group both hold only the same two digits.
- XY-ChainA chain of squares that each hold exactly two numbers.
Related wings
- VWXYZ-WingThe same idea stretched to five squares and five numbers.
- W-WingTwo squares far apart hold the same two numbers.
- WXYZ-WingFour squares holding four numbers between them.
- XY-WingThree squares, each with two numbers left.
- XYZ-WingLike the XY-Wing, but the middle square has three numbers instead of two.
How often does it come up?
Our rough estimate: uncommon, but visually distinctive and satisfying to spot because every cell shows the same two digits.