Remote Pairs
A chain of bi-value cells all sharing the same two candidates lets you eliminate both digits from cells seeing each end.
Remote pairs is a coloring technique restricted to one pair of digits. Take a chain of bi-value cells that all show the identical pair {x,y}, where consecutive cells in the chain see each other. The values alternate along the chain, so cells an odd number of links apart hold opposite digits.
For any two endpoints of opposite parity, one is x and the other is y. Any cell that sees both endpoints can therefore contain neither x nor y.
How to spot it
Collect cells that all show exactly {x,y}. Link those that share a unit into a chain. Colour them alternately along the chain. Two cells of opposite colour at the chain’s ends form a remote pair: eliminate x and y from any cell that sees both.
- A chain of bi-value cells all showing the same {x,y}.
- Consecutive cells share a unit, so values alternate.
- Cells seeing two opposite-parity ends lose both x and y.
Worked example
- Four cells all show {3,8}, linked A–B–C–D so each sees the next.
- Colour them: A and C are one colour, B and D the other.
- A and D are opposite parity — one is 3, the other 8.
- A cell sees both A and D.
- Remove 3 and 8 from that cell.
Try it yourself
Tap a cell, then a number, to practise.
Frequently asked questions
- How is this different from simple coloring?
- Simple coloring colours a single digit using strong links. Remote pairs colours bi-value cells of a fixed pair, so it can eliminate both digits of the pair at once.
- How long must the chain be?
- At least four cells (so the ends are of opposite parity and far enough apart to share peers); longer chains create more elimination opportunities.
Related techniques
Practice: Remote Pairs
Put the Remote Pairs to work on a live board — free puzzles with notes, hints and four difficulty levels.
Try it on a live board