Two Strong Links: The Simple Chain Behind Sudoku Eliminations
The Two Strong Links technique chains two strong links so that a candidate seen by both ends of the chain can be eliminated, forming the backbone of many advanced Sudoku strategies. This simple but powerful logic allows you to make deductions that connect cells across the grid, even when they are not in the same row, column, or box. Mastering this concept is a key step in progressing from intermediate to advanced solving, as it provides a clear framework for understanding more complex [Sudoku Chains](/blog/sudoku-chains).
What is a Strong Link in Sudoku?
A strong link describes a relationship between two cells for a specific candidate digit. It exists when that digit can only appear in one of those two cells within a given row, column, or 3x3 block. This creates an 'either-or' situation: if the digit is not in one of the cells, it must be in the other. Strong links are the fundamental building blocks for creating logical chains. Recognizing them is the first step toward using the Two Strong Links technique.
- Look for a row, column, or box where a candidate appears exactly twice to find a potential strong link.
How Two Strong Links Form a Chain
The technique connects two separate strong links to form a logical chain. The first strong link connects cells A and B for a candidate 'X'. The second strong link connects cells C and D for the same candidate 'X'. For the chain to work, one end of the second link (cell C) must be weakly linked to one end of the first link (cell B). A weak link means those two cells share a house (row, column, or box), so they cannot both contain 'X'. This alternating pattern of strong and weak links creates a connected inference path from A to D.
- When looking for the chain, start by identifying two separate strong links for the same candidate digit.
- The weak link is often in the same row, column, or box where cells B and C can 'see' each other.
The Elimination Rule: Which Candidate to Remove
Once the A-B-C-D chain is established, a powerful elimination becomes possible. The rule is: you can eliminate candidate 'X' from any cell that sees both ends of the chain (cells A and D). This works because the chain's logic forces 'X' to be placed in either A or D. If 'X' were in a cell that sees both A and D, it would conflict with one of those placements. This elimination can crack open a difficult puzzle by removing a candidate you previously thought was possible.
The Engine Behind Skyscraper and X-Chains
The Two Strong Links pattern is not an isolated trick. It is the core logic behind several named advanced techniques. For example, the X-Wing pattern is essentially two parallel strong links in two rows that connect via weak links in two columns. The popular Skyscraper pattern is a direct application of two strong links. Even longer, more complex single-digit chains, universally called X-Chains, are built by extending this same principle of alternating strong and weak links. Understanding Two Strong Links gives you the blueprint to recognize and use these patterns without memorizing each one individually. It also connects deeply to Simple Colouring, a visual method for tracking these strong link chains.
How to Spot Two Strong Links in a Puzzle
To find this pattern, pick a candidate digit and scan the grid. First, look for two different rows, columns, or boxes where that candidate appears exactly twice. These are your two potential strong links. Next, check if one cell from the first link shares a house (row, column, or box) with one cell from the second link. This creates the necessary weak link. Finally, look for any cells that can 'see' both of the unconnected ends of this chain. If such a cell contains your candidate, you can eliminate it. With practice, spotting these connected strong links becomes a reliable part of your solving toolkit.
- Focus on one candidate at a time to reduce visual clutter.
- Use pencil marks accurately; missing a candidate can hide a strong link.
- If you spot a pattern like a Y-Wing, see if you can also interpret it through the lens of strong links for deeper understanding.
Key Facts
- ▪A strong link exists for a candidate when it can only go in one of two cells within a row, column, or box.
- ▪The Two Strong Links technique chains two strong links together via a weak link to connect four cells.
- ▪You can eliminate the chained candidate from any cell that sees both the starting and ending cell of the chain.
- ▪This technique is the foundational logic for advanced patterns like Skyscraper, 2-String Kite, and X-Chains.
- ▪A weak link, required to connect the strong links, means two cells share a house and cannot both contain the candidate.
- ▪Finding two strong links for the same digit in different parts of the grid is the first step to applying this technique.
- ▪The elimination is valid because the chain forces the candidate to be placed at one end or the other.
- ▪Mastering Two Strong Links helps solvers understand more complex strategies without rote memorization of many patterns.
Frequently Asked Questions
What's the difference between a strong link and a weak link?
A strong link is an 'either-or' relationship: a candidate must be in one of two cells. A weak link is a 'not both' relationship: two cells share a house, so they cannot both contain the candidate.
Can this technique work with more than two strong links?
Yes. Longer single-digit chains that follow the same alternating strong/weak link principle are called X-Chains. The elimination rule is the same: remove the candidate from cells that see both ends of the chain.
Is the Two Strong Links technique the same as an X-Wing?
An X-Wing is a specific, symmetrical pattern that uses the Two Strong Links logic. The X-Wing has two strong links in two rows, connected by weak links in two columns, leading to eliminations in those columns.
How do I practice finding these chains?
Use the hint system on SudokuHint.com. Start with intermediate puzzles, focus on a single candidate, and look for rows/columns/boxes where it appears only twice. The hint engine can guide you to spot the connections.