Hidden Quads is the rarest and most challenging of the hidden subset techniques. A Hidden Quad occurs when four candidate digits appear in exactly four cells within a row, column, or box, but those cells also contain additional candidates that mask the pattern. Once you identify the four digits confined to four cells, you can remove all non-quad candidates from those cells, often dramatically simplifying the grid.
Hidden Quads are the logical extension of Hidden Pairs and Hidden Triples, but they are significantly harder to spot because you must track four digits across a unit and verify that all four are confined to the same four cells. The cells themselves might each contain five, six, or even seven candidates, making the quad nearly invisible to casual inspection. This is why Hidden Quads are considered a capstone technique for the intermediate level.
Despite their rarity, Hidden Quads are worth learning because they complete your understanding of subset logic. In practice, if a Hidden Quad exists, it means the complementary Naked subset (the remaining digits in the remaining cells) also exists and may be easier to spot. Experienced solvers often find the naked complement first, but understanding both perspectives deepens your analytical toolkit and prepares you for the pattern-based techniques in the advanced tier.
Try It Yourself
Walk through each step of the hidden quads technique on a real puzzle. Follow the instructions and try entering the correct value when prompted.
Look at row 1 (index 0). Several cells are empty: (0,3), (0,4), (0,5), (0,6), (0,7), and (0,8). Compute the candidates for each empty cell using row, column, and box constraints.
Step-by-Step Guide
Select a row, column, or box and list every candidate digit that still needs to be placed.
For each unplaced digit, record exactly which cells in the unit can contain it.
Look for four digits whose possible cells are all drawn from the same four cells.
Verify that each of the four digits appears only in those four cells within the unit.
Remove all non-quad candidates from those four cells, keeping only the four quad digits.
Check whether the simplified candidate lists reveal any singles or enable further techniques.
Scan other units, though Hidden Quads are very rare -- also check the complementary Naked subset.
Four specific ingredients can only be stored in four particular jars, even though those jars currently hold all sorts of other things too. Once you realize those ingredients have no other home, you can clear out everything else from those jars.
If four digits each appear as candidates in only four cells within a unit, those four cells are the exclusive means of placing all four digits. Since a unit requires each digit exactly once and these four digits have no alternative locations, the four cells must collectively house all four. With four cells fully committed to four digits, any non-quad candidate in those cells would need to displace one of the quad digits, which would leave that digit unplaceable in the unit -- a contradiction of Sudoku's rules.
When to use: Use Hidden Quads as a last resort within subset techniques, after checking for pairs, triples, and their naked counterparts. Look for four digits that are each confined to the same four cells in a unit, even if those cells have many other candidates.
Common Mistakes to Avoid
Spending excessive time hunting for Hidden Quads when a simpler technique would work. They are extremely rare in practice.
Always exhaust Naked Pairs, Hidden Pairs, Naked Triples, Hidden Triples, and Naked Quads before searching for Hidden Quads. Consider whether the complementary Naked subset might be easier to find.
Miscounting which cells a digit can occupy, leading to a false quad identification.
Carefully verify every cell in the unit for each of the four digits. A single missed cell invalidates the Hidden Quad and could lead to incorrect eliminations.
Removing the quad digits from the cells instead of removing the non-quad candidates.
Keep the four quad digits in the cells. Remove every OTHER candidate from those four cells. This is the same logic as Hidden Pairs and Triples, just extended to four digits.
More Examples
See hidden quads applied in different puzzle configurations to strengthen your pattern recognition.
Row Hidden Quad
Highlighted cells show the hidden quads pattern
Practice Puzzles
Apply the hidden quads technique on these mini challenges. Tap a highlighted cell and enter the correct digit.
Quick Reference
- Pattern:
- Four candidates appear in only four cells within a unit
- Action:
- Remove all other candidates from those four cells
- Look for:
- Four digits confined to the same four cells in a unit