The Hidden Triple is a powerful "Hard" level strategy that cleans up your grid. It's called "Hidden" because the three numbers you're looking for are buried under other random candidates ("noise").
If you can find three numbers that don't appear anywhere else in a row, column, or box except for three specific cells, you've found a Hidden Triple.
Interactive Example
Click "Apply Logic" to see the strategy in action.
The "Reserved Seating" Logic
Think of it like reserving tables at a restaurant:
- Imagine a Row has 3 VIP guests (the numbers 2, 5, and 7).
- There are only 3 tables (cells) in that entire row where these VIPs are willing to sit.
- Even if other people (candidates like 8) are trying to sit at those tables, they must be kicked out.
- Why? Because if you let an 8 sit there, one of the VIPs won't have a place to sit, breaking the puzzle!
Real Example Walkthrough
Let's look at the example puzzle above. Focus on Row 8 (the 8th row down).
1. The Situation
Scan the candidates in Row 8. You'll notice something special about the numbers 2, 5, and 7:
- R8C3: Candidates are {2, 5, 7, 8}
- R8C8: Candidates are {2, 5, 7}
- R8C9: Candidates are {2, 5, 7}
2. The Locking Mechanism
Check the rest of Row 8. Do the numbers 2, 5, or 7 appear anywhere else? No. They are completely absent from all other cells in that row.
3. The Logic
Since 2, 5, and 7 (3 numbers) are restricted to R8C3, R8C8, and R8C9 (3 cells): * These 3 cells must eventually become 2, 5, and 7 (in some order). * They are effectively "reserved" for this trio.
4. The Elimination
Look at R8C3 again. It contains an 8. If we placed an 8 in R8C3, we would have only two cells left (R8C8, R8C9) to hold our three VIP numbers (2, 5, 7). That's impossible!
Result: We can safely eliminate 8 from R8C3.
How to Spot a Hidden Triple
Finding them can be tricky because of the "noise." Here is the best way to scan:
Step 1: Count Candidate Frequency
Pick a house (row, column, or box) that has many empty cells (5+). mentally count how often each number appears as a candidate. * "1 appears 4 times..." * "2 appears 2 times..." (Keep an eye on this!) * "5 appears 3 times..." (Interesting...)
Step 2: Look for Overlaps
You are looking for 3 numbers that appear in 3 or fewer cells. If you see that {2, 5, 7} are all clustered into the same three cells, check if they exist anywhere else.
Step 3: Verify the "Hidden" Status
To be a specific Hidden Triple: * The cells must contain extra candidates (noise) that aren't part of your triple. * If the cells contain only your triple (e.g., {2,5,7}, {2,5}, {5,7}), that's a Naked Triple, which is easier to spot but works the same way.
Hidden Triple vs. Naked Triple
| Feature | Hidden Triple | Naked Triple |
|---|---|---|
| What do you look for? | A few numbers restricted to a few cells. | A few cells restricted to a few numbers. |
| Visual clue | Harder. Cells have "noise" (extra numbers). | Easier. Cells are clean (only the triple). |
| Action | Eliminate the noise from the triple cells. | Eliminate the triple from the rest of the house. |
| Result | Confirms where the numbers must go. | Confirms where numbers cannot go. |
Pro Tips for Mastery
- Pencil Marking is Essential: You typically cannot spot Hidden Triples without full pencil marks (notes).
- Start with Pairs: Often, you'll look for a Hidden Pair and realize a third number follows the same pattern.
- Don't Force It: If you have 3 numbers in 4 cells, that's not a triple. It must be exactly N numbers in N cells (or fewer).
- Check "Bivalue" Cells: Cells with only 2 candidates often give clues. If two cells are {2,5} and {2,7}, look for a third cell with {5,7} or similar to complete the set.
Related Strategies
- Hidden Pair: The simpler cousin. Two numbers in two cells.
- Hidden Quad: The bigger cousin. Four numbers in four cells (very rare!).
- Naked Triple: The exact inverse of this strategy.
- Intersection Removal: A simpler way to rule out candidates.