"Hidden Triples" Technique

What is a "Hidden Triple"?

The "Hidden Triples" technique is very similar to "Hidden Pairs" and works on the same concept. "Hidden Triples" applies when three cells in a row, column, or 3x3 block are the only cells that contain a specific set of three numbers (e.g., 5, 6, 7).

These three cells also contain other candidates (notes), which is what makes the triple "hidden".

The Logic Behind It

If the numbers {5, 6, 7} only appear in Cell A, Cell B, and Cell C within a specific block, then those three cells must contain the numbers 5, 6, and 7.

Therefore, we can confidently eliminate all other notes (the "victim" candidates) from those three cells.

How to Find a Hidden Triple

It will be easier to understand this technique if you look at the example in the top-middle 3x3 block.

Hidden triples example - numbers 5, 6, and 7 appear exclusively in only three cells of block

Step 1: Scan the Entire Block's Notes

This technique requires a careful scan of all the empty cells in the block. We are looking for three numbers that only appear in three cells.

Let's look at the notes. We can see the numbers for the filled cells are 1, 3, and 9. We must scan the notes of the 6 empty cells (R1C4, R1C5, R1C6, R2C4, R2C6, R3C4) to find our triple.

Step 2: Find the Triple

After scanning, we notice a pattern. As the example states, there are only three cells in this block that contain the notes 5, 6, and 7.

(Example Cell A might have notes: {2, 4, 5, 6, 7})
(Example Cell B might have notes: {5, 6, 7, 8})
(Example Cell C might have notes: {2, 5, 6, 7})

No other cell in this block (like R1C4 or R2C4) has a 5, 6, or 7 in its notes. This means the numbers {5, 6, 7} are "hidden" in these three cells.

Step 3: Eliminate Other Notes

Since we know these three cells must be 5, 6, or 7, we can remove all the other "victim" notes from them.

In Cell A {2, 4, 5, 6, 7}, we would delete 2 and 4.
In Cell B {5, 6, 7, 8}, we would delete 8.
In Cell C {2, 5, 6, 7}, we would delete 2.

Powerful transformation - hidden triple {5,6,7} becomes clean naked triple after massive cleanup

After this cleanup, all three cells will have their notes reduced to {5, 6, 7}, creating a new "Naked Triple" and making the board much cleaner.

Master This Powerful Technique

That is how the "Hidden Triples" technique works while solving Sudoku. It is a major step in solving very complex puzzles!