## Hidden Pairs, Hidden Triples, Hidden Quads Strategy

The hidden pairs, triples, and quads strategy involves looking for a group of candidates that can only occur in the appropriate number of squares, then eliminating other candidates from those same squares. They are called "hidden" because there are other candidates in the same squares as the pairs, triples, and quads.

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### Hidden Pair

A hidden pair occurs when a pair of numbers appears in exactly two squares in a row, column, or block, but those two numbers aren't the only ones in their squares.

In the above example, the 5 and 9 in red are a hidden pair. The 5 and 9 only occur in those two squares and nowhere else in the row, so those two squares can only contain 5 and 9 and no other numbers. Because of that, you can get rid of the other candidates in those squares, as shown crossed out in red.

#### Interactive Example

There is hidden pair in the following interactive example. Can you find it?

At the end of the third row, two cells have 2,3. They do not appear anywhere else in that row, so the candidate 5s in those cells can be removed.

Puzzle string:

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### Hidden Triple

A hidden triple occurs when three cells in a row, column, or block contain the same three numbers, or a subset of those three. The three cells also contain other candidates.

In the above example, 1, 2, and 5 (shown in red) are a hidden triple. Those three numbers are only seen in three squares in the row. Since they only appear there, those three squares MUST contain 1 or 2 or 5 and no other numbers. For that reason, the other candidates can be removed from those squares as shown crossed out in red.

Keep in mind that, as with naked triples, some of the cells of a hidden triple might only contain a subset of the three numbers that form the triple. You can see this in the above example with the cell that only contains 1 and 2.

#### Interactive Example

There are two hidden triples in the following interactive example. Can you find them?

In the third column, exactly three cells have 1, 3, and 8. They do not appear anywhere else in that column, so the other candidates in those three cells can be removed. Similarly, in the second row, exactly three cells have 2, 4, and 6, so the other candidates in those three cells can be removed.

Puzzle string:

If you are using Internet Explorer 8 or lower, or if you are using Android Browser 2 or lower, please upgrade to a newer web browser to play Thonky Sudoku.

Hidden quads are pretty rare, and they can be difficult to spot unless you are specifically looking for them.

In the above example, since the four numbers 1, 6, 7, and 8 (shown in red) appear only in four squares, they are a quad. Those four numbers MUST occur in those four squares. For that reason, the other candidates can be eliminated from those squares, as shown crossed out in red.