Four digits confined to four cells, the rarest of the standard subset techniques.
A Hidden Quad is the four-digit extension of the Hidden Pair and Hidden Triple. Four digits appear as candidates in exactly four cells within a unit, and these digits don't appear in any other cell of that unit. Since all four digits must go in those four cells, remove every other candidate from those cells.
In practice, Hidden Quads are extremely rare. Most solvers will go months without encountering one. When they do appear, it's almost always easier to find the complementary Naked subset instead. If four digits are hidden in four cells, the remaining digits form a Naked subset in the remaining cells.
Still, understanding Hidden Quads completes your knowledge of subset techniques and strengthens your ability to think about Sudoku constraints in both directions (cell-focused vs. digit-focused).
The approach mirrors Hidden Pairs and Triples. Map each unplaced digit to the cells where it can go within a unit. If four digits all map to the same four cells (with no appearances outside those cells), you've found a Hidden Quad.
Remove all candidates from those four cells except the four digits that form the quad. This can produce dramatic simplification, as cells with 5-6 candidates might drop to 2-3.
In practice, the complement approach is often easier: if you spot five cells in a row that span only five digits, the other four cells must contain the remaining four digits, effectively a Hidden Quad. But recognizing it as a Naked Quint (five) of the other cells is simpler.
Hidden Quads follow the same ironclad logic as every subset technique: N digits in N cells means those digits are locked to those cells, and everything else can be stripped away.
Example 1: Hidden Quad in Box 3
Look at box 3 (top-right). Map each unplaced digit to the cells where it can go. Digits 1, 4, 7, and 8 can only be found in cells R1C8, R1C9, R2C8, and R2C9. No other cell in the box has any of these four digits.
R1C8 has {1, 2, 6, 7, 8}. R1C9 has {1, 4, 6, 7}. R2C8 has {1, 2, 6, 8}. R2C9 has {1, 3, 4, 6}. Not every cell contains all four hidden digits, but across these four cells, digits {1, 4, 7, 8} appear nowhere else in box 3. Since they must fill these cells, remove all extra candidates.
Eliminate 2, 6 from R1C8; 6 from R1C9; 2, 6 from R2C8; 3, 6 from R2C9. After cleaning, R1C8 becomes {1, 7, 8}, R1C9 becomes {1, 4, 7}, R2C8 becomes {1, 8}, and R2C9 becomes {1, 4}.
Example 2: Hidden Quad in a Box
Now look at box 8 (bottom-center). Map digit positions: digits 2, 4, 5, and 8 can only appear in cells R7C5, R7C6, R8C5, and R8C6, the four center cells of the box. No other cell in the box has any of these digits.
R7C5 has {3, 4, 5, 6, 8}. R7C6 has {4, 5, 8}. R8C5 has {2, 4, 5, 6}. R8C6 has {2, 4, 5}. The hidden digits {2, 4, 5, 8} are confined to these four cells, mixed in with extras 3 and 6.
Eliminate 3, 6 from R7C5 and 6 from R8C5. R7C5 becomes {4, 5, 8} and R8C5 becomes {2, 4, 5}. R7C6 and R8C6 were already clean, they only contained hidden quad digits.
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