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Hidden Quad

Four digits confined to the same four cells of a unit — every other candidate is stripped from those cells.

A hidden quad is the largest of the hidden subsets. Four digits can each be placed in only the same four cells of a unit, so those four cells must hold those four digits. Any other candidate in the four cells can be removed.

It is the hardest subset to spot by eye because the four cells are often heavily marked; it is usually found only with complete candidate lists.

How to spot it

For a unit, find four digits that, between them, appear in only four cells. Those cells form a hidden quad: keep only the four digits in them and delete everything else.

  • Track candidate cells for each digit in the unit.
  • Find four digits restricted to the same four cells.
  • Erase all other candidates from those four cells.
Four digits confined to four cells; their other candidates are erased.

Worked example

  1. In a row, digits 3, 5, 7 and 8 each appear only in cells A, B, C and D.
  2. They appear in no other cell of the row.
  3. So {3,5,7,8} are locked into A–D.
  4. Cell B showed {1,3,5,9}; strip 1 and 9, leaving {3,5}.
  5. The reduced marks frequently uncover a single or a wing.

Try it yourself

7
8
3
1
8
6
2
4
6
1
2
8
5
1
2
3
4
7
6
9
4
1
3
3
7

Tap a cell, then a number, to practise.

Frequently asked questions

When does a hidden quad actually appear?
On hard and expert puzzles where a unit has four sparsely-placed digits. It is uncommon, so reach for it only after simpler subsets fail.
Is it ever a quad and a pair at once?
A hidden quad in a unit implies a complementary naked subset among the remaining cells; solving either gives the same eliminations.

Related techniques

Practice: Hidden Quad

Put the Hidden Quad to work on a live board — free puzzles with notes, hints and four difficulty levels.

Try it on a live board

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