Subsets

Hidden quad

A hidden quad is four digits that, within one row, column or box, can only go in the same four cells. Each of those digits needs a home in that unit, and these four cells are the only ones on offer, so the four cells are spoken for: they hold those four digits and nothing else. Every other candidate in them can be removed.

Written by Georgi Nedyalkov

Level
Advanced

The pattern

Hidden quad: what it does.

It's the hidden pair and the hidden triple one size up, and it's hidden for the same reason: the four cells usually carry other candidates as well, so nothing about them stands out until you count digits instead of cells.

Each of the four digits doesn't need to appear in all four cells. What counts is that none of them has a home in the unit outside those cells.

It mirrors the naked quad. When a unit has eight empty cells, a hidden quad in four of them means the other four form a naked quad, so the same removals can be found either way.

Example

Hidden quad: a worked example.

  1. List the homes of each digit

    In one unit, write down where each missing digit can still go. Digits with two, three or four homes are the ones to work with.

  2. Find four digits that share four cells

    Look for four of those digits whose homes, together, cover only four cells. Each digit may use some of the four cells or all of them.

  3. Check that nothing escapes

    None of the four digits may have a home in the unit outside those four cells. One stray candidate and there's no quad.

  4. Strip the four cells

    Remove every other candidate from the four cells. They keep only the four digits, and the rest of the unit is untouched.

Spotting it

Hidden quad: how to spot it.

  • Work from the digits, not the cells. Pick a unit with many empty cells and list each missing digit's homes; quads show up in that list, not in the grid.
  • Hidden quads hide best in units with eight or nine empty cells, where the four cells are crowded with other candidates.
  • The result is often large: a hidden quad can clear several candidates from each of its four cells at once.
  • Like every subset, it needs complete marks. Check every cell of the unit before trusting that a digit has no other home.

Where it stops working

Hidden quads are rare and slow to find by eye, and they only tidy the four cells' own candidates, removing nothing elsewhere. A candidate left out of one cell can make four digits look confined when they aren't, and the removals would then be false.

Keep going

Related topics.

New to sudoku? The rules take two minutes to read, and the first-puzzle walkthrough covers the basics that come before any of these.

Beyond the lessons.

The game's lessons stop at X-Wing, so there's no Hidden quad lesson. The eight it does teach will get you through almost any puzzle; this page is here for when you run into the pattern anyway.

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