Subsets

Naked quad

A naked quad is four cells in the same row, column or box whose candidates, taken together, are only four digits. Four cells and four digits: each of those digits has to land in one of the four cells, so none of them can go anywhere else in that unit. Every other cell there loses those four digits.

Written by Georgi Nedyalkov

Level
Advanced

The pattern

Naked quad: what it does.

It's the naked pair and the naked triple one size up. The cells don't each need all four digits: {1, 2}, {2, 3}, {3, 4} and {1, 4} make a quad just as well as four cells holding {1, 2, 3, 4}.

What matters is the count. Four cells have to be filled with four different digits, and these four cells can only use the same four, so between them they use up exactly those digits. The rest of the unit has to do without them.

In a unit with eight empty cells, a naked quad and a hidden quad are the same discovery seen from two sides: the four cells left over hold the other four digits. Use whichever one you see first.

Example

Naked quad: a worked example.

  1. Pick a crowded unit

    A quad needs a row, column or box with at least five empty cells, or there's nothing left to clear. Units with seven, eight or nine empty cells are where quads hide.

  2. Keep the narrow cells

    Only cells holding two, three or four candidates can belong. A cell with five or more is already too wide for a quad.

  3. Find four that share four digits

    Look for four of those cells whose candidates, combined, are exactly four digits. Write the combined set down as you add each cell; the moment it reaches five, that group is out.

  4. Clear the four digits

    Remove those four digits from every other cell in the unit. The four cells themselves keep their candidates.

Spotting it

Naked quad: how to spot it.

  • Quads come late, after the smaller subsets have stopped working. Check for pairs and triples first: they're quicker to find and often clear the same cells.
  • Look at the other side of the unit too. If a unit has eight empty cells and you can't see a naked quad, look for four digits confined to four cells instead.
  • Write the combined candidates down as you go. Four cells are hard to hold in your head, and a fifth digit is easy to miss.
  • The removals land only inside the same unit. A naked quad says nothing about cells elsewhere in the grid.

Where it stops working

Naked quads are rare, and when one exists, a simpler pattern often makes the same removals first. It needs a complete candidate list in the unit: a forgotten mark can make four cells look like a quad when they really hold five digits, 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 Naked 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.

Pre-order on the App Store

Out 1 December

Thanks. You'll get one email on launch day.

One email on launch day, then your address is deleted.Privacy