Hidden Quad

The principle

A zone is a row, a column or a box. Choose four digits, say 2, 4, 6 and 8, and look at where each can still go in the zone. If, between them, they appear in only four cells, those four cells belong to them: there are four digits to place and only four places for them.

Those four cells are therefore entirely taken by 2, 4, 6 and 8, whatever their other candidates are. Remove those other candidates from their notes. The other cells of the zone do not change: the cleanup happens in the cells of the quad itself.

As with the smaller groups, each digit does not need to appear in all four cells. A digit may be possible in only two of them. What counts is that the four digits together do not touch a fifth cell.

How to spot it

You need candidate notes. In a zone, look for digits that remain possible in only a few cells, two, three or four. Pick four and list the cells where they appear: if that list holds exactly four cells, you have a Hidden Quad. If it holds five, there is nothing to eliminate.

The complement helps. In a zone with n empty cells, a hidden group of k digits always matches a naked group of n − k cells. With eight empty cells, a Hidden Quad equals a Naked Quad on the other four cells. With seven, a Naked Triple. With six, a Naked Pair.

A worked example

In one row, 2 is possible in only two cells, A and B. 4 is possible only in B and C, 6 in C and D, 8 in A and D. The four digits touch only cells A, B, C and D. No digit is possible in all four cells at once, but the count is right: four digits, four cells.

Cell A has candidates 2, 5 and 8, cell C has 1, 4, 6 and 9. The 5 has no business in A, because the four cells are reserved for 2, 4, 6 and 8: remove it, and 2 and 8 remain. Likewise in C, remove 1 and 9: 4 and 6 remain.

Common mistakes

The most common confusion is to remove candidates in the wrong place. The Hidden Quad does not touch the other cells of the zone: it cleans its four cells. It is the opposite of the Naked Quad, which cleans the other cells.

Another trap is to miss a position of one of the four digits. If one of them shows up in a fifth cell, the group falls apart. Reread the whole zone, counting every cell where the digit is still possible.

When to use it

The Hidden Quad is expected at the Expert level, along with both triples, the Naked Quad and the X-Wing. It is very rare in practice: in a zone with nine empty cells, four digits grouped like this match a Naked Quintuple on the other five cells, which is much harder to spot.

Frequently asked questions