What are naked quads?
A naked quad is four cells in the same row, column or box whose candidates, taken together, are exactly four numbers. Each cell can show two, three or all four of them. The four numbers must fill the four cells, so they can be removed from every other cell in that group.
It is the bigger sibling of the naked pair and the naked triple. Quads are rarer and harder to see, because no single cell has to show all four numbers. In Marble Sudoku the candidates are small marbles.
Use it in 3 moves
- 1Scan. Pick one row, column or box and look at the candidates in its empty cells.
- 2Find four. Find four cells that use only four numbers between them.
- 3Clear. Remove those four numbers from every other cell in the group.
Then look for singles in the cells you cleared.
TRY IT · GUIDED EXAMPLE
Find the naked quad
Column 8 glows, and every empty hole shows its small marbles. Find four holes that share just four colors, clear those colors from the other holes, and place the single that appears.
This is the real board from Marble Sudoku. The nine marble colors stand for the numbers 1 to 9.
- Quad
- Clear
- Place
Find the naked quad
Read the example in words
In column 8, the holes in rows 1, 7, 8 and 9 can only take Red, Teal, Green and Yellow: rows 1 and 8 show all four, row 7 shows Red and Green, and row 9 shows Teal and Yellow. Four holes, four colors, so those colors fill exactly these holes. The other holes in the column lose them. Row 2 had Orange, Red, Green and Yellow, so it is left with a single color: Orange. With numbers turned on, the quad is 2, 4, 5 and 6, and Orange is 1.
YOUR TURN · PRACTICE
Spot the naked quads
Every round is a fresh board with small marbles in every hole. Tap four holes in one row, column or box that use only four colors between them and clear something. On Easy the group glows. On Hard you find it yourself.
Round color:
Why naked quads work
The four quad cells can only hold 2, 4, 5 and 6. Four cells need four different numbers, and these are the only four they have, so 2, 4, 5 and 6 fill these four cells, one each.
Each number appears only once in a column. With 2, 4, 5 and 6 used up by the quad, no other cell in the column can hold any of them. We don’t need to know which quad cell gets which number.
How to spot naked quads faster
- Look in crowded groups. Quads only matter when a group has at least six empty cells. In a group with five, the other cell is already a single.
- Count the colors, not the cells. Pick cells with two to four candidates and add up the different numbers. Stop when you pass four.
- Look for the mirror. If a group has eight empty cells, a naked quad always comes with a hidden quad in the other four cells. Use whichever is easier to see.
- Check smaller sets first. A naked pair or triple inside the four cells is easier to spot and may already do the job.
Naked pairs vs. triples vs. quads
| Naked pair | Naked triple | Naked quad | |
|---|---|---|---|
| Cells | Two | Three | Four |
| Candidates together | Exactly two | Exactly three | Exactly four |
| Each cell shows | Both numbers | Two or three of them | Two, three or four of them |
| Difficulty | Intermediate | Intermediate | Intermediate |
Common mistakes
- Five numbers between the cells. Count the numbers across all four cells. Five or more means it is not a quad.
- Cells in different groups. All four cells must share one row, column or box. Three in a row and one outside don’t count.
- Clearing the quad cells. The four quad cells keep their candidates. Only the other cells of the group lose the four numbers.
- Clearing outside the group. A column quad only clears its column, unless all four cells also share a box.
Naked quads FAQ
What is a naked quad in Sudoku?
A naked quad is four cells in the same row, column or box whose candidates together are only four numbers. Those numbers must fill the four cells, so they can be removed from every other cell in the group.
Does every quad cell need all four numbers?
No. A cell can show two, three or four of the numbers. Only the total across the four cells must be exactly four.
What is a hidden quad?
A hidden quad is four numbers that fit in only four cells of a group. Those cells lose every other candidate. Whenever a naked quad leaves four other empty cells, those cells form a hidden quad, and the other way round.
Are there naked quints?
In theory yes, but you never need them. In a group with nine cells, a naked quint always comes with a hidden quad, which is easier to see.
Does this work in Marble Sudoku?
Yes. Turn on small marbles, look along one row, column or box, and find four holes whose small marbles show only four colors between them.
When should I look for naked quads?
After singles, pairs and triples stop finding moves. Quads are uncommon, but in hard puzzles they can be the only easy step.
PRACTICE IN THE GAME
Find a naked quad in a real puzzle
When a hard puzzle stalls, pick a crowded row, column or box and count colors in its holes. Four holes with four colors between them can break the puzzle open.
Next technique2-String Kite
