Mini Sudoku

Mini Sudoku · Techniques

Techniques on a six-by-six grid

Guides to Sudoku list dozens of techniques. On a six-by-six grid you need very few of them. This page goes through what a small grid uses, what turns up only now and then, and what you can forget about. Each technique links to its full explanation on the nine-by-nine grid.

Singles do nearly all the work

A naked single is a cell with only one digit left that fits. On a nine-by-nine grid a cell needs to see eight different digits before it is settled. On a six-by-six it needs five, and it sees 12 other cells, so it gets there often.

In the opening position on the right, the top-left cell is settled before you place anything. Its row holds 5, 2 and 4. Its column adds 3 and 1. Only 6 is missing.

We tested 600 daily puzzles from our own generator. Every one could be solved with singles alone, and all but five with naked singles alone. For Mini Sudoku, getting quick at singles is nearly the whole game.

The shaded givens cover 1 to 5, so the marked cell must be 6. This is the start of a real daily puzzle.

Hidden singles, box by box

A hidden single starts from a digit and finds the only cell that can take it. In the same position, look for a 6 in the left-hand box of the middle two rows. The box has three empty cells.

Row 3 already has a 6, which rules out the box’s empty cell in that row. Column 3 has a 6 further down, which rules out another. The cell in row 4, column 2 is the only one left.

Because a box is only two rows tall, one digit in the same row is often enough to finish the job. That makes hidden singles quicker to see here than on the classic grid.

The shaded 6s cross off two of the box’s three empty cells. The 6 goes in the third.

Pairs: possible, and uncommon

A naked pair works on any size of grid. Two cells in a row, column or box that can only hold the same two digits use those digits up, and the rest of the unit can drop them.

In this position, from a harder six-by-six than the daily puzzle, two cells in row 3 can only be 5 or 6. The first cell of the row had the notes 1, 4, 5 and 6, and it loses the 5 and the 6.

You will rarely need this in the daily puzzle, but it is the first thing to try on the day singles don’t finish it. It is also good practice: pairs matter much more on the nine-by-nine.

The outlined cells in row 3 are a pair on 5 and 6, so the red cell at the start of the row can’t be either.

Pointing, and the lopsided boxes

A pointing pair is a digit whose only places in a box lie in one row or column. The digit can then be removed from the rest of that line.

In this position the shaded box needs a 4. Its empty cell in row 3 can’t take one, because column 1 already has a 4, so the two cells in row 4 are the only places. The cell at the far end of row 4 loses the 4 from its notes.

The rectangular boxes make this lopsided. A box covers half of each row it touches, so a digit confined to one row of a box clears just three other cells. A box covers only a third of each column, so a digit confined to one column of a box clears four cells, and there are only two cells in the box to confine it to.

In the shaded box, 4 can only go in the outlined cells in row 4. The red cell in the same row can’t be 4.

What you never need

Some techniques from the big grid have nothing to do on a small one, and the reason is simple arithmetic. A row, column or box has only six cells.

  • Quads. A group of four cells tied to four digits leaves at most two other cells in the unit, and those two form a pair or a single that is far easier to see. You never have to look for a quad.
  • Hidden triples. Three digits confined to three cells leave at most three other cells, which form a naked triple, a pair or a single. Look for the smaller group.
  • Long chains and coloring. These exist to crack nine-by-nine grids that resist everything else. A six-by-six puzzle with 15 givens doesn’t get that far.

The X-Wing can be drawn on a six-by-six grid, and it does occasionally appear in very sparse puzzles. The daily Mini Sudoku has never needed one in our tests.

A solving order for the small grid

  • Scan each digit from 1 to 6 for hidden singles in the boxes.
  • Check any row, column or box with four or five cells filled.
  • Look at crowded cells for naked singles.
  • Only if all of that stalls, write notes and look for a pair or a pointing pair.

The words used on this page are defined in the Sudoku glossary. For getting through that order faster, see solving for speed.