Last Remaining Cell
Last Remaining Cell is a basic sudoku technique that starts from a number, not from a cell. Pick a row, column, or 3×3 box and a number it still needs. If that number is blocked from every empty cell there except one, it must go in the one cell that is left. You need no pencil marks for it, and you will use it at every difficulty level. Many guides call this a hidden single.
A cell is blocked for a number when the same number is already in that cell's row, column, or box. The cell that is left can still look undecided on its own, with room for several numbers. That does not change the answer, because the region has no other place for this one.
When To Look For It
- A number is already on the grid several times. Each copy blocks a whole row and a whole column, so the boxes still missing it have only a few cells left for it.
- You have just placed a number. Look at the boxes it lines up with, because the new number blocks cells in them too.
- The number already sits in two of the rows or columns that cross a box. Those copies block most of the box, as in the example below.
How It Works
- Choose a region and a number: Pick a row, column, or 3×3 box, and a number from 1 to 9 that is not in it yet.
- Find the copies already placed: Look for that number in every row and column that passes through the region. If the region is a row or a column, also check the three boxes it runs through.
- Cross out the blocked cells: Every empty cell that shares a row, column, or box with one of those copies cannot take the number.
- Place the number: If exactly one empty cell is not blocked, the number goes there.
Worked Example From a Real Puzzle
The board below is the start of one of the easy puzzles on this site, with only its 30 given numbers. No empty cell on it is settled by its own row, column, and box yet, so Last Remaining Cell is the first step the site's solver finds here. You can open this board in the solver and ask for a hint to see the same step.
1.Pick the box and the number
Take the middle-left box: rows 4 to 6, columns 1 to 3. It already holds 4, 7 and 5, and six of its cells are empty. It has no 8 yet, so ask where an 8 can go.
243756812924751867634728698246The starting board, with the middle-left box highlighted.2.Follow the 8s already on the grid
Row 5 already has an 8, in column 4. That blocks the three empty cells of row 5 inside the box. Column 3 already has an 8, in row 9. That blocks the two other empty cells of column 3 inside the box. Five of the six empty cells are now ruled out for the 8.
243756812924751867634728698246The two 8s that do the work, and the five cells they block.3.Place the 8 in the cell that is left
Only row 6, column 2 is still open. Read on its own, that cell could hold 1, 3, 6, 8 or 9, so it gives no answer by itself. The box decides it: an 8 has to be somewhere in the box, and this is the only cell left for it. The 8 goes in row 6, column 2.
2437568129247581867634728698246The 8 placed. Its cell still had five possible numbers.
Why It Works
Every row, column, and box must contain each number from 1 to 9 exactly once. So the region needs this number in one of its empty cells. A blocked cell cannot take it without repeating the number in a row, column, or box. When only one cell is not blocked, the number has to go there. No guessing is involved.
How It Differs From Last Possible Number
Last Possible Number starts from a cell and asks which numbers can still go in it. Last Remaining Cell starts from a number and asks which cells of a region can still take it. On the board above, the first question gives nothing for row 6, column 2, which still allows five numbers. The second question settles it at once.
Tips
- Scan one number at a time: Start with the number that appears most often on the grid and check each box that still needs it.
- Rescan after every move: A new number blocks cells in its row, column, and box, which can leave another number with a single cell nearby.
- Use it with Last Possible Number: Switching between the two basics gives fast runs of safe placements.
Common Mistakes To Avoid
- Missing a blocking number: Before you call a cell open, check its row, its column, and its box for the number.
- Mixing regions: Count the open cells of one row, column, or box at a time.
- Confusing it with the last free cell: When a row, column, or box has only one empty cell left, you fill in the one number it is missing. That is the last free cell. Last Remaining Cell works while the region still has several empty cells, as long as only one of them can take the number.
Where You Will Use It
Last Remaining Cell is common in easy puzzles and still essential in harder ones. In a hard puzzle, an advanced technique often removes a candidate and leaves a number with only one possible cell in some row, column, or box. This is the step that places it.
واصل استكشاف استراتيجيات السودوكو
عد إلى مركز المقالات لاكتشاف المزيد من الإرشادات والتحديثات.