A candidate is a digit a cell can still take, because nothing in its row, column or box rules it out. Pencil marks are those candidates written small inside the cell, so you see them at a glance.
Corner marks and center marks
Players on paper use two styles. Center marks list every candidate in the middle of the cell. Corner marks are sparing: a digit goes in a corner only when it has two or three places left in a box.
This site's boards and game draw candidates like center marks, every one in the cell, but give each digit a fixed place in a three-by-three pattern: 1 top left, 5 in the middle, 9 bottom right, like a phone keypad. In the game, the Notes button makes the digits you enter go in as pencil marks.
Before marking
The puzzle with nothing written in has 30 empty cells, four of them in box five.
Take row five, column four. Row five holds only a 1. Column four adds 3, 4, 5, 6 and 8, and box five adds nothing new. That leaves 2, 7 and 9, written in small.
One box marked
Do the same for box five's other gaps. Row four, column six gets 8 and 9. Row five, column six gets 2, 8 and 9. Row six, column four gets a single 9.
A cell with one mark can only be that digit.
Every cell marked
Now every empty cell. Most get two or three marks, row five, column seven gets four, and 12 cells are down to one.
Check each cell against all three houses. An extra mark gets crossed out later, but a missing one hides the digit that belongs there.
Place a digit, cross out its marks
Row six, column four has one mark, so the 9 goes in. Every cell that shares a house with it loses its 9.
Row six loses one, at column three. Column four loses two, in rows five and seven. Box five loses two more, at row four, column six and row five, column six. The 9 in row four, column seven stays, because it is in box six.
Two cells drop to one mark: row four, column six is now an 8, and row seven, column four a 1. The game does the crossing out for you when you enter a digit.
Every cell, or only where it helps
You need not mark the whole grid. Early on, mark a box or a row with few gaps, use what you find, and move on. When that finds nothing more, mark everything. The game's Start in auto candidate mode setting fills every empty cell for you at the start.
Why the techniques ahead start from marks
The singles that come next can be found on a bare grid. From the pointing pair on, every technique reads pencil marks, and most of them never place a digit at all. They prove that some marks can go. Without the marks written in, there is nothing for them to remove.
Row one, column eight has one mark left, so a 4 goes in. Which 4s have to be crossed out?
Check its row, its column and its box. A cell has to share one of them to lose a mark.
الخلاصة
- ابحث عن
- The digits each empty cell can still take.
- النطاق
- One cell, one box or row, or the whole grid.
- النتيجة
- Small marks in fixed places. A placed digit takes its marks out of its row, column and box.
- العلامة
- One mark left: the cell is solved. No marks left: an earlier mistake.
- إذا لم تنجح
- If a cell has no candidates, recheck the last digit you placed. Then look for cells with one mark: the last possible number, the next stop.