Every edition this week can be finished with singles. Six of the seven never need more than a square with one candidate left. Saturday's Master, No. 89, also needs the hidden single, so that is this week's lesson.
The digit with one square
A naked single starts from a square. You look at one empty square, rule out every digit its row, column and box already hold, and one digit is left.
A hidden single starts from a digit. You choose one digit and one group (a row, a column or a box), and you check every empty square in that group for it. If only one square can take the digit, the digit goes there. The group must contain that digit somewhere, and every other place is closed. The square is certain.
The two methods can disagree about the same square. A square can still hold three candidates and be certain anyway, because its row has nowhere else to put one of them.
Here is the moment from No. 89. Count rows 1 to 9 from the top and columns 1 to 9 from the left. Start by finishing row 3, which goes by singles: 4 in column 1, 5 in column 6, 2 in column 3, 7 in column 8, and the last square, column 7, takes the 3.
Now the grid has no naked singles left. Every empty square has at least two candidates. A solver who only looks at squares stops here.
Take row 1 and the digit 4. Row 1 has seven empty squares, in columns 1, 3, 4, 6, 7, 8 and 9.
Columns 1 and 3 sit in the top left box, and that box now has a 4 at row 3, column 1. Column 4 has a 4 at the bottom, in row 9. Columns 7, 8 and 9 sit in the top right box, which has a 4 at row 2, column 7.
That leaves row 1, column 6. Look at that square alone and it allows 4, 6 and 9. Look at row 1 and the 4 has nowhere else to go. Write the 4.
The usual mistake is in the first step. The 4 that closes columns 1 and 3 is one you wrote yourself a minute earlier. Solvers who scan only the printed digits miss it, and they count three homes for the 4 in row 1 when there is one. When you follow a digit, count every copy on the grid, the ones you placed as well as the ones you were given.
One more from the same position, for practice. Take row 5 and the digit 7. This one uses only the printed digits. The answer is at the end of the next section.
This week's editions
Monday's No. 84 and Tuesday's No. 85 were Easy, with 46 and 48 givens. Wednesday's No. 86 and Thursday's No. 87 were Medium, with 36 and 38. Friday's Hard, No. 88, had 31.
Saturday's Master, No. 89, had 25 givens. Solved by always taking the easiest move available, it calls for a hidden single seventeen times. Sunday's Expert, No. 90, had 27 givens and needs nothing beyond naked singles. A grid with fewer givens is not always the one that asks for the harder technique.
The row 5 answer: the 7 goes in column 1. Column 2 has a 7 at the top, the middle box has one in row 4, and the right box has one in row 6. Column 1 is the only square left.
From Claire's desk
The 19th World Sudoku Championship opens in Kolkata on October 11, hosted by Logic Masters India alongside the World Puzzle Championship. The sudoku rounds are played on October 12 and 13, and the championship site carries the schedule. I will write about the results once they are in.
In Claire's Sudoku
The School teaches the hidden single on a board of its own. It is the last lesson of the White belt. I follow one digit across a group with you and check every square for it, and then you find the digit's only square and tap it. Every lesson in the School is free.
This week, open the School in Claire's Sudoku and take the hidden single lesson.