Hidden Single in Sudoku: The Only Place Left
A cell can have several candidates and still be forced. Instead of asking what a cell can hold, ask where a digit can go. Cells are named by row and column: r8c7 is row 8, column 7.
Step 1 of 4
One place for the 8
Box 9, the bottom-right box, still needs an 8, and has four empty cells. The 8 in r7c1 rules out the two in row 7. The 8 in r3c9 rules out r9c9 at the foot of column 9. That leaves one cell for the 8: r8c7, the ringed cell.
Its notes show 2, 4 and 8, so it is not a naked single. But the 8 has nowhere else to go in the box. A digit with only one place left in a row, column or box is a hidden single.
Place the hidden single
What step 1 did is called cross-hatching: follow each 8 outside the box along its row or column, and cross off the cells of the box it passes through. The cell nothing crosses is the 8's.
Your move
Place box 9's 8.
Why the 8?
r8c7 could hold a 2, a 4 or an 8. Why must it be the 8?
Hidden in a row
A hidden single can hide in a row or a column as well as a box. No cell in this grid has a single candidate, but one row has a digit with only one place to go. Pick a row with few gaps, list the digits it lacks, and check where each one fits.
Your move
Find the hidden single and fill it.
What you learned
- A hidden single is a digit with only one place left in a row, column or box.
- Its cell can have other candidates. The digit decides, not the cell.
- To find one, pick a row, column or box, list the digits it lacks, and check where each one fits.
In this course
Unit 1The rules
Unit 2Solving techniques
Take it to the table.
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