Spot Hidden Singles Faster

The hidden single is the deduction that carries you through most easy and medium boards. Here is how to find them without scanning the whole grid over and over.

What a hidden single is

A cell can look crowded with candidates and still have only one real home for a given number. If a row, column or box has just one square where a particular digit can legally go, that digit belongs there — even if the square could, on paper, hold others. That is a hidden single, and learning to see them quickly is the single biggest jump in early solving speed.

The one-number sweep

Instead of staring at a single cell and asking "what goes here", pick a number and hunt it across the board. Take the 1s: look at each box that still needs a 1, then cross off the rows and columns that already contain a 1 elsewhere. Often that leaves exactly one open square in the box, and the 1 drops in. Work 1 through 9 this way and the grid opens far faster than random scanning, because every placement you make closes lines for the next number.

Where they hide

Hidden singles cluster around the numbers that already appear most on the board — those digits have the most lines closed off, so the remaining squares are tightly constrained. Start your sweep with the most common numbers and you will find the easy placements first. Keep your pencil notes tidy as you go; a clean candidate map makes the lone survivor obvious.

A worked example

Imagine the top-left box still needs a 7. Three of its cells are empty, so at a glance the 7 could go in any of them. Now look outward. If one of the box's rows already holds a 7 somewhere across the grid, that row is closed inside the box. If one of its columns holds a 7 as well, that column is closed too. Very often those two lines rule out two of the three empty cells, leaving exactly one square where the 7 can legally sit. That is a hidden single: the cell looked open, but only one number truly fits. You did not solve the cell by staring at it — you solved it by chasing a single digit across the board.

Hidden singles versus naked singles

It helps to know the difference between the two easiest deductions, because you hunt for them in opposite ways. A naked single is found by looking at one cell and noticing that eight of the nine numbers already surround it, so only one is left. A hidden single is found by looking at one number and noticing it has only one home left in a unit. Beginners tend to search only for naked singles, which is why they stall: on medium boards the hidden singles are usually the moves that keep the grid flowing. Training your eye to switch between the two doubles the number of placements you can see.

Turn the sweep into a habit

The trick is to make the one-number sweep automatic rather than something you do only when stuck. Every time you place a digit, take three seconds to ask where else that same digit can still go in the surrounding rows, columns and box. You will frequently find that your placement just created a fresh hidden single a few cells away. Chaining these together is what makes fast solvers look fast: they are not thinking harder, they are simply following one number at a time and letting each placement set up the next.

Practise the sweep on a gentle board first at Easy Sudoku, then carry it into Medium, where hidden singles do most of the heavy lifting. When you are ready for a shared challenge, try the same technique on today's Daily Sudoku.