Obvious Singles: The Pencil Mark Foundation

Obvious Singles, also known as Naked Singles in Sudoku literature, is the first technique that formally introduces pencil marks — the practice of writing small candidate numbers in empty cells. While the three beginner techniques (Last Free Cell, Last Remaining Cell, Last Possible Number) can be performed mentally, Obvious Singles requires you to systematically track what numbers each cell could possibly contain. When a cell has exactly one candidate, that candidate is an Obvious Single — and you place it immediately.

How Obvious Singles Work

The process is methodical and, with practice, becomes second nature:

• Step 1: For each empty cell, list all possible candidates — numbers 1-9 that do not appear in the cell's row, column, or 3×3 box. In digital apps, the app does this for you. On paper, you write tiny numbers in the corner of each cell.
• Step 2: Scan every cell with candidates. Look for cells that list only a single candidate. These are your Obvious Singles.
• Step 3: Place the number in that cell. Then, critically, update the candidates for every cell in the same row, column, and box. Removing this candidate from neighboring cells often creates new Obvious Singles.
• Step 4: Repeat until no more Obvious Singles remain.

Why "Naked" Singles?

The term "naked" comes from the visual metaphor of candidate numbers. Imagine each empty cell has its candidate numbers written inside it. A cell with only one candidate has a single number sitting there — it's "naked" because there's no other candidate to hide behind. This contrasts with Hidden Singles, where the correct candidate is "hidden" among other candidates in the cell but is the only instance of that number in the unit.

Obvious Singles are the simplest application of candidate tracking. They represent the fundamental truth of Sudoku solving: identify which numbers can and cannot go in each cell, then act when only one possibility remains. Every other technique in this guide — pairs, triples, pointing pairs, and beyond — is ultimately a more sophisticated way of eliminating candidates until Obvious Singles emerge.

Real-World Example

Consider cell R4C7. After eliminating all numbers present in row 4 (1, 5, 8, 9), column 7 (2, 3, 5, 8), and the box containing R4C7 (4, 6, 8, 9), the remaining possible numbers are 7 and only 7. The number 7 is the sole survivor — it's an Obvious Single. You place 7 in R4C7, then update all affected cells: remove 7 as a candidate from row 4, column 7, and the surrounding box.

When to Use This Technique

Obvious Singles is the primary solving technique for Medium and Hard difficulty puzzles. While Easy puzzles can often be solved without pencil marks, Medium puzzles deliberately require candidate tracking. Obvious Singles become your main tool — you'll cycle through the board repeatedly, finding and placing single-candidate cells, updating candidates, and scanning again. Each placement cascades into new Obvious Singles, creating a rhythm that experienced solvers find deeply satisfying.

In harder puzzles (Hard, Expert, Extreme), Obvious Singles alone won't crack the puzzle. You'll need to apply elimination techniques like Obvious Pairs, Obvious Triples, and Hidden Singles to remove candidates from cells and create Obvious Singles. The goal is always the same: reduce a cell to a single candidate so you can fill it.

A key habit to develop: after placing any number using any technique, always scan the affected cells for new Obvious Singles. A single placement often eliminates the last obstacle for several neighbors, triggering a chain of rapid placements.