- Medium puzzles are always solvable with Naked Singles and Hidden Singles only
- The key step most beginners skip: filling complete candidate notes before looking for patterns
- Hidden Singles appear in units where one digit has only one valid cell — even if that cell has multiple candidates
- After each placement, immediately update candidates in all affected cells
- If you're truly stuck, you've likely missed a Hidden Single — re-scan all units
What Makes Medium Different from Easy
An Easy puzzle always has a Naked Single available (a cell with only one candidate). A Medium puzzle may not — you might reach a point where every cell has two or more candidates. At that point, you need Hidden Singles: digits that can only go in one specific cell within a row, column, or box, even if that cell has other candidates too.
The Three-Phase Medium Strategy
Phase 1: Quick Wins
Scan for nearly-full rows, columns, and boxes. Fill in any cell that is the last empty slot in its unit. Cross-hatch each digit to find boxes where only one cell can hold it. These moves cost no effort and often fill 10–20 cells immediately.
Phase 2: Full Candidates
Once quick wins are exhausted, write candidate notes for every remaining empty cell. Do not skip this step — Medium puzzles are designed to require it. A complete set of candidates turns Hidden Singles from invisible to obvious.
Phase 3: Hidden Singles Hunt
For each unit (27 total), check every digit 1–9. Ask: how many cells in this unit still have this digit as a candidate? If the answer is one, place it immediately and update candidates across all peers. One Hidden Single often triggers a chain of Naked Singles that solves several more cells.
The Update Loop
After every placement — whether from a Naked Single or a Hidden Single — immediately remove that digit from the candidates of all 20 peer cells. This is what makes Sudoku cascade: one placement enables another, which enables another. Skipping the update step is how most Medium solvers get stuck when they shouldn't be.
If You're Genuinely Stuck
On a properly rated Medium puzzle, Hidden Singles are always available. If you cannot find one, check your candidate notes for errors — a missed elimination is the most common cause of artificial dead ends. Go unit by unit and verify that no digit has been missed. The Daily Challenge at Medium difficulty is a good controlled environment to practice this process.