- Medium puzzles are solvable with Naked Singles and Hidden Singles alone
- Hard puzzles require at least Naked Pairs, Hidden Pairs, or locked candidates
- The key skill shift: from cell-by-cell analysis to unit-wide pattern recognition
- Pencil marks become non-optional at Hard level — you cannot solve without them
- Every Hard technique builds on the same one rule — just applied to larger patterns
What Medium Requires
A well-constructed Medium puzzle is solvable using Naked Singles and Hidden Singles throughout. The grid has enough givens that scanning alone reveals one or two new cells after every placement, keeping the logic flowing without requiring you to look at multi-cell patterns.
What Changes at Hard
A Hard puzzle reaches a point where no individual cell has a single candidate remaining and no single unit has a digit confined to one cell. You have hit what solvers call a stall. To break it, you need techniques that work across multiple cells at once:
| Technique | What It Does |
|---|---|
| Naked Pair | Two cells in a unit share the same two candidates — eliminates those candidates from other cells in the unit |
| Hidden Pair | Two candidates confined to two cells in a unit — all other candidates in those cells can be removed |
| Locked Candidates | A candidate in a box is restricted to one row/column — eliminates it from the rest of that row/column |
| Naked Triple | Three cells share a pool of three candidates — eliminates those candidates elsewhere in the unit |
The Mindset Shift
Medium solving is mostly reactive: a digit gets placed, you update candidates, another digit becomes obvious. Hard solving is more proactive: you scan for structural patterns (pairs, locked groups) before any digit is forced. You are looking for what must be true about groups of cells, not individual cells.
Building the Hard Skill Set
The fastest way to bridge the gap:
- Always use full pencil marks. Fill in every candidate before making your first move. This makes pairs and locked candidates visible at a glance.
- Scan for pairs before singles. Once you've filled candidates, look for units where exactly two cells share exactly two candidates. These naked pairs are often the key that unlocks Hard puzzles.
- Check box-to-line interactions. Look for candidates in a box that are all confined to one row or column — this is the locked candidates pattern and it appears constantly in Hard puzzles.
Practice Path
Solve 5–10 Medium puzzles until the Hidden Singles feel automatic, then move to Hard. Expect Hard to take 3–5× longer than Medium at first — that is normal. The techniques library has worked examples for every pattern you will encounter. The Daily Challenge offers a new puzzle at your chosen difficulty every day, which is ideal for deliberate practice.