Pencilmark

What does “solver-certified” mean?

By Andrew Boyko · Updated Nov 2026

Every Pencilmark puzzle passes two checks before you see it. Here is what they are and why they matter.

The promise

Every puzzle in Pencilmark has exactly one solution and can be solved without guessing. That sounds like a baseline, but plenty of puzzle apps skip one half of it. The usual shortcut is to generate a grid, check that it has a single solution, and call it done.

Two checks, not one

  1. Uniqueness. A brute-force search counts the solutions of the grid. If it finds more than one, the puzzle is thrown away.
  2. Logical solvability. A second solver tries to finish the grid using only named techniques (such as last candidate or region groups), never trial and error. If it gets stuck, the puzzle is thrown away.

The difficulty rating comes from the hardest technique the second solver needed. An easy puzzle needs only the basic ones; an expert puzzle requires groups.

Why this matters for you

How the hints work

Hints are not canned messages. The solver looks at your current board, finds the next step it would take, and explains it using the cells involved. There are three levels: a nudge to the right area, the reason, and the move itself.

See it in action: play a puzzle and press Why?

Play in the app

FAQ

What does solver-certified mean?

A program verified that the puzzle has exactly one solution and that logical techniques alone reach it.

Can a puzzle with a unique solution still need guessing?

Yes. Uniqueness is necessary but not sufficient. A puzzle can have one solution and still need trial and error to find it. Pencilmark checks both.

Who verifies the puzzles?

A solver written for Pencilmark, which the app also uses to generate the Why? hints.

Are there any errors?

We test every puzzle automatically. If you ever find one that breaks the promise, please report it.