Sudoku Flow

The world's hardest Sudoku, put through a hint engine

There is no official hardest Sudoku: it depends on how you measure. We measured it the way a player solves, one step at a time with the easiest technique that works, using the hint engine from our Sudoku app.

Quick answer

Two puzzles by the Finnish mathematician Arto Inkala, AI Escargot (2006) and his 2012 puzzle, were reported around the world as the hardest Sudoku ever made. Our app's hint engine cannot explain every step of either: both need Forcing Chains, where you try a number and follow what it leads to, and both have steps that no technique the app knows explains. None of the app's 60,000 puzzles needs either.

How we measured

The hint engine is the same code as the hint in our app. It finds the easiest technique that places a number, places it and looks again, until the grid is full. Forcing Chain is the last technique it tries; when even that does not work, the engine still knows the number but has no step to explain it with. You can watch every step in the Sudoku solver.

The results

PuzzleCluesStepsForcing ChainsSteps without an explanationHardest named technique
Arto Inkala's 2012 puzzle216064Forcing Chain
AI Escargot235832Forcing Chain
A puzzle made to beat brute force176400Hidden Single

Arto Inkala's 2012 puzzle

Published in June 2012, when news outlets around the world reported it as the hardest Sudoku ever made.

6 Forcing Chains and 4 steps without an explanation: past the app's hardest level, Extreme.

Solve it step by step →

Source: SudokuWiki: Arto Inkala Sudoku

AI Escargot

In late November 2006 its maker, the Finnish mathematician Arto Inkala, said it was the world's hardest Sudoku. He named it after its snail-like shape.

3 Forcing Chains and 2 steps without an explanation: past the app's hardest level, Extreme.

Solve it step by step →

Source: SudokuWiki: Escargot

A puzzle made to beat brute force

Wikipedia shows it as a Sudoku designed to work against brute-force solving programs: its top row is empty, and the answer in that row is 9 8 7 6 5 4 3 2 1, the worst order for a program that tries 1 first.

Every step has a name. The hardest is Hidden Single, so the app would rate this puzzle Medium.

Solve it step by step →

Source: Wikipedia: Sudoku solving algorithms

What this shows

  • Fewer clues do not make a puzzle harder. The brute-force puzzle has 17 clues, the fewest a Sudoku with one answer can have, and a person solves it with singles alone. Inkala's 2012 puzzle has 21 clues and still needs trial.
  • Hard for a computer is not the same as hard for a person. A program that tries every number in turn has to try a great many on the brute-force puzzle; a person never has to guess on it.
  • The app's hardest level stops short of trial. None of its 60,000 puzzles needs a Forcing Chain; its Extreme level is mostly decided by ALS-XZ, in 86.3% of Extreme puzzles.

Which puzzle is hardest depends on the measure. On SudokuWiki's own measure, Inkala's 2012 puzzle comes third, behind two puzzles by David Filmer. SudokuWiki: Arto Inkala Sudoku

Sudoku solver →What each Sudoku difficulty level asks of you →Extreme Sudoku →
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Want more boards like this?

We also make a Sudoku app for iPhone, iPad, Mac and Android. There are no ads in it at all, it works offline, and when you ask for a hint it shows you the technique instead of just filling in a number.

App StoreiPhone, iPad, Mac Google PlayAndroid

Sudoku Flow is made by Rubigo Games, the developer of the Sudoku app recommended on this site.