Seventeen: the fewest clues a Sudoku can have

By David, 26 September 2026

How few numbers can you start a Sudoku with and still have only one way to finish it? For years nobody knew for sure. People had found thousands of puzzles with 17 given numbers, but nobody had ever found one with 16. Was that because 16 was impossible, or because nobody had looked hard enough?

In January 2012 the question was settled. The answer is 17.

What was proved

Gary McGuire, Bastian Tugemann and Gilles Civario, working at University College Dublin, showed that no 9 by 9 Sudoku with 16 clues has a unique solution. Any puzzle with 16 or fewer given numbers can always be finished in more than one way.

Since 17-clue puzzles with one answer were already known, 17 is the minimum.

How they did it

There was no clever formula. They checked.

Checking every possible 16-clue puzzle directly would take far too long, so they turned the problem around. For each finished grid, they asked: is there any set of 16 squares in this grid that, on their own, pin down the whole answer? If such a set existed in any grid, a 16-clue puzzle would exist.

The number of essentially different finished grids is about 5.5 billion. That is a lot, but it is a number a computer can work through. The team wrote a program that searched each grid for a set of 16 clues that would work, using some smart shortcuts to skip hopeless cases. The full search took around seven million hours of computer time on a large cluster, spread over about a year.

It found nothing. No grid has a working set of 16 clues.

Why fewer clues is not always harder

It seems natural that fewer numbers means a harder puzzle, and on average that is true. But it is not a rule. Some 17-clue puzzles fall apart with simple scanning, while some puzzles with 25 or more numbers need very advanced techniques.

What really makes a puzzle hard is the kind of reasoning it needs, not just the count. Fewer numbers tends to mean fewer easy first moves, which is why the levels here are set by the count, but two puzzles with the same count can feel quite different.

Why our Extreme stops at about 22

Making a 17-clue puzzle is hard even for a computer. Most finished grids do not contain a working set of 17 clues at all, and finding one takes a long search. When you press New game you expect a puzzle in a fraction of a second, so our Extreme level aims for around 22 given numbers. That is well below what most newspapers print, and every one of those puzzles still has exactly one answer.

If you want to know more about how the puzzles are built, read why every puzzle here has exactly one answer. Or skip the reading and try an Extreme puzzle.

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