The story of Number Place

Number Place is a puzzle on a 9×9 grid. You fill in the digits 1 to 9 so that no digit repeats in any row, any column, or any of the nine 3×3 boxes marked by thick lines. There is no arithmetic. All you use is elimination: “this can't go here”. The most surprising fact: with 16 or fewer clues visible at the start, you can never make a puzzle with exactly one solution.

At least 17 clues

The digits given at the start are called clues. More clues sounds easier, so how few can there be? The answer is 17. No puzzle with 16 or fewer clues has exactly one solution. In 2012 a team of researchers showed this by having a computer check the possibilities exhaustively. It is a proof by massive computer search, not one worked out by hand. Many 17-clue puzzles with a single solution are said to have been found.

How many completed grids are there? The known count is 6,670,903,752,021,072,936,960 (about 6.67×10 to the 21st power). If you treat rotations, reflections, relabelled digits and similar rearrangements as the same grid, the figure is said to be about 5.5 billion (5,472,730,538). This site's program has not verified either number; they are reported results from the sources listed below.

History

The modern form of the puzzle is believed to have first appeared in 1979, when an American magazine published it under the name “Number Place”. Its creator is believed to be Howard Garns, a retired architect. The puzzles were printed without an author, so this was worked out later from the evidence.

Relatives are older. French newspapers in the 1890s are said to have printed magic-square-like puzzles in a grid, but they needed arithmetic and were different from today's puzzle. The mathematician Euler studied “Latin squares”, tables where each symbol appears once in every row and column, which are a relative of this puzzle. They have no box rule, so they are not Number Place itself.

In Japan, the puzzle magazine Nikoli is said to have introduced it in 1984, under a name that jokingly means “digits should be single”, a pun on using only one-digit numbers. Born in America and named and nurtured in Japan, it became a worldwide craze from around 2004, when British and other newspapers began printing it.

One more note: the name most commonly used for this puzzle in Japan is a registered trademark of a puzzle publisher. This site therefore uses the original name, Number Place.

How to think about it

• Look for “only one place”. If a row has just one empty cell, the missing digit goes there. The same works for columns and boxes.
• Search by digit. Where can a 5 go in this box? Cross out every cell whose row or column already holds a 5, and sometimes only one is left.
• Write candidates. Small notes for each cell reveal clues such as two cells that share exactly the same two digits.
• No guessing needed. Every puzzle here can be finished by reasoning alone. When stuck, look for ways to remove candidates.

Every puzzle on this site is original. Our program checks that each of the 30 has exactly one solution and can be solved using only logical deductions. If you get stuck, the Hint button shows a strategy first, then where to look, then the answer.