From Euler's 36 officers to Number Islands

Long before newspapers printed puzzles, mathematicians were studying grids in which each symbol appears once in every row and column. Such a grid is called a Latin square, and every finished Number Islands board is one.

Euler and the 36 officers

In 1782 the Swiss mathematician Leonhard Euler wrote about a puzzle that is famous to this day. Take six regiments, each with six officers of six different ranks: 36 officers in all. Can you arrange them in a 6×6 square so that every row and every column contains one officer of each regiment and one of each rank?

Euler suspected it was impossible, and he was right. A proof had to wait until 1900, when the French mathematician Gaston Tarry checked the cases and showed that no such arrangement exists. The 6×6 square turned out to be special. Pairs of Latin squares like this exist for almost every size, but not for 6.

That's a nice bit of trivia for a game played on a 6×6 grid. Number Islands asks for something gentler than Euler did, but it lives on the same famous board.

Number Place

The modern puzzle was born in the United States. Howard Garns, a retired architect and puzzle constructor from Indiana, is generally credited with it. His puzzle appeared as Number Place in Dell Pencil Puzzles and Word Games in May 1979: a 9×9 Latin square split into nine 3×3 boxes, with some numbers given.

Sudoku

The Japanese puzzle publisher Nikoli picked up the idea in the 1980s and named it Sudoku, often explained as short for a phrase meaning “the digits must remain single”. Nikoli also popularised the house style many solvers still love: hand-made puzzles, a limited number of givens, and a symmetrical pattern of clues.

The worldwide craze came later. Wayne Gould, a retired judge from New Zealand living in Hong Kong, wrote a computer program to produce puzzles. In late 2004 sudoku began appearing in The Times in London, and within a year it was in newspapers around the world.

The shapes start to move

Once millions of people knew the rules, constructors began bending them. One of the most popular variants swaps the 3×3 boxes for irregular, jigsaw-like regions. It goes by names like jigsaw sudoku, irregular sudoku and squiggly sudoku. The logic changes in interesting ways, because regions no longer line up neatly with rows and columns.

Some setters then went a step further and stopped drawing the regions at all. In the style puzzle fans call Chaos Construction, the solver must work out where the regions are while placing the numbers. The usual rule is that each region is a connected group of cells of a fixed size.

Where Number Islands fits

Number Islands belongs to that last family. Its six islands are hidden regions of exactly six connected squares, and the puzzle gives you coastline and bridge clues to find them. What makes it different is its focus on being approachable. The grid is a calm 6×6, the 1,001 levels rise slowly in difficulty, and every level can be solved one explainable step at a time. That way the oldest grid puzzle on the books becomes something you can finish on the bus.

Dates and attributions here follow widely published histories of sudoku. Early puzzle history is patchy, and sources sometimes disagree on details.