The history of Calcudoku

Calcudoku began in a classroom. It was made to teach children to think patiently rather than to calculate fast, and it turned out adults liked it just as much.

A teacher's puzzle

The cage puzzle was invented in 2004 by Tetsuya Miyamoto, a Japanese maths teacher who ran a small cram school in Yokohama. He believed children learned more by working things out for themselves than by being told, and he wanted a puzzle that rewarded persistence. Arithmetic was only the way in; the real work was logic.

The puzzles spread through books in Japan, and around 2008 and 2009 British and American newspapers began printing them daily. Many publishers and apps have since made their own, under names such as Calcudoku and Mathdoku — the rules are the same everywhere.

Latin squares again

A finished Calcudoku is a Latin square: a grid in which every symbol appears once in each row and column, the same structure that sits under every Sudoku. Leonhard Euler studied them in the 18th century, and mathematicians have been counting them ever since. The numbers grow astonishingly fast:

• 4×4: 576 Latin squares.
• 5×5: 161,280.
• 6×6: 812,851,200.
• 8×8: about 1.1 × 10²⁰ — more than a hundred billion billion.

The cages are what pick one of those squares out. A good puzzle uses just enough of them, with just the right targets, that only one square fits.

The cousins

• Killer Sudoku uses the same idea of caged sums, on a full Sudoku grid with boxes, and only addition.
• Hidden operations: some versions show only the target, and you have to work out the operation too.
• Bigger and stranger grids: 9×9 versions, grids that use 0 as well as positive numbers, and even modular arithmetic for the very determined.