Where small grids come from
The nine-by-nine puzzle has a well-recorded past, told on the history of Sudoku page: an American magazine in 1979, a Japanese name in the 1980s, and a worldwide boom from 2004.
The small grids have no such story. Nobody is credited with inventing them, and they don’t have a famous first appearance. They spread along with the boom, in children’s puzzle books, on the junior pages of newspapers and as warm-ups printed beside the main grid. The four-by-four version is often called Shidoku.
The idea needed no inventing. Once you know the rule, each digit once in every row, column and box, you can apply it to any grid that divides into equal boxes.
Why the boxes are rectangles
A box has to hold each digit once, so it needs as many cells as the grid has digits. On a nine-by-nine grid, nine cells make a three-by-three square. On a four-by-four grid, four cells make a two-by-two square.
Six is not a square number, so a six-cell box has to be a rectangle: three cells one way and two the other. In Mini Sudoku the boxes are three wide and two tall, which gives six boxes arranged in three rows of two.
Sizes like five and seven don’t divide at all, because they are prime. Puzzles of those sizes use irregular “jigsaw” boxes instead. Larger sizes work the same way as six: eight uses four-by-two boxes, and 12 uses four-by-three.
Small grids by the numbers
Shrinking the grid shrinks everything about it, and some of the numbers fall a very long way.
- Cells: 16 on a four-by-four, 36 on a six-by-six, 81 on a nine-by-nine.
- Cells that share a row, column or box with any one cell: 7, then 12, then 20.
- Different finished grids: 288, then 28,200,960, then about 6.67 sextillion.
- Fewest givens a puzzle with one solution can have: 4, then 8, then 17.
The daily Mini Sudoku starts with 15 givens, nearly double the minimum of 8. That leaves 21 cells to fill.
How a six-by-six plays differently
The rules are the same as the classic. The experience isn’t. With only six digits, a cell runs out of options quickly, and most cells can be settled by looking at them directly. You can hold the whole board in your head.
The rectangular boxes make rows and columns behave differently from each other, which never happens on a nine-by-nine. A row passes through two boxes, three cells in each. A column passes through three boxes, two cells in each. A digit placed in one box tells you a lot about the box beside it and less about the boxes above and below.
A small grid is also over quickly. Each placement is about a twentieth of the puzzle, so a run of three or four finds can decide the whole thing. There’s more on each of these points in techniques on a six-by-six grid and solving for speed.
The LarkSpark version
Mini Sudoku here is a six-by-six grid with boxes three wide and two tall. There is one puzzle a day, the same for everybody, with 15 givens and exactly one solution. Your time is recorded, so you can compare it with friends.
If you’re new to it, the rules take a minute to read. If you’ve outgrown it, moving up to the nine-by-nine explains what changes.