Sudoku Variations
Surprising Origins and Unusual Layouts
In my spare time — when I find it — I write puzzles. I use the puzzles for our PragProg Twitter feed, for my own pleasure, and for book contents. Recently, I’ve focused on one category of digit placement challenges. I’ve been playing around with layout puzzles in many forms.
The most famous digit puzzle is, undoubtedly, sudoku. It’s the puzzle with rows, columns, and zones, all of which contain one instance of each digit, 1 through 9. Sudoku, is a big game. It takes time and attention to perfectly solve each challenge. I’ve been looking to design puzzles with a lighter touch that better fit my style of quick fun interactions.
The sudoku class of puzzles has a worthy heritage touching on Magic Squares and Euler’s Latin Squares. Puzzles based on these two appeared long before the familiar game first appeared in print in the 1970s. The puzzle type was called Number Place and was designed by Howard Garns. According to David Zivan, who wrote “A Puzzling Life” in Indianapolis Monthly, Garns was an architect with a taste for puzzles. Number Place was first published anonymously in 1979 in Dell Pencil Puzzles and Word Games and took off from there.
How an American-designed puzzle became more famous as a Japanese import took a strange route, indeed.
Zivan writes:
In 1984, a Japanese puzzle-magazine editor traveling in the U.S. saw one of Garns’ “Number Place” puzzles and brought it back to his company, which began publishing the game under the name “suuji wa dokushin ni kagiru,” meaning “the numbers must be single;” that was soon shortened to “Su Doku” and then to “sudoku.” From there, the craze spread to New Zealand, and to The Times of London, and then to the New York Post. Zivan adds that there are hundreds of books on Amazon devoted to the game.
The fun and the challenge of Number Place puzzles isn’t limited to the original 9x9, 3x3 format. For example, a nonomino is a 9x9 version with non-square groups. The digits 1–9 must be placed along every row, every column, and within every group. The word “nonomino” is a variation on “polyomino,” a shape made by joining squares along their edges.
I started playing with Number Place games to see where they might take me, and started developing smaller versions. This is one of the first I designed. It uses the digits 1–4, in a 2x2 layout. It follows the larger 9x9/3x3 model, just shrunk down a bit.
I found the 4x4 grid wasn’t very fun to play. That said, I rather like 5x5 and 6x6 puzzles. They are quick to solve, and are like the familiar sudoku/Number Place challenge. Every number on the grid limits the possibilities for the next placement. It’s a wonderful use of logic balanced by a small investment of time.
Following are examples of a 5x5 grid. I decided to use standard pentomino shapes. Each pentomino sets out the region for its five digits in addition to the column and row constraints. There are many ways to set up the 5x5 board. They all follow this rule: fill in the grid with the digits 1 through 5 so that every column, every row, and every region contains distinct digits.
Enjoy the puzzles and note how they provide a fast and furious challenge in a small form-factor. They’re quick to solve, and I hope they’re as fun for you to play as they are for me to create.
How the boards are generated, the hints chosen, and the regions colored are topics for other posts. For this post, I wanted to share Sudoku’s surprising American origin and the possibilities it offers for unusual layouts.
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