## Juxtapositions: Killer Sudoku

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In a comment on an earlier post aboout Sudoku and Kakuro, Batman mentioned a combination of the two games known alternately as Killer Sudoku, Samunamupure or Sum Number Place. As in traditional Sudoku, Killer Sudoku is played on a 9×9 grid in which the digits 1-9 are placed so that each digit appears once in each row, each column, and each 3×3 grid (nonet). As in Kakuro, groups of cells (cages) add to given sums, and within each cage the digits must be distinct.

These cages are made up of cells that share a common edge, but (unlike Kakuro) the cages need not be strictly horizontal or vertical. The cages can be grouped by color, as in the example below, or with dotted lines.

As the example above (from Wikipedia) shows, it is possible to have a game of Killer Sudoku in which no numbers are given initially. For example, the two yellow cells in the upper left add to 3 and so must be a 1 and 2 in some order; likewise, the two green cells in the top of the 7th column add to 4, and so must be a 1 and 3 in some order. But now, still looking at those two green cells, we already know that there are a 1 and 2 in the top row (from the yellow cells), so the top green cell must have the 3 and the one below it the 1. The puzzle can be solved by continuing in this manner.

So who invented these puzzles? According to this article in The Times (and its correction here), the first Killer Sudoku puzzles were created several years ago by Miyuki Misawa. She has a website of puzzles and hints here (translated into English) and a blog (in Japanese) that appears to be updated frequently.

If Killer Sudoku strikes your fancy, you can find daily puzzles here or here. And if that doesn’t stretch your mind enough, there are a tremendous number of other Sudoku variations in this article of Math Games by Ed Pegg, Jr. Happy Solving!