Chapter 1.2, Problem 31PS

HISTORICAL QUEST Magic squares remind us of Sudoku number puzzles. Sudoku (or su doku) is a number puzzle, usually consisting of a $9\times 9$ grid divided into nine $3\times 3$ boxes, into which numbers already appear in a few cells. You may have seen such a puzzle online or in your newspaper, but would you believe that Sudoku was invented by a 74-year-old Indianapolis man who never received credit for his invention of this type of puzzle problem? In May 1979, a puzzle created by Howard Gams was published, but few paid attention.* Then, in April 1984, Japan's puzzle group Nikoli discovered Garns's puzzle, invented the word Sudoku—(Su = number, Doku = single)—trademarked the name, and published new versions of the puzzle. At that time, and with this new name, the puzzle became a worldwide phenomenon. The object of the puzzle is to complete all the remaining cells with the numbers from 1 to 9, so that:

• each row contains all the numbers from 1 to 9

• each column contains all the numbers from 1 to 9

• each $3\times 3$ box contains all the numbers from 1 to 9

Complete the Sudoku puzzles in Problems 31-32.