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Sunday, July 24, 2005

Two wonderful mathematical puzzles

I’ve recently been stretching my skills with two new mathematical puzzles, Sudoku and Planarity.

Thanks to the Boston Globe and other papers, Sudoku has now become quite popular. Although the Sudoku page claims that it’s non-mathematical, these puzzles actually involve both mathematical logic and proof by contradiction. They also invite at least two different ways of thinking: either “Where does the 7 go?” or “Which numbers could fit in this cell?” I think the reason that these puzzles are deemed non-mathematical is that the numbers are used purely as glyphs, not for their numeric values; what the page really means is that the puzzles are non-arithmetic. If you haven’t tried sudoku yet, just go to the new Sidekick section in any daily edition of the Globe. It’s my theory, supported by a couple of weeks of data but not confirmed, that the Globe’s sudoku sequence follows Will Shortz’s system for the New York Times daily crossword puzzles: start with an easy one on Monday, then get harder and harder each day until Saturday, which features the most difficult puzzle of the week. Give it a try any day, but maybe you should start with a Monday.

Planarity is a graph theory puzzle. Great for honing those spatial skills as well as mathematical reasoning skills. Unfortunately the point system is time-dependent, so you’re penalized for stopping and thinking (unless you adroitly use the Pause button), but it’s still a wonderful puzzle and well worth trying. Your scores are remembered between sessions, so you can start wherever you left off.

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