# The Beauty of Logic (and Sudoku Puzzles)

There are currently two distinct groups reading these words. The first group is those who are nodding their heads in agreement with the “beauty of logic” sentiment in the title and saying, “Yes, logic does have a certain beauty and precision.” The other group are non-math people who are wondering what in the world I could be referring to, while shaking their heads and thinking, “She has really gone off the deep end this time — logic is just painful and confusing!”

By “the beauty of logic,” I mean that there is always a right answer and a wrong answer in logical situations. You know where you stand with logic. Numbers, for example, are logical concepts with finite definitions: two always means exactly two; two never means three; two never means purple. Word meanings can become fuzzy and illogical, especially in the English language, where a word such as love can mean things as diverse as: 1) a deep emotional attachment [love my husband]; 2) nothing, such as a score of zero in a tennis game [two-love]; or 3) an intense desire for or appreciation of something [love this pizza; love that song].

I had tried to share my appreciation of math and logic with my children, but my young son’s distaste of anything math-related kept him from developing a similar emotion. Until now. The summer of his pre-calculus course revealed to him his true abilities in math, but his current semester of university math is opening the door to fun math and logic. And dragging him in. As a computer science major, he is taking a class with the tongue-twisting name of Combinatorics — an exploration of math as arrangements and patterns of numbers. That professor recently assigned some math puzzles of a sort that I have been doing for a long time just for fun. (Yes, I am a sick, sick person, and I do need to get out more often.) It seems that a large portion of the world is discovering these puzzles (now called “Sudoku”), as newspapers are adding them to their daily fare of crosswords and “Jumble” word puzzles.

My son was home for a weekend recently and inquired about these puzzles. He knew they were included in his upcoming assignments and wanted some inside information on how to solve them. Sudoku puzzles consist of a 9 x 9 grid in which the digits 1-9 are entered into each row, column, and 3×3-grid portion so that the digits do not repeat. Enter the Beauty of Logic concept. Logic dictates that the puzzles can be solved through systematic strategies, not merely through trial-and-error guessing. As I explained a few tips to my son for solving the puzzles, his admittedly-non-math-person girlfriend became interested and asked for a sample puzzle to try. When I headed to the computer to print some, my husband called after me, “Print one for me, too.” Our evenings since then have been consumed with clipboards, pencils, erasers, and puzzles as we compare notes on solving strategies and progress to higher difficulty levels.

Finding the one correct digit for any square of the puzzle should be done through a process of elimination: these could work, but those cannot work, so this one must work. I cannot arbitrarily decide that a three would look nice in this spot or that I have not used any fives lately, so I should give a five the opportunity to participate in this corner. The best digit for completing a row is not a matter for discussion: when the other eight digits have already been used, there can be only one possible choice for the final digit. The rules of the game specify that each of the digits must be used only once in each subsection. Therefore, if a digit appears twice, I must assume it is a mistake to be corrected, not something to be tolerated as an alternative solution. If you and I work at solving identical puzzles, our solutions should also be identical — if they do not match, we cannot both be right.

That is what I see as The Beauty of Logic: there are distinct strategies that can be employed to arrive at the correct answer; we do not have to stumble blindly, depending on guesswork and instincts to succeed. There can be many wrong answers, but there is one correct answer. Logic is not a matter of interpretation, nor is it different things to different people. A wrong answer is not open to debate. Incorrect answers must be changed, not tolerated or lauded as “diversity.” If only the rest of life could be so simple.