Solving Suduko

Suduko is a spatial and logic puzzle. Numbers 1 to 9 are scattered in 81 spaces with nine blocks of nine spaces marked by darker borders or shading. Letters or other symbols could be substituted for numbers without changing any of the concepts of the puzzle. The objective is to fill each block with the numbers 1 to 9. In doing so, each row and column of the puzzle must contain the numbers 1 to 9.

A word about difficulty: Suduko puzzle providers rank puzzles from easy to hard. The number of filled spaces, ranging from about 40 to 24, determines the difficulty—the fewer the filled spaces, the more difficult the puzzle. The position of numbers has some effect on difficulty. The label, however, may have no relationship to difficulty. I offer these two puzzles, both marked, "Moderate."

 

Solution Techniques

There are lots of suggstions and techniques available online for solving suduko puzzles. In my humble opinion, they miss an essential characteristics of the puzzle. A suduko puzzle is basically a spatial problem that requires no math and little logic. Solving any suduko puzzle requires working in two dimensions to find what is missing in the blank spaces. Therefore, the most powerful tool to solve the puzzle is what I have chosen to call, "triangulation." As puzzles become more difficult, triangulation gives way to other techniques that do require logic but I always come back to triangulation whenever I discover any missing number.

Here are the techniques that I use to solve suduko puzzles:

• Triangulation—using the position of one or more of each number to determine the position of the same number. This addresses the spatial aspects of the puzzle;
• Elimination—using several numbers to determine the position of one or more of them. This addresses the logical aspects of the puzzle;
• The Magic of Pairs, Part 1—using the possible position of numbers to determine other numbers. This preserves information you discover and is used in combination with triangulation and elimination;
• The Magic of Pairs, Part 2—pairs of numbers, i.e., two numbers which appear together in two spaces in a row, column or box; and
• Cornered Pairs—pairs of numbers which appear in the corners of a rectangle within the puzzle.

Paper vs. Computer

In discussing techniques, I refer to penciling in preliminary numbers, two or more numbers in a single space that you are sure belong there but aren't sure which one is correct. In difficult puzzles, this can be complicated and burdensome with lots of penciling and erasing. It makes a mess of paper. I prefer doing sudoku puzzles on my computer, table or smart phone where the computer does the grunt work of penciling and erasing. My favorite app is Sudoku Fun from Smoote Mobile

The Killer Error

A common mistake is to put a number in a row, column, or block that already contains the same number. It sounds like a stupid mistake. It is. I make it all the time.