Sudoku is a puzzle of pure logic based on a single premise -- that each digit 1-9 must appear once, and only once, in each row, column, and 3X3 box. Puzzles are constructed by placing certain numbers in certain squares as clues to the solution, and the number and placement of the starting numbers determines the level of difficulty of the puzzle. Ideally, sudokus are constructed in such a way that there is only one solution and no guessing is required. Assuming that these two conditions are both true, as they have been for every sudoku posted on www.doublecrostic.com, the best approach to solving a sudoku is to look for answers requiring the least amount of reasoning and then progress to deeper levels of reasoning as necessary.
Here are some examples of how to reason out answers starting with the simplest level of reasoning and progressing to deeper levels in the later examples.
The number 1 must be filled into the top center square of the top center 3X3 box because it cannot occupy any other square in the box without appearing twice in one row. Another way of looking at this example is that the number 1 cannot appear in any other square in the top row without appearing twice in a 3X3 box.
The number 1 must be filled into the top right square of the top left 3X3 box because the number 1 must be filled into one of the two empty second-row squares in the top center box and it cannot be filled into the top center square without appearing twice in one column. Another way of looking at this example is that the number 1 cannot be filled in anywhere in the top row of the top right 3X3 box since it is already filled into that box in a different row, and it also cannot be filled into the top center square of the top left box since it already appears in column 2.
The number 1 must be filled into the top center square of the top right 3X3 box because this square
must contain either 1, 3, 6, or 7 (since 2, 4, 5, 8, and 9 already appear in the top row) and
3, 6, and 7 already appear in the 8th column.
This one takes a bit of explaining, so bear with me. Look at the center 3X3 box. 2 and 5 must be filled into the top right and bottom right squares (though not necessarily in those positions) because they cannot be filled into the left column or the center row of this box. Therefore, 3 must be filled into either the center or center right square of this box since it cannot be filled in anywhere in the left column of that box. The center right square of the center right box must contain 1, 3, 4, 7, or 9 since 2, 5, 6, and 8 are already filled into the 5th row; but since 3 must be filled into the middle row of the center box, it cannot also be filled into the center right square of the center right box. Since 1 is already filled into the center right box and 4 & 9 are already filled into the 9th column, the center right square of the center right box must be 7. Whew!
The majority of sudokus that appear on www.doublecrostic.com can be solved using the levels of reasoning in examples 1 & 2 (although occasionally Sue will spring a real tough one!). For sudokus that consistently require the use of deeper reasoning, try the "fiendish" sudokus on the London Times web site (http://www.timesonline.co.uk/section/0,,18209,00.html)
1. DON'T OVER-ANALYZE. As these examples illustrate, there are often several ways of arriving at an answer for any given square; but it only takes one. The better you get at solving sudokus, the less you will feel the need to "double-check" your answers.
2. When starting out, go through each number 1-9 and fill in as many of each number as you can using simpler reasoning. Then go back through each number (if you haven't already eliminated it) again using simpler reasoning and try to eliminate each number. Unless the puzzle is one of Sue's surprises, you will probably be able to complete at least 1/2 and possibly as much as 2/3 of the solution just by going through the 9 digits twice. (By the way, those puzzles are surprises to Sue as well as to everyone else.)
* If a number is initially filled in only once or not at all, don't bother trying to find answers for that number using simpler reasoning. Get back to it when more of the puzzle is filled in.
3. ANSWERS lead to OTHER ANSWERS. This may seem like an obvious point; but if, for example, you are able to fill in a 1 in the bottom left 3X3 box, the next answer to look for is another 1 in a nearby row, column, or box. This is especially true when a number is initially filled in only once or not at all -- once the first or second occurrence of that number is found, others usually follow.
4. It is ALMOST ALWAYS faster to try to eliminate numbers than to try to figure out which answers are remaining in a row, column, or box; i.e., if a 3X3 box has one empty square left, going through the other eight answers in the box (even aided by Sue's nifty color scheme) is likely to take much longer than just going through the numbers 1-9 and filling them in using simpler reasoning.
5. If it becomes necessary to get into deeper reasoning to find an answer or two, try to get back to simpler reasoning as soon as possible to solve the rest of the puzzle. The more answers you are able to fill in, the less likely you are to need deeper reasoning to fill in the rest of them; and even the most difficult sudokus seldom have more than a few answers that require deeper reasoning.
6. Practice, practice, practice. If possible, practice on puzzles that are more difficult than the ones on this site (see London Times link above). The more proficient you get at solving difficult puzzles, the better you will be able to solve easier puzzles quickly.
Any comments or suggestions (from any interested solvers) would be welcome.