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How to Solve Very Hard Sudoku Puzzles

Sudoku puzzles consist of blocks of nine numbers.
Sudoku image by Claude Wangen from Fotolia.com

Sudoku is a logic puzzle that involves plugging numbers into blocks in a grid system in order to fill every empty spot without repeating numbers. Though the puzzle originated in China, the name, “su,” which means number, and “doku,“ or single, as well as many of the modern rules, hail from Japan. While math is not involved in Sudoku, a handful of strategies can help puzzle aficionados solve puzzles. For the difficult puzzles, players can use multiple techniques that build upon each other to maximize problem solving.

Single Possibility Technique

Identify rows that have all but one block filled in.

Enter the only available number, eliminating it as a possibility for other blocks and rows.

Move on to the next section with the fewest possibilities and enter in those numbers.

Repeat this process until all the single possibility blocks blocks are filled in.

Check work. Go row by row and block by block, making sure numbers aren’t duplicated. Then move on to the sub-group exclusion technique.

Sub-Group Exclusion Technique

Write all the possible answers in small print along the edges of the empty blocks. Alternatively, players can create a grid for larger puzzles. Assign rows letter and numbers, and write out the possibilities of each box with its corresponding letter and number combination. For example, if the grid is 9 groups of nine boxes, assign the top rows letters “A” through “I” and the across rows numbers one through nine. If box A3 could be either six or seven, record that on a sheet of paper. If the number seven appears elsewhere in the set of boxes, mark it out, leaving number six the only possibility.

Cross reference potential answers in each row to see if they exist in the corresponding three by three blocks. Eliminate potential answers as you find them in the block groupings.

Check your work when all the boxes are filled in. Then move on to the naked pairs technique.

Naked Pairs Technique

Look for boxes with the same possible numbers in each row and set of blocks. If boxes A1 and A6 both have the numbers three and four as a possible answer, then three and four cannot be a potential answer for any other box, and can be eliminated.

Repeat this process. Eliminating potential answers reveals the correct answers, and the more you eliminate, the more correct answers will appear. Eventually, all the blocks will be filled in.

Check your work.

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