How can I Design a Sudoku Puzzle Within Minutes?
Whether you are recovering in the hospital or you are traveling, designing a number puzzle game – Sudoku – would be a perfect brain workout for you! Grab a piece of paper, draw a nine by nine grid, and design a Sudoku puzzle in minutes!
But wait… How can I design a Sudoku puzzle in minutes, i.e., design a Sudoku puzzle with some squares that are pre-filled in a given nine by nine grid, and this Sudoku has one and exactly one solution?
All I can think of is a straightforward method as follows:
1. Start with a blank nine by nine grid.
2. Choose some squares that will be filled with numbers.
3. Fill numbers into the chosen squares carefully to make sure there is no violation of constraints. (You may need to try many times if you did not succeed at the first temptation).
4. Check this designed Sudoku to see whether it has one and at least one solution. If it is, then we made it; otherwise go back to Step 3 or Step 2.
Shortcoming: The possibility that you made a Sudoku using this straightforward method is low (as low as the probability of winning a lottery). Even step 3 may include many tries. After you tried for ten times, you may want to give up.
To avoid the shortcoming, we can design a Sudoku in the exact REVERSE WAY of solving a Sudoku.
First, we get a nine by nine grid with every row, column, or 3×3 mini-box pre-filled with numbers 1-9.
Second, we remove digits from a pair of symmetrical squares (around the center square) if it is a safe removal. If there exists a path to infer these removed digits, we call it a safe removal.
Repeat the second step until no more digits can be safely removed from a pair of symmetrical squares.
For the first step, we may recycle a solved Sudoku (i.e., a fully filled Sudoku), or we can use a shortcut, which is extensively explained in the Create Classic Sudoku book available on Amazon.com. The shortcut uses group filling plus circular shift methods. For the second step, it is a gradual step by safely removing digits from the grid and guaranteeing it has one and exactly one solution.
A very easy Sudoku can be created using this innovative method in minutes.