Yesterday, I tried to solve a regular Sudoku puzzle. Of course, the Sudoku puzzle had a unique solution. But, I was feeling a little lazy, so, rather than solve the puzzle properly, I made guesses! At every step, I put a random number in one of the empty cells, as long as it didn't contradict any rules!
Feeling lucky, I decided to continue solving the puzzle in that way. So far so good: I hadn't found any contradictions yet! The puzzle was almost complete; I grinned...
And yes... as you could have guessed... the final empty cell... I just couldn't put any number! Every other number followed the rules, yet, in this single cell, any number I put would break the rules of Sudoku!
Thus, I decided to leave this puzzle... Until today! This morning, I saw the solution for yesterday's Sudoku puzzle. And I was badly shocked. If I compare my (incorrect) solution to this, every number I put is wrong! I felt that bad karma happened to me.
Question: Do you believe my story?
- If yes, could you construct an example of what puzzle I was working on? What were my guesses and what was the intended solution?
Bonus: Could you construct such a puzzle with the minimum number of initial given clues as possible?
- If no, could you prove that I was wrong?
Bonus: What is the minimum number of empty cells in the end such that every other cell follows the rules but any number we put in any empty cells will break the rules?
This is a fictional story btw if you are curious...