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I wonder if there are proper $9\times9$ Sudokus having $7$ or less different clues. I know that $17$ is the minimum number of clues. In most Sudokus there are $1$ to $4$ clues of every number. Sometimes I found a Sudoku with only $8$ different clues.

In this example the number $9$ is missing, but the Sudoku was very well solvable. Is it possible to have a $9\times9$ Sudoku with less than $8$ different clues?

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Have you seen Mathematicians Solve Minimum Sudoku Problem ? – Peter Phipps Mar 18 '14 at 12:25
must resist urge to solve sudoku... – ratchet freak Mar 18 '14 at 14:50

If I understand you correctly the answer is no. If the only numbers in the initial grid are $1,2,3,4,5,6,7$ then in any solution you will be able to swap $8$ and $9$ and you will still have a valid solution.

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In case of any confusion, it should also be said that it is a stated rule of Sudoku that puzzles have a single, unique solution. – ColinK Mar 18 '14 at 16:42
We need more concise but informative proofs like this one. – Anonymous Pi Mar 18 '14 at 17:54
@AnonymousPi That would be lovely but many interesting problems don't admit such proofs: "Everything should be made as simple as possible, but not simpler." (attributed to Einstein) – TooTone Mar 19 '14 at 1:15

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