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What is the fewest number of clues on a rotationally symmetrical sudoku grid with a unique solution?

Puzzling Asked on June 6, 2021

It is known that the minimum number of clues a sudoku must have to have a unique solution is 17. But on every website I’ve seen for them, I haven’t found any that are rotationally symmetrical.

I once saw a puzzle in a book which only had 19 clues and was rotationally symmetrical, but I don’t remember whether the solver I ran it through said that there was a unique solution or not. My question is, what is the minimum number of already-filled-in squares that a rotationally symmetrical Sudoku must have in order to have a unique solution?

Note: by rotationally symmetrical, I’m referring to it in the standard sense that if a clue appears in one position, a clue will also appear in the position opposite it on the board.

One Answer

This book appears to have a puzzle with only 18 clues that is rotationally symmetrical.

7 2 . | . . . | . . .
. 5 . | . . 9 | . . .
. . . | . 3 8 | . . .
------+-------+-------
. . . | 4 . . | 5 . .
. . 3 | . . . | 9 . .
. . 1 | . . 3 | . . .
------+-------+-------
. . . | 2 5 . | . . .
. . . | 6 . . | . 3 .
. . . | . . . | . 1 9

But I still don't know if a rotationally symmetrical 17 exists.

Answered by user88 on June 6, 2021

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