This puzzle started life as a theoretical exploration. I had considered setting puzzles where one of the clues is not given to the solver, and the solver must deduce the unique clue that could be placed in a particular position that would subsequently lead to a uniquely-solvable puzzle, and then solve the puzzle. Thankfully that idea has been abandoned, but it did lead to the following question: what's the largest set of values that, when placed in a particular cell of a Sudoku, each lead to a uniquely-solvable puzzle?
This puzzle proves that at least 7 is possible. I think that all of the resulting Sudokus are actually pretty nice to solve!
Rules
Before starting the puzzle, choose a number from 1 to 7 and place it into the central cell of the grid. Then solve the puzzle as a classic Sudoku: place a number from 1 to 9 into each empty cell so that every row, column, and bold-outlined region contains every number exactly once.
Difficulty: ?/10
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