18
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Ahem, let's formalize your task...

A Sudoku is a puzzle consisting of a grid to be filled with symbols, such that each constraining unit contains each symbol exactly once. The regular Sudoku is a $9 \times 9$ square to be filled with the numbers $1$ to $9$, where the constraining units are rows, columns, and $3 \times 3$ blocks.

Irregular Sudoku is similar to regular Sudoku but the $3 \times 3$ blocks constraints are changed to $9$ nonominoes (polyominos with a size of $9$). Rows and columns constraints still apply.

Some numbers are initially given in the grid. Those numbers are called clues. A valid Sudoku grid must have exactly one solution.

Contrast to the answers here: Why is this considered to be “The World's Hardest Sudoku”?, we define our own hardness level. A Sudoku is harder if the number of clues in its grid is lesser. That means, the world's hardest irregular Sudoku is defined as the irregular Sudoku with the least number of clues.

Simple, your task is to create the world's hardest irregular Sudoku! (And prove it!)

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The 'hardest' possible Irregular Sudoku has

just 8 clues!

and it looks like this:

enter image description here

You can fill in the 9 in the top row, then use the logic from this answer by hexomino to show that the answer is unique.

And this is the maximum because if you had less clues, at least two numbers would be missing -- in any solution, you could just interchange those two numbers!

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  • $\begingroup$ Amazing, this is correct, well done! My construction is using the same layout, but the numbers are given in the first column instead of the first row, :) $\endgroup$ – athin Feb 15 at 1:27
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    $\begingroup$ Given the structured pattern, is it really the "hardest"? $\endgroup$ – Earlien Feb 15 at 7:17
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    $\begingroup$ @Earlien No, not according to the usual meaning of the word - that's why I put the word "hardest" in quotes. But that's how the word "hard" is being defined for this question. $\endgroup$ – Deusovi Feb 15 at 7:45
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    $\begingroup$ I thought this looked familiar. $\endgroup$ – hexomino Feb 15 at 11:45

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