Do there exist sudoku's with clues that only contain $1$'s and $2$'s

Question

I read this article saying it was mathematically proven that if a sudoku has a unique solution, then it has at least $17$ initial hints.

In which case, is it possible to have a sudoku with $17$ initial hints that consist of nine $1$'s and eight $2$'s (of course the $1$'s and $2$'s are chosen arbitrarily, I could have said $5$'s and $3$'s)?

This was just a small thought I had. Apologies if the answer is obvious in any case. Is there any examples, or, if not, reasons as to why we can't have this.

Answer 1

A sudoku with a unique solution has to have at least eight distinct numbers amongst its initial clues. If it were missing two, say $8$ and $9$, then if we had a valid solution, then swapping all $8$s and $9$s therein would give a second valid solution,