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.

Do not confuse having at least one solution with having a unique solution. — JMoravitz, May 29 '20 at 16:12

score 4 · Accepted Answer · answered May 29 '20 at 16:11

4

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,

answered May 29 '20 at 16:11

Angina Seng

158,341

Brilliant, thank you! – kam May 29 '20 at 16:12

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

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