The New Sudoku Players' Forum

[dobrichev]

In How Many Clues To Give? A Bilevel Formulation For The Minimum Sudoku Clue Problem article from May 2023, among others, I found this conjecture

We observed no unavoidable sets of size 5 and 7, which leads us to conjecture that none exist for any instance.

[Serg]

Hi, Mladen!
What do you mean? Nonexistance of U5 and U7 UAs is well known.

Serg

[champagne]

Hi Mladen and Serg,

Agreed, the term of "conjecture" is not correct.
The first Ua with and odd number of clues is an UA size 9.
Easy to spot, with 3 digits in a box, a row and a column
In the list of templates of Gary Mc Guire, we have "nearly" all UAs size <=12. We have here all templates for 9 clues.

[dobrichev]

The non-existence of U5 and U7 UA is well known to many of us, but not to the authors who claim expertise in this area.

Reading the references section you will find that this work is Bachelor’s Thesis from 2022 of one of the authors.

If one takes 5 minutes to look at a few U4s and U6s, he will understand the impossibility of realizing a U5.