## Proof of Minimum Clue >= 17

Everything about Sudoku that doesn't fit in one of the other sections
Smythe Dakota wrote:1. Do all bases for the same (solved) puzzle have the same number of clues?
No, they don't.

2. For which integers n (n=0 through n=81) do there exist at least one puzzle/basis where the basis has size n?
At the time of writing, the max known is n=32.
Red Ed

Posts: 633
Joined: 06 June 2005

Smythe Dakota wrote:Define a set of clues as a "basis" if (1) it generates a unique solution, and (2) no proper subset of it generates a unique solution.

this is a definition for "minimal puzzle"
gsf
2014 Supporter

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Joined: 21 September 2005
Location: NJ USA

gsf wrote:.... this is a definition for "minimal puzzle"

OK. Rather than searching this entire forum for existing concepts (I just found this forum two days ago), I guess I am re-inventing the wheel here and there. "Basis" is in line with what I (and many others) know about vector spaces.

Bill Smythe
Smythe Dakota

Posts: 546
Joined: 11 February 2006

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`.xx...... x.x...... xx....... ....x.... ...x.x... ....x.... .......xx ......x.x ......xx. `

Whaaaat? oh, I suhpous so, it's right? Right? RiGhT? RIGHT???!!!???
Yah, That's right, for a second I thought
Code: Select all
`..xx...... x.x...... xx....... ....xx.......x.x... ....x.... .......xx .....xx.. ......xx. `
deam3r

Posts: 10
Joined: 12 February 2006

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