## Sparsest trivial 3x3 soduku?

Everything about Sudoku that doesn't fit in one of the other sections

### Sparsest trivial 3x3 soduku?

Greetings!

Today's completely pointless question:

For the purpose of this discussion, a "trivial" sudoku is one whose initial configuration leaves at least one cell with a single candidate, and filling in all initial single candidate cells eliminates other candidates so that other single-candidate cells are left, repeating the process until the puzzle is solved.

What is the minimum number of initialized cells needed to create a trivial 3x3 sudoku?

RobR
RobR

Posts: 6
Joined: 24 September 2005

Sorry do you mean a 3X3 with only 9 squares or a standard one with 81

if the later try the "minumum number of clues thred"
http://forum.enjoysudoku.com/viewtopic.php?t=605&highlight=maths

if the earlie then i don't think this is feasible as there is no wayt of applying stardard rules.

Unless it was a latin square
Pi

Posts: 389
Joined: 27 May 2005

I mean an 81-square grid.

The thread you refered me to discusses solvable sudokus. The 17-square sample presented is certainly not trivial. I'm curious about the minimum number for a trivial sudoku.

RobR
RobR

Posts: 6
Joined: 24 September 2005

### Re: Sparsest trivial 3x3 soduku?

RobR wrote:For the purpose of this discussion, a "trivial" sudoku is one whose initial configuration leaves at least one cell with a single candidate, and filling in all initial single candidate cells eliminates other candidates so that other single-candidate cells are left, repeating the process until the puzzle is solved.

This would depend on what rules you allow for eliminating candidates.
One can eliminate all candidates but one from *any* cell in *any* sudoku puzzle by repeated brute force.

Anyway, I assume you mean using only the simplest deductive rules. Even in that case I bet there is a puzzle with 17 clues.
Moschopulus

Posts: 256
Joined: 16 July 2005

I asume by trivial you mean one that requires only Hidden and Naked Singles

And an easy one at that
Pi

Posts: 389
Joined: 27 May 2005

Is This trivial Enough for you

It got a particularly low rating from my program

Code: Select all
`|3--|--6|9-1||--4|-17|3--||62-|--9|-5-||582|-3-|---||-1-|8-5|-7-||---|-6-|548||-5-|9--|-26|--3|24-|1--||2-9|6--|--7|This is the Times easy no 395`
Pi

Posts: 389
Joined: 27 May 2005

### Re: Sparsest trivial 3x3 soduku?

RobR wrote:For the purpose of this discussion, a "trivial" sudoku is one whose initial configuration leaves at least one cell with a single candidate, and filling in all initial single candidate cells eliminates other candidates so that other single-candidate cells are left, repeating the process until the puzzle is solved.

Or in traditional sudoku lingo, a trivial puzzle requires only naked singles.

My guess would be somewhere in the region of 25 clues.
Lardarse

Posts: 106
Joined: 01 July 2005

There was a fiendish in the Times awhile ago that required only naked singles. Something must have made it fiendish, maybe it was that it was rather sparse. There's a topic about it in The Times forum ("Easiest fiendsih yet?"). Might be a good place to start.
PaulIQ164

Posts: 533
Joined: 16 July 2005

I ran the puzzle paul is talking about through my progrma and it did come out as a more difficult puzzle, mainly because there were never many boxes that could be filled in, only a few at a time. it was actully quite difficult dispite being trivial.

I think that it is actually eaier to spot hidden singles than naked ones, especially ones within boxes rather than rows and colums
Pi

Posts: 389
Joined: 27 May 2005

minimal such puzzles have in average 1-2 more clues than normal minimal sudokus.
So, I guess the minimum is 18 or 19.
I found four with 22 after 1000 random trials:

...4..8....9..2...8.5..3..4491....2.....6.57.....9..4......53....8.....2....1....
..67...8.....13.....9.6.......2....1.5......9..4.....35.....67..28.......3.8.9.4.
61......4......9.2.37............14.....7......23.67...5.4.....14....35...69.....
.6.4..73.1.7.......2.......5....2..88...7.9.2...31................5...49...1.6.7.
dukuso

Posts: 479
Joined: 25 June 2005

Pi wrote:I think that it is actually eaier to spot hidden singles than naked ones, especially ones within boxes rather than rows and colums

I agree completely with this.
PaulIQ164

Posts: 533
Joined: 16 July 2005

18 clues:

Code: Select all
`.1....6.....3...7....7.....7..43...8..5...1........2..8......4.....62......51....`
dukuso

Posts: 479
Joined: 25 June 2005

That puzzle is solvable usiong only the simplest tactics yes, however i wouldn't describe it as trivial as it has a similar rating in my program to a Papocom medium
Pi

Posts: 389
Joined: 27 May 2005

Posted by Ruud on the other forum
Code: Select all
`. . .|. . .|. 1 2. . .|. 3 5|. . .. . .|6 . .|. 7 .-----+-----+-----7 . .|. . .|3 . .. . .|4 . .|8 . .1 . .|. . .|. . .-----+-----+-----. . .|1 2 .|. . .. 8 .|. . .|. 4 .. 5 .|. . .|6 . .`

If that's not easy enough I still bet there is a 17 clue puzzle that is completely and utterly trivial.
Moschopulus

Posts: 256
Joined: 16 July 2005

Posted by Gfoyle a long long time ago:

Code: Select all
`. . . . 6 . . 3 .. . . 8 . . 2 . .2 . . 5 . . . . .. . . 2 9 . 5 . .. 7 6 . . . . . .. . . . . . 1 . .. . . . . 7 . 6 45 . . . . . . . .. . . . . . . 7 .`

It's the unique layout with 5 singleton and 4 triple appearing clues, yet very straight forward to solve...
udosuk

Posts: 2698
Joined: 17 July 2005

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