## Making 17 clues

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

### Making 17 clues

Studing the Gordon file I found somes rules that I submit to the autors o 17 clues

Beware the rules does't give valid solutions they eliminate bad
The grid must respect the rules but a grid respecting the rules is not necessary a valid sudoku.
I get the rules only with observations not with math computing so they can be bad!

If you have other technics of if a rule is bad said it
The rules are ONLY for 17 clies!!!!

A Box2 is a box with two clues
2 Row4 are 2 rows with each 4 clues
2 Digit4 means that you have two digits present 4 times
A set is a row, a column or a box of 9 cells.
A empty set is a row, column or box with no clue

1-You cannot have four empty row or col.
2-There only one combination with 3-2 empty rows cols.
3-Maximum 2 empty box
4-2 Empty boxes are exceptional but possible
5-If you have two empty boxes you cannot have empty row or col
6-The maximum of clues for a row, a column or a box is 5
7-You never have the maximum of two set at the same time.
8- If you have 5 clues in a box you can have only one empty box
9- If you don’t have a box with only one clues You have 1 or two empty box
10- If you don’t have a box with only one clues Dont have box with 4 or 5 clues
11- You can have only two boxes with 4 clues
12- If you have a Box4 you cannot have 5 boxes
13- If you have two 4 boxes you have at less 2 box2
14- If you have only 1 Box1 and no empty box the 8 other boxes are 8 box2
15- Maxi 4 box3
16- You never have the same digit 5 times
17- You don’t have more than 2 digit4
18- You have 5 digit1 you have 3 digit3
19- 18 is the only problem where you don’t have Digit2
20- You always have at 8 or 9 differents digits (Only 7 differents digit is ompossible)

Papy
It's the fordt set of rules I found others but I prefer to verify them
Have a lot of fun
Papy

Posts: 131
Joined: 15 August 2006

### Re: Making 17 clues

Papy wrote:Studing the Gordon file I found somes rules that I submit to the authors of 17 clues ...

Some of your observations can possibly condensed into the probability of a clue appearing in a given cell of Gordon's set:

Code: Select all
 0.369 0.328 0.199 0.372 0.315 0.191 0.344 0.302 0.198 0.292 0.245 0.133 0.294 0.227 0.137 0.278 0.238 0.142 0.151 0.117 0.037 0.152 0.101 0.041 0.127 0.095 0.033 0.418 0.307 0.182 0.425 0.319 0.199 0.383 0.323 0.199 0.324 0.232 0.118 0.316 0.229 0.121 0.292 0.231 0.128 0.207 0.125 0.049 0.199 0.126 0.048 0.153 0.119 0.048 0.400 0.287 0.164 0.409 0.295 0.179 0.400 0.306 0.181 0.334 0.231 0.121 0.333 0.232 0.124 0.298 0.225 0.118 0.214 0.130 0.048 0.217 0.121 0.043 0.162 0.106 0.042sum = 17.000

Note the big discrepancies in the values depending on position within a box.

I haven't found any way to use this to generate a 17-clue puzzle, but applying it to guide one of my generators it was possible to produce, for instance:

Code: Select all
  .  6  4  9  .  5  .  .  8  8  .  .  .  .  .  5  9  .  3  .  .  .  .  .  .  .  .  9  .  .  8  7  .  .  5  .  .  .  .  .  4  .  .  .  .  6  .  .  .  .  .  7  .  3  .  5  .  .  2  .  4  .  .  .  3  .  7  .  .  9  .  .  .  .  .  6  .  .  .  .  .

which Sudoku Explainer rates at 8.4. Note that there are 4 entries in top left-hand box corners, but only 1 in lower right-hand corners.

Regards,

Mike Metcalf

m_b_metcalf
2017 Supporter

Posts: 8983
Joined: 15 May 2006
Location: Berlin

### Global approch

Hi,
I beleive (not sure) that the repartition like you shows it is not a good way
Why? Bexause of isomorphs. If you take all the gordon sudoku
If we only flip your resulte rthe cell7 become the 79 and the numbre pass from 43 to 191

make a morph on each probleme and compute the repartition I'm not sure that you get the same...
Equal for the digit!s
But surrely there is a link some where!!!
Perhaps the repartition of the clues on a specific grid but I dont found how the compute this repartition
A strange things:

You take theGordon files and you compute the number of clue of each block (for example the tree horizonta) 1+27 28-54 55-81
You only have 20 combinatiuons for t he 36000 problems
Strange no?

Papy
Papy

Posts: 131
Joined: 15 August 2006

Papy wrote:You only have 20 combinations for the 36000 problems
Strange no?

Gordon has canonicalized all the puzzles in his collection to prevent duplicate mathematically equivalent puzzles.

This may be the reason that the placement of the 17 clues is not as random as you might expect.

Ruud
Ruud

Posts: 664
Joined: 28 October 2005

### Gordon

I expect nothing!!!

Just It seams strange that starting with 36000 we arrive to 20!!!
In fact you have 17 clues in 3 blocks so you have 17*16*15=4080
Possibilities (Perhaps I make e mistake?)
With 4080 it's strange to have only 20 possobiltyies used! Why 20 not 16,32,18,27 ????

The unique use is if your grid doesn't have one of the 20 combinaison the
But is the combinaison is good the grid is not necessary goos!

Papy
Papy

Posts: 131
Joined: 15 August 2006

Ruud wrote:.... canonicalized ....

I prefer "canonized".

Bill Smythe
Smythe Dakota

Posts: 543
Joined: 11 February 2006

Smythe Dakota wrote:
Ruud wrote:.... canonicalized ....
I prefer "canonized".
Are canonical representatives particularly saintly where you come from, Bill?

\begin{troll}The correct word is clearly "canonicalised".\end{troll}
(Actually Wikipedia is with Ruud on this one.)
Red Ed

Posts: 633
Joined: 06 June 2005