This discussion on semantic is interesting, but...

Can anybody help to find a puzzle with 23 clues ?

Suggested patterns :

23 clues, one empty group :

- Code: Select all
` x . . | . x . | x . x`

. . x | . . . | . . .

x . . | . x . | x . x

-------+-------+-------

. . x | . . . | . . .

x . . | . x . | x . x

. . x | . . . | . . .

-------+-------+-------

x . . | . x . | x . x

. . . | . . . | . . .

. x . | x . x | . x .

23 clues, two empty groups :

- Code: Select all
` x . x | . . . | x . x`

. . . | . x . | . . .

x . x | . . . | x . x

-------+-------+-------

. . . | . x . | . . .

x . x | . . . | x . x

. . . | . . . | . . .

-------+-------+-------

. x . | x . x | . x .

. . . | . . . | . . .

x . x | . x . | x . x

Thanks.

JPF

PS : about semantic...

Let G be the set of cells of the grid.

Each cell C is characterized by a row i and a column j (1<=i<=9 ; 1<=j<=9)

In G, we can define the distance between two cells A(i, j) and B(i’, j’) by:

d(A, B) = Max{ |i-i’|, |j-j’| }

d is a metric-distance and (G, d) is a metric-space.

I suggest the following definitions :

adjacent cells : two distinct cells A, B are adjacent if d(A, B)=1

Let Z be a set of cells : Z=(A, B, C,...) ; with at least 2 cells.

Connected set : a set Z of cells such that for every A of Z there exist B of Z such that d(A, B)=1.

Obviously, the set made by 2 adjacent cells is a connected set.

Non mutually adjacent set (of cells) : a set such as for every couple of distinct cells (A, B) : d(A, B)>1

Note that the exercise proposed by tso requires more than a non mutually adjacent set of clues. (who knows why ?)

Let's call the altitude between 2 cells A(i, j) and B(i', j') the number :

a(A, B)=|i-i'|

A "tso-set" is defined by the additional condition : if a(A, B)=1 then 1<d(A, B)<9