Let's consider this valid, minimal 24-puzzle :

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

. . . | . . . | . 7 1

. . . | . . . | 6 9 8

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

. . 4 | . . . | . . .

. . 7 | . 1 . | 8 . .

. 5 . | 3 . 6 | 1 2 .

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

. . 9 | . . 5 | . . 4

. 3 . | . . 8 | . . 6

. 6 . | . 7 . | 2 . 5

We are in Sudokuland, a place where all the puzzles have one (and only one) solution... but here, this puzzle is not minimal...

Too many data !

As all the puzzles have one (and only one) solution, you can hide the number in r2c9.

Effectively, in r2c9, only the number 1 gives one (and only one) solution to this fantastic puzzle.

The other potential candidate is 2, but it gives me five... solutions

So, in Sudokuland, the puzzles look like :

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

. . . | . . . | . 7 x

. . . | . . . | 6 9 8

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

. . 4 | . . . | . . .

. . 7 | . 1 . | 8 . .

. 5 . | 3 . 6 | 1 2 .

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

. . 9 | . . 5 | . . 4

. 3 . | . . 8 | . . 6

. 6 . | . 7 . | 2 . 5

But even this one has too many data.

For example you can also hide the number in r5c7 :

If you don't know r2c9 and r5c7, don't worry , the following puzzle :

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

. . . | . . . | . 7 x

. . . | . . . | 6 9 8

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

. . 4 | . . . | . . .

. . 7 | . 1 . | x . .

. 5 . | 3 . 6 | 1 2 .

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

. . 9 | . . 5 | . . 4

. 3 . | . . 8 | . . 6

. 6 . | . 7 . | 2 . 5

has one (and only one) solution iff r2c9=1 and r5c7=8.

In Sudokuland, a puzzle is minimal if you can not replace any more number by an "x".

Is the last puzzle minimal ?

It's easy to get puzzles with 16 numbers and one "x", using the gfroyle list.

Any puzzles with 15 numbers and 2 "x" ?

JPF