- Code: Select all
`*-----------*`

|...|4.6|7.8|

|...|7.9|1.3|

|...|2.1|5.6|

|---+---+---|

|2.5|...|4.1|

|6.1|...|3.9|

|...|...|...|

|---+---+---|

|3.4|1.8|...|

|...|...|...|

|8.2|5.4|...|

*-----------*

Can anybody construct the 9 and 10?

RW

4 posts
• Page **1** of **1**

Theoretically there could be 10 empty units in a valid puzzle (3 rows, 3 columns and 4 boxes), right? It seems to me a puzzle with 7 empty units is quite easy to make and I found one 8:

Can anybody construct the 9 and 10?

RW

- Code: Select all
`*-----------*`

|...|4.6|7.8|

|...|7.9|1.3|

|...|2.1|5.6|

|---+---+---|

|2.5|...|4.1|

|6.1|...|3.9|

|...|...|...|

|---+---+---|

|3.4|1.8|...|

|...|...|...|

|8.2|5.4|...|

*-----------*

Can anybody construct the 9 and 10?

RW

- RW
- 2010 Supporter
**Posts:**1000**Joined:**16 March 2006

RW wrote:Theoretically there could be 10 empty units in a valid puzzle (3 rows, 3 columns and 4 boxes), right? It seems to me a puzzle with 7 empty units is quite easy to make and I found one 8:

Can anybody construct the 9 and 10?

RW

Yes, tso made one 9 :

(3 boxes & 6 rows/cols)

- Code: Select all
`. . . | . 2 5 | . 3 9`

. . . | . 3 7 | . 4 1

. . . | . . . | . . .

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

. . . | . . . | . . .

4 7 . | . . . | . 6 8

1 9 . | . . . | . 5 2

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

. . . | . . . | . . .

6 4 . | . 5 3 | . . .

7 8 . | . 1 2 | . . .

I made a 8 (4 boxes & 4 rows/cols) here :

- Code: Select all
`. . . | . . . | 9 . 6`

. . . | . . . | 3 . 5

. . . | . . . | 8 . 4

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

5 . 4 | . 7 2 | . . .

3 . 6 | . 5 9 | . . .

9 . 7 | . 8 1 | . . .

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

. . . | . . . | . . .

6 . 9 | . 4 3 | . . .

2 . 3 | . 1 6 | . . .

To make a 10 empty units, we need 4 boxes and 6 rows/cols empty

(as 7 rows/cols or 5 boxes is impossible).

The only valid 4 empty boxes shape is :

00X

XX0

XX0

So, it means that a 10 empty units pattern is isomorphic to :

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

. . . | . . . | . x x

. . . | . . . | . . .

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

x x . | . x x | . . .

x x . | . x x | . . .

. . . | . . . | . . .

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

x x . | . x x | . . .

x x . | . x x | . . .

. . . | . . . | . . .

JPF

- JPF
- 2017 Supporter
**Posts:**3754**Joined:**06 December 2005**Location:**Paris, France

Interesting, tso posted a 9 almost on the day 1 year ago... Someone should make a nice index of all topics already discussed in the General/puzzle section...

I also think 9 is the most empty units there can be, a 10 would have to be equivalent to:

and I cannot find that in the fully symmetrical thread.

Could a 9 with 4 boxes & 5 rows/columns be possible?

RW

I also think 9 is the most empty units there can be, a 10 would have to be equivalent to:

- Code: Select all
`X.X ... X.X`

... ... ...

X.X ... X.X

... X.X ...

... ... ...

... X.X ...

X.X ... X.X

... ... ...

X.X ... X.X

and I cannot find that in the fully symmetrical thread.

JPF wrote:I made a 8 (4 boxes & 4 rows/cols)

Could a 9 with 4 boxes & 5 rows/columns be possible?

RW

- RW
- 2010 Supporter
**Posts:**1000**Joined:**16 March 2006

Hard work, but you're right : "someone" should make it...RW wrote:Someone should make a nice index of all topics already discussed in the General/puzzle section...

right, no puzzle has been posted for this F.S. pattern [20-0-4-2-0] or for its 2 equivalents [0-12-4-2-0] & [24-8-0-2-0]RW wrote:I cannot find that in the fully symmetrical thread.

In the Fractal Sudoku thread I posted this puzzle (+5 clues) with 2 solutions :

- Code: Select all
`6 . 2 | . . . | 8 . 7`

. 3 . | . . . | . 1 .

7 . 8 | . . . | 9 . 2

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

. . . | 2 . 9 | . . .

. . . | . 6 . | . . .

. . . | 8 . 3 | . . .

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

9 . 1 | . . . | 3 . 4

. 7 . | . . . | . 8 .

2 . 4 | . . . | 7 . 6

Ocean, posted one with 3 solutions.

Even this pattern seems difficult to match !

doubt it, but who knows ?RW wrote:Could a 9 with 4 boxes & 5 rows/columns be possible?

JPF

- JPF
- 2017 Supporter
**Posts:**3754**Joined:**06 December 2005**Location:**Paris, France

4 posts
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