## How many 1-clue-box and 2-clue-box?

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

### How many 1-clue-box and 2-clue-box?

For a very easy sudoku.

000 000 079
604 079 001
000 802 000
009 000 347
000 000 000
100 068 000
040 200 000
000 087 006
020 000 800

There are 4 "2-clue-box".
Because the less clue of sudoku is 17s,
there might be 9 "2-clue-box" and 7 "1-clue-box".
Eioru

Posts: 182
Joined: 16 August 2006

### Re: How many 1-clue-box and 2-clue-box?

Eioru wrote:For a very easy sudoku.

000 000 079
604 079 001
000 802 000
009 000 347
000 000 000
100 068 000
040 200 000
000 087 006
020 000 800

There are 4 "2-clue-box".
Because the less clue of sudoku is 17s,
there might be 9 "2-clue-box" and 7 "1-clue-box".

Here is a post from Ocean giving stats on the clues distribution in the 17-clues gfroyle's list
He found 1405 "122222222", based on 32930 distinct 17-clue sudokus at that time.

Based on a more recent list (36628), I counted 1565 "122222222"

Now, pick one of this puzzle and add one (compatible) clue in the 1 clue-box.

For example :
Code: Select all
` 8 . . | . . . | . 2 4 . 1 . | . . 8 | . . . . . . | . 7 . | . . .-------+-------+------- 6 . . | 2 . 1 | 5 . . 4 . . | . . . | . . 3 . . . | . . . | . . .-------+-------+------- . 7 . | . . . | 8 1 . 5 . . | 4 3 . | . . . . . . | . . . | . . .`

On the second point (7 one-clue boxes), i have some doubt about the existence of valid puzzles with this kind of pattern :
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 . . . | . x . | . . . . x . | . . . | . . .`

but who knows ?

In any case, in the gfroyle list : there are no 111111155 and the maximum of 1-clue boxes is 5.

JPF
JPF
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Posts: 6017
Joined: 06 December 2005
Location: Paris, France

I cant do any better than 4 clues in Box 9
Code: Select all
`+---+---+---+|123|...|7..||456|...|...||789|..5|...|+---+---+---+|...|148|...||...|259|.1.||..8|736|...|+---+---+---+|...|9..|.46||.7.|...|1..||...|...|..5|+---+---+---+`

C
coloin

Posts: 2283
Joined: 05 May 2005
Location: Devon

Here is a puzzle with 3 clues in Box 9

Code: Select all
` 4 . . | . . . | 7 . . . 9 5 | . . . | . . . 6 3 8 | . . 9 | . . .-------+-------+------- . . . | . 4 3 | . . . . . . | 1 . . | . 9 . . . 1 | 7 2 5 | . . .-------+-------+------- . . . | 2 . . | . . 7 . 8 . | . . . | . 3 . . . . | . . . | 1 . .`

JPF
JPF
2017 Supporter

Posts: 6017
Joined: 06 December 2005
Location: Paris, France

Well done ..it spurred me on to make this one.......

Which I think is the first symetrical puzzle Ive ever made

Code: Select all
`+---+---+---+|.79|...|..3||386|...|...||21.|7..|...|+---+---+---+|..3|.46|...||...|879|...||...|21.|8..|+---+---+---+|...|..4|...||...|...|.69||5..|...|.7.|+---+---+---+`

No doubt Ocean is waiting in the wings with an improvement !
C
coloin

Posts: 2283
Joined: 05 May 2005
Location: Devon

### Re: Cold case : How many 1-clue-box and 2-clue-box?

coloin wrote:No doubt Ocean is waiting in the wings with an improvement !

no response from Ocean. So it's my turn now:
Code: Select all
`+---+---+---+|123|...|...||456|..2|...||789|...|.3.|+---+---+---+|...|148|...||...|369|..7||.4.|725|...|+---+---+---+|...|...|.4.||5..|...|2..||...|8..|...|+---+---+---+`

JPF
JPF
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Posts: 6017
Joined: 06 December 2005
Location: Paris, France

### Re: How many 1-clue-box and 2-clue-box?

Very nice
Must have taken a long time to make !!
It can be morphed to have diagonal symmetry and reduced to 20C

If there is no empty box it seems 6 clues are always necessary in the 5 boxes [B36789] in your puzzle

So with 5 clues always needed in B12369 ......can you find a smaller puzzle - removing clues from B4578 ?

Code: Select all
`+---+---+---+    +---+---+---+      |...|...|..1|    |...|...|..1|      |...|...|.23|    |...|...|.23|      |...|..4|...|    |...|..4|...|      +---+---+---+    +---+---+---+      |168|295|4..|    |.68|295|4..|      |234|687|...|    |2..|.8.|...|      |759|341|...|    |.5.|...|...|      +---+---+---+    +---+---+---+      |972|163|...|    |9.2|1.3|...|      |581|479|...|    |..1|.7.|...|      |346|528|...|    |34.|5..|...|      +---+---+---+    +---+---+---+   22C`
coloin

Posts: 2283
Joined: 05 May 2005
Location: Devon

### Re: How many 1-clue-box and 2-clue-box?

can you find a smaller puzzle - removing clues from B4578 ?

sure!
Code: Select all
`+---+---+---+   +---+---+---+|...|...|..1|   |...|...|..1||...|...|.2.|   |...|...|.2.||...|..3|..4|   |...|..3|..4|+---+---+---+   +---+---+---+|482|956|7..|   |..2|.56|7..||539|781|...|   |.3.|7.1|...||176|234|...|   |1..|..4|...|+---+---+---+   +---+---+---+|245|168|...|   |.4.|1.8|...||697|325|...|   |..7|.2.|...||318|497|...|   |31.|.9.|...|+---+---+---+   +---+---+---+   21C`

JPF
JPF
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Posts: 6017
Joined: 06 December 2005
Location: Paris, France

### Re: How many 1-clue-box and 2-clue-box?

Gets a bit tricky now ... !
But further to go I think ...

Code: Select all
`+---+---+---+|...|...|..1||...|...|.23||...|..4|...|+---+---+---+|9.6|..1|4..||5..|...|...||78.|.25|...|+---+---+---+|...|.38|...||..4|79.|...||.13|...|...|+---+---+---+  20C`
coloin

Posts: 2283
Joined: 05 May 2005
Location: Devon

### Re: How many 1-clue-box and 2-clue-box?

Here are three more 21-clue puzzles, each with three empty boxes:
Code: Select all
` . . . . . . . 1 2 . . . . . . . . 3 . . . . . . 4 . . . 2 . 1 . . . . . . 1 . 3 5 . . . . . . 6 . 7 . 8 . . 4 . . 6 8 . . . . 9 . . . . 2 . . . 3 8 5 . . 4 . . .   ED=2.0/1.2/1.2 . . . . . . . 1 2 . . . . . . . . 3 . . . . . . 4 . . . 2 . 3 . . . . . . 5 . . 6 . . . . . . 1 . 7 8 9 . . 7 . . 4 9 . . . . 4 . . . . 7 . . . 8 1 6 . . 5 . . .   ED=2.0/2.0/2.0 . . . . . . . 1 2 . . . . . . . . 3 . . . . . . 4 . . . 5 . 1 . . . . . . 1 . 3 6 . . . . . . 2 . 7 . 8 . . 4 . . 2 8 . . . . 9 . . . . 5 . . . 8 7 3 . . 4 . . .   ED=2.3/1.2/1.2`

On the way, I picked up this too:
Code: Select all
` . . . 4 . . . . . . . . . . . 2 . 1 . . . . . . 5 . 7 4 1 . . . 7 . . . . 2 . 5 . . . 8 . . 7 . . . 2 . . . . . 8 3 . . . . . . . . . . 1 . . . 6 . 3 . 9 . . . .   6 clues in  B12369, but only 19 overall`

Regards,

Mike

m_b_metcalf
2017 Supporter

Posts: 13322
Joined: 15 May 2006
Location: Berlin

### Re: How many 1-clue-box and 2-clue-box?

Code: Select all
` . . . . . . . . 6 . . . . . . . 2 3 . . . . . 4 . . . 5 . . . . 6 4 . . 2 . . . . . . . . 8 3 . . 7 1 . . . . . . . 3 7 . . . . . 4 5 2 . . . . . 6 9 . . . . . .   19C`

and two cousins:
Code: Select all
`........1.......23.....4...5....64..2........76..81.......38.....452.....19......   19    5         ........1.......23.....4...5....64..2........76..81.......37.....452.....19......   19    5         `

m_b_metcalf
2017 Supporter

Posts: 13322
Joined: 15 May 2006
Location: Berlin

### Re: How many 1-clue-box and 2-clue-box?

cousin of cousins...
Code: Select all
`+---+---+---+|...|...|..1||...|...|.23||...|..4|...|+---+---+---+|5..|..6|4..||2..|...|...||37.|.89|...|+---+---+---+|...|.2.|...||..1|37.|...||.48|...|...|+---+---+---+   18C`

JPF
JPF
2017 Supporter

Posts: 6017
Joined: 06 December 2005
Location: Paris, France

### Re: How many 1-clue-box and 2-clue-box?

There are no 17 with two empty boxes. So the game is over.

Here is a first try:
Code: Select all
`+---+---+---+|...|...|..1||...|...|234||...|...|5..|+---+---+---+|...|..3|...||2.5|.6.|...||13.|4.7|...|+---+---+---+|...|.2.|...||3.6|.89|...||.78|..5|...|+---+---+---+   21C`

JPF
JPF
2017 Supporter

Posts: 6017
Joined: 06 December 2005
Location: Paris, France

### Re: How many 1-clue-box and 2-clue-box?

My first try:
Code: Select all
` . . . . . . . . 1 . . . . . . . 4 6 . . . . . . 8 5 9 2 4 . 1 9 6 . . . . . . . 7 . . . . . 3 . . . 2 . . . . . 1 8 . . . . . 6 . 7 . . 4 . . . . . 8 . . 3 . . .  21C . . . . . . . 3 2 . . . . . . 4 . 6 . . . . . . 8 5 . 3 2 9 . . . . . . . 1 . 6 . . . . . . . . . 4 8 . . . 1 4 8 . 6 . . . . . . . 5 . 9 . . . . 6 . . . 3 . . .  21C`

m_b_metcalf
2017 Supporter

Posts: 13322
Joined: 15 May 2006
Location: Berlin

### Re: How many 1-clue-box and 2-clue-box?

20C remains too elusive (for me). Here are a few more 21Cs, with patterns slightly different from those already posted:
Code: Select all
` . . . . . . . 1 2 . . . . . . 3 . . . . . . . . 4 5 6 1 2 6 . . . . . . . 7 . 8 . . . . . . . . . 3 4 . . . 7 3 4 . 8 . . . . . . . 5 . 6 . . . . 8 . . . 1 . . .   ED=2.0/1.2/1.2 . . . . . . . . 1 . . . . . . . 2 3 . . . . . . 4 5 6 7 2 . 1 6 . . . . . . . . 8 . . . . . 9 . . 4 7 . . . . . 1 4 . . . . . 3 . 8 . . 2 . . . . . 4 . . 9 . . .   ED=2.3/1.2/1.2 . . . . . . . . 1 . . . . . . 2 3 4 . . . . . . 5 . . . . . . 6 3 . . . 2 . 5 . . . . . . 1 3 . 4 . 7 . . . . . . . 2 . . . . 3 . 8 . 9 6 . . . . 7 9 . . 5 . . .   ED=2.5/1.2/1.2`

Regards,

Mike

m_b_metcalf
2017 Supporter

Posts: 13322
Joined: 15 May 2006
Location: Berlin

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