New challenges - 1

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

New challenges - 1

Postby JPF » Tue Jun 16, 2020 3:35 pm

In the good old days on this forum, we used to have challenges.

Here is a new one:
What is the minimum number of solutions of a pattern having atmost one clue in each box B2B3B4B6B7B8B9?

There is possibly an exhaustive search, but here my first proposal after a quick review:

Code: Select all
+---+---+---+
|..1|...|...|
|2.3|.4.|...|
|567|...|8..|
+---+---+---+
|.9.|628|...|
|...|1.5|.7.|
|...|.94|...|
+---+---+---+
|..8|...|...|
|...|...|..4|
|...|5..|...|
+---+---+---+    550 sol.

I am sure one can get something better.
Any taker?

JPF
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Re: New challenges - 1

Postby tarek » Tue Jun 16, 2020 3:51 pm

I may have had a tool from 14 years ago that may be worth reviving as it may suit this challenge. I'll try to see if I can find it

T
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Re: New challenges - 1

Postby Mathimagics » Thu Jun 18, 2020 8:46 am

It's tough going ... :?

This is another case of 550 on the same B1/B5 combo:

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

Postby tarek » Thu Jun 18, 2020 1:41 pm

My best result is:
Code: Select all
 . . 1 | . . . | . . . 
 2 . 3 | . 8 . | . . . 
 5 6 7 | . . . | 4 . . 
-------+-------+------
 . 9 . | 6 2 8 | . . . 
 . . . | 1 . 5 | . 7 . 
 . . . | . 9 4 | . . . 
-------+-------+------
 . . 4 | . . . | . . . 
 . . . | . . . | . . 8 
 . . . | 5 . . | . . . 

626 solutions
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Re: New challenges - 1

Postby Mathimagics » Thu Jun 18, 2020 3:10 pm

I rather suspect 550 is not going to be beaten ... I have found a grid that is ED to JPF's original, but it has the same solution count.

Here is a "normalised" version of JPF's original grid. Box 1 is fixed, and box 5 is in reduced form:

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


There are (at least) 36 different forms that give the same result, ie 550:
36 x 550: Show
Code: Select all
123......4562.....789...3.....129....1.458......673.4...7...........4...........1
123......4562.....789...3.....129....1.458......673.4...7..............1.....4...
123......4562.....789...3.....129....1.458......673.4......4.....7..............1
123......4562.....789...3.....129....1.458......673.4.........1..7...........4...
123......4562.....789...3.....129....1.458......673.4......4...........1..7......
123......4562.....789...3.....129....1.458......673.4.........1.....4.....7......
123......4562.....789...3.....129....1.458......673..4..7...........4..........1.
123......4562.....789...3.....129....1.458......673..4..7.............1......4...
123......4562.....789...3.....129....1.458......673..4.....4.....7.............1.
123......4562.....789...3.....129....1.458......673..4.......1...7...........4...
123......4562.....789...3.....129....1.458......673..4.....4..........1...7......
123......4562.....789...3.....129....1.458......673..4.......1......4.....7......
123......4562.....789....3....129....1.458......6734....7...........4...........1
123......4562.....789....3....129....1.458......6734....7..............1.....4...
123......4562.....789....3....129....1.458......6734.......4.....7..............1
123......4562.....789....3....129....1.458......6734..........1..7...........4...
123......4562.....789....3....129....1.458......6734.......4...........1..7......
123......4562.....789....3....129....1.458......6734..........1.....4.....7......
123......4562.....789....3....129....1.458......673..4..7...........4.........1..
123......4562.....789....3....129....1.458......673..4..7............1.......4...
123......4562.....789....3....129....1.458......673..4.....4.....7............1..
123......4562.....789....3....129....1.458......673..4......1....7...........4...
123......4562.....789....3....129....1.458......673..4.....4.........1....7......
123......4562.....789....3....129....1.458......673..4......1.......4.....7......
123......4562.....789.....3...129....1.458......6734....7...........4..........1.
123......4562.....789.....3...129....1.458......6734....7.............1......4...
123......4562.....789.....3...129....1.458......6734.......4.....7.............1.
123......4562.....789.....3...129....1.458......6734.........1...7...........4...
123......4562.....789.....3...129....1.458......6734.......4..........1...7......
123......4562.....789.....3...129....1.458......6734.........1......4.....7......
123......4562.....789.....3...129....1.458......673.4...7...........4.........1..
123......4562.....789.....3...129....1.458......673.4...7............1.......4...
123......4562.....789.....3...129....1.458......673.4......4.....7............1..
123......4562.....789.....3...129....1.458......673.4.......1....7...........4...
123......4562.....789.....3...129....1.458......673.4......4.........1....7......
123......4562.....789.....3...129....1.458......673.4.......1.......4.....7......


Box 5 can really only have 10,080 ED settings, and so I've been testing only those.

The only other B5 setting for which I've had any joy is this one, and it seems to be closely related:
Code: Select all
 +-------+-------+-------+
 | 1 2 3 | . . . | . . . |
 | 4 5 6 | 3 . . | . . . |
 | 7 8 9 | . . . | 2 . . |
 +-------+-------+-------+
 | . . . | 1 3 8 | . . . |
 | . . 1 | 4 6 9 | . . . |
 | . . . | 5 7 2 | . 4 . |
 +-------+-------+-------+
 | . 7 . | . . . | . . . |
 | . . . | . . 4 | . . . |
 | . . . | . . . | . . 1 |
 +-------+-------+-------+


Once again, all solution counts are 550, and there are 36 different puzzles. Note that the clue values in B6-B9 are the same as above (1,4,4,7).

36 x 550 (case 2): Show
Code: Select all
123......4563.....789...2.....138.....1469......572.4..7............4...........1
123......4563.....789...2.....138.....1469......572.4..7...............1.....4...
123......4563.....789...2.....138.....1469......572.4......4....7...............1
123......4563.....789...2.....138.....1469......572.4.........1.7............4...
123......4563.....789...2.....138.....1469......572.4......4...........1.7.......
123......4563.....789...2.....138.....1469......572.4.........1.....4....7.......
123......4563.....789...2.....138.....1469......572..4.7............4..........1.
123......4563.....789...2.....138.....1469......572..4.7..............1......4...
123......4563.....789...2.....138.....1469......572..4.....4....7..............1.
123......4563.....789...2.....138.....1469......572..4.......1..7............4...
123......4563.....789...2.....138.....1469......572..4.....4..........1..7.......
123......4563.....789...2.....138.....1469......572..4.......1......4....7.......
123......4563.....789....2....138.....1469......5724...7............4...........1
123......4563.....789....2....138.....1469......5724...7...............1.....4...
123......4563.....789....2....138.....1469......5724.......4....7...............1
123......4563.....789....2....138.....1469......5724..........1.7............4...
123......4563.....789....2....138.....1469......5724.......4...........1.7.......
123......4563.....789....2....138.....1469......5724..........1.....4....7.......
123......4563.....789....2....138.....1469......572..4.7............4.........1..
123......4563.....789....2....138.....1469......572..4.7.............1.......4...
123......4563.....789....2....138.....1469......572..4.....4....7.............1..
123......4563.....789....2....138.....1469......572..4......1...7............4...
123......4563.....789....2....138.....1469......572..4.....4.........1...7.......
123......4563.....789....2....138.....1469......572..4......1.......4....7.......
123......4563.....789.....2...138.....1469......5724...7............4..........1.
123......4563.....789.....2...138.....1469......5724...7..............1......4...
123......4563.....789.....2...138.....1469......5724.......4....7..............1.
123......4563.....789.....2...138.....1469......5724.........1..7............4...
123......4563.....789.....2...138.....1469......5724.......4..........1..7.......
123......4563.....789.....2...138.....1469......5724.........1......4....7.......
123......4563.....789.....2...138.....1469......572.4..7............4.........1..
123......4563.....789.....2...138.....1469......572.4..7.............1.......4...
123......4563.....789.....2...138.....1469......572.4......4....7.............1..
123......4563.....789.....2...138.....1469......572.4.......1...7............4...
123......4563.....789.....2...138.....1469......572.4......4.........1...7.......
123......4563.....789.....2...138.....1469......572.4.......1.......4....7.......
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Re: New challenges - 1

Postby Mathimagics » Thu Jun 18, 2020 4:55 pm

Same deal, different B5, 36 flavours, all with NS = 550:

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

Postby coloin » Thu Jun 18, 2020 6:32 pm

my top 4
Code: Select all
264......835.9....971...4...8.723......459.7....186.....9..................2....8    550 sol.
264......835.9....917...4...8.123......459.2....786.....9..............8...2.....    687 sol.
624......835.9....917...4...8.123......459.2....786.....9..............8...2.....    784 sol.
264......385.9....917...4...3.128......459.2....736.....9..................2....3    785 sol.

the 550 is the same as JPF's - which is isomorphic to the 36 others

btw there are 124 ED B1B5 combinations only

Hidden Text: Show
Code: Select all
123......456......789.........256......137......984..............................
123......456......789.........162......845......739..............................
123......456......789.........162......859......734..............................
123......456......789.........162......958......734..............................
123......456......789.........162......754......938..............................
123......456......789.........162......745......938..............................
123......456......789.........162......758......934..............................
123......456......789.........162......754......839..............................
123......456......789.........162......759......834..............................
123......456......789.........162......758......943..............................
123......456......789.........164......758......932..............................
123......456......789.........164......738......952..............................
123......456......789.........164......752......839..............................
123......456......789.........164......752......938..............................
123......456......789.........164......738......259..............................
123......456......789.........164......735......829..............................
123......456......789.........164......739......852..............................
123......456......789.........164......925......738..............................
123......456......789.........164......258......739..............................
123......456......789.........164......725......938..............................
123......456......789.........164......725......839..............................
123......456......789.........164......738......529..............................
123......456......789.........168......943......725..............................
123......456......789.........168......934......752..............................
123......456......789.........168......749......253..............................
123......456......789.........168......759......234..............................
123......456......789.........168......734......925..............................
123......456......789.........168......954......732..............................
123......456......789.........168......945......723..............................
123......456......789.........168......943......752..............................
123......456......789.........168......735......942..............................
123......456......789.........168......753......942..............................
123......456......789.........168......745......932..............................
123......456......789.........168......754......329..............................
123......456......789.........168......735......249..............................
123......456......789.........168......753......924..............................
123......456......789.........168......743......952..............................
123......456......789.........168......243......759..............................
123......456......789.........168......742......935..............................
123......456......789.........168......724......953..............................
123......456......789.........168......945......732..............................
123......456......789.........169......734......258..............................
123......456......789.........169......734......528..............................
123......456......789.........169......534......728..............................
123......456......789.........169......754......823..............................
123......456......789.........169......748......532..............................
123......456......789.........169......758......234..............................
123......456......789.........169......854......723..............................
123......456......789.........169......745......832..............................
123......456......789.........169......842......753..............................
123......456......789.........169......842......735..............................
123......456......789.........169......824......735..............................
123......456......789.........169......254......738..............................
123......456......789.........169......758......324..............................
123......456......789.........169......754......328..............................
123......456......789.........169......724......358..............................
123......456......789.........169......524......738..............................
123......456......789.........169......758......243..............................
123......456......789.........169......724......538..............................
123......456......789.........169......342......758..............................
123......456......789.........169......352......748..............................
123......456......789.........169......345......728..............................
123......456......789.........674......318......259..............................
123......456......789.........674......358......219..............................
123......456......789.........674......913......258..............................
123......456......789.........674......213......859..............................
123......456......789.........674......291......853..............................
123......456......789.........674......951......328..............................
123......456......789.........674......915......328..............................
123......456......789.........674......921......853..............................
123......456......789.........674......253......819..............................
123......456......789.........674......123......958..............................
123......456......789.........674......315......928..............................
123......456......789.........679......413......825..............................
123......456......789.........679......813......425..............................
123......456......789.........679......214......853..............................
123......456......789.........679......324......158..............................
123......456......789.........679......453......128..............................
123......456......789.........679......815......243..............................
123......456......789.........679......218......354..............................
123......456......789.........357......426......981..............................
123......456......789.........357......296......148..............................
123......456......789.........352......147......968..............................
123......456......789.........352......841......967..............................
123......456......789.........352......186......497..............................
123......456......789.........352......964......187..............................
123......456......789.........352......164......897..............................
123......456......789.........351......987......426..............................
123......456......789.........351......297......486..............................
123......456......789.........456......298......371..............................
123......456......789.........456......219......873..............................
123......456......789.........451......387......269..............................
123......456......789.........457......289......361..............................
123......456......789.........457......689......213..............................
123......456......789.........457......219......863..............................
123......456......789.........457......289......163..............................
123......456......789.........453......816......297..............................
123......456......789.........453......279......168..............................
123......456......789.........918......645......327..............................
123......456......789.........918......362......745..............................
123......456......789.........917......345......628..............................
123......456......789.........917......328......645..............................
123......456......789.........231......546......798..............................
123......456......789.........854......967......321..............................
123......456......789.........854......367......921..............................
123......456......789.........853......421......967..............................
123......456......789.........835......471......926..............................
123......456......789.........349......176......258..............................
123......456......789.........349......168......257..............................
123......456......789.........349......167......258..............................
123......456......789.........349......167......285..............................
123......456......789.........349......852......167..............................
123......456......789.........348......159......267..............................
123......456......789.........348......672......915..............................
123......456......789.........185......296......374..............................
123......456......789.........182......653......479..............................
123......456......789.........194......672......853..............................
123......456......789.........543......129......786..............................
123......456......789.........123......789......564..............................
123......456......789.........465......789......123..............................
123......456......789.........417......568......239..............................
123......456......789.........456......789......123..............................
123......456......789.........834......672......159..............................
123......456......789.........417......528......639..............................
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Re: New challenges - 1

Postby JPF » Thu Jun 18, 2020 10:39 pm

coloin wrote:btw there are 124 ED B1B5 combinations only

I agree and there are 237083 ed-B1B5B9.

If 550 is the lowest number of solutions, I am really lucky because I found it almost by chance starting from:

Code: Select all
+---+---+---+
|123|...|...|
|456|...|7..|
|897|...|...|
+---+---+---+
|...|625|...|
|...|914|.2.|
|...|783|...|
+---+---+---+
|...|...|851|
|...|...|342|
|...|...|697|
+---+---+---+   23  sol.

JPF
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Re: New challenges - 1

Postby Mathimagics » Fri Jun 19, 2020 8:49 am

Ok, trying again ... :roll:

These 2 have distinct Minlex forms, so presumably one corresponds to JPF's and one must be new:

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

Postby JPF » Fri Jun 19, 2020 7:23 pm

some improvements:
Code: Select all
 1 2 3 | 8 . . | . . .
 4 5 6 | . . . | . . 2
 7 8 9 | . . . | . . .
-------+-------+-------
 . . . | 1 2 9 | . . .
 . . 2 | 3 5 6 | . . .
 . . . | 4 8 7 | . 1 .
-------+-------+-------
 . . . | . . . | . . .
 . . . | . . 5 | . . .
 3 . . | . . . | . 8 .    251 sol.

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Re: New challenges - 1

Postby JPF » Fri Jun 19, 2020 11:34 pm

more:

Code: Select all
 1 2 3 | . . . | . . .
 4 5 6 | . 3 . | . . .
 7 8 9 | . . . | . 1 .
-------+-------+-------
 . . . | 1 2 7 | . . .
 . . 4 | 9 5 6 | . . 3
 . . . | 8 4 3 | . . .
-------+-------+-------
 . . . | . . . | . . .
 . . . | . . . | . . .
 . 1 . | 2 . . | . 8 .    154 sol.


and [edit]

Code: Select all
 1 2 3 | . . . | . . .
 4 5 6 | . . . | . . .
 7 8 9 | . 1 . | 2 . .
-------+-------+-------
 8 . . | 1 5 7 | . . .
 . . . | 4 8 3 | . . .
 . . . | 6 9 2 | . . 3
-------+-------+-------
 . . . | . . . | 8 . .
 . . 4 | 3 . . | . . .
 . . . | . . . | . . .    117 sol.

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Re: New challenges - 1

Postby coloin » Sun Jun 21, 2020 5:04 pm

That is very surprizing, though for clarity, it has been shown that 5 clues, one in each box B3B6B7B8B9 cant produce valid puzzles...
and an example of 8 cues solving the puzzle [2 clues in B9]

Code: Select all
+---+---+---+
|672|...|..1|
|318|...|...|
|..5|6..|...|
+---+---+---+
|5..|.63|.9.|
|...|5.8|...|
|...|271|...|
+---+---+---+
|...|...|.4.|
|...|...|...|
|..1|..2|..8|
+---+---+---+

I searched 4 patterns , there seems to be a favourite !
Hidden Text: Show
Code: Select all
362.....1918........53.....4...39.7....2.1......478.......................1..2..8   154
362.....1918........53.....4...39.7....2.1......478.......................1..2..8   154
672.....1318........56.....4...63.9....4.8......271.......................1..2..8   154
672.....1918........56.....4...69.3....4.8......271.......................1..2..8   154
958.....1312........73.....4...69.3....4.8......251.......................1..2..8   154
958.....1312........73.....4...69.3....4.8......251.......................1..2..8   154
978.....1312........53.....4...69.3....2.1......438.......................1..2..8   154
978.....1312........53.....4...69.3....2.1......438.......................1..2..8   154
672.....1318........56.....5...63.9....5.8......271.......................1..2..8   184
958.....1312........73.....4...79.3....4.8......251.......................1..2..8   186
732.....1918........67.....4...79.3....5.8......231.......................1..2..8   222
372.....1918........53.....4...39.7....2.1......648.......................1..2..8   222
938.....1712........67.....4...79.3....5.8......231.......................1..2..8   240
968.....1312........53.....7...39.6....2.1......478.......................1..2..8   240
362.....1918........53.....7...49.3....7.8......231.......................1..2..8   252
362.....1918........53.....4...79.3....2.1......468.......................1..2..8   252
372.....1918........53.....4...69.3....2.1......478.......................1..2..8   252
372.....1918........53.....4...69.3....4.8......231.......................1..2..8   252
958.....1612........76.....4...69.3....4.8......231.......................1..2..8   252
958.....1612........76.....4...69.3....4.8......231.......................1..2..8   252
578.....1312........63.....4...35.9....2.1......478.......................1..2..8   252
958.....1612........76.....4...69.3....2.1......458.......................1..2..8   252
678.....1912........49.....4...96.3....2.1......478.......................1..2..8   258
978.....1312........43.....4...39.5....2.1......478.......................1..2..8   258
978.....1312........43.....4...39.6....2.1......478.......................1..2..8   258
938.....1712........57.....4...79.3....4.8......231.......................1..2..8   278
372.....1918........53.....4...69.7....4.8......271.......................1..2..8   278
362.....1918........53.....4...79.6....2.1......438.......................1..2..8   278
958.....1612........76.....4...69.5....2.1......438.......................1..2..8   278
462.....1718........54.....9...67.3....9.8......231.......................1..2..8   294
352.....1918........63.....4...59.7....2.1......438.......................1..2..8   294
478.....1312........53.....9...74.3....6.8......291.......................1..2..8   294
468.....1312........53.....9...64.3....9.8......231.......................1..2..8   294
468.....1312........53.....9...64.3....2.1......738.......................1..2..8   294
578.....1312........63.....4...75.3....2.1......498.......................1..2..8   294
372.....1918........53.....4...39.7....4.8......271.......................1..2..8   300

but not as good as the latest one !!
coloin
 
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Re: New challenges - 1

Postby tarek » Sun Jun 21, 2020 6:28 pm

I couldn't get below 500 :oops:

Colin's method of starting from a valid puzzle with 8 clues is a good idea for a different approach

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Re: New challenges - 1

Postby coloin » Sun Jun 21, 2020 6:53 pm

Well, I too couldnt get below the 550 when I searched with +9 clues and three in box 9 [ remove 2]
Searching with 9 clues , 2 boxes having 2 clues [ remove 1 from each] 4 ways was more profitable
There are relatively not many puzzles with +8 clues [and no empty box ]...
coloin
 
Posts: 1925
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Re: New challenges - 1

Postby JPF » Tue Jun 23, 2020 4:22 pm

With the technique I am using my limit seems to be 117 sol.
I got many 146 and 154 sol. and nothing in between.

Here's an example with 146 sol.
Code: Select all
123...4..456......789.6....3..271......954......683.5........6.2....7............   146 sol.

I'll try a last run and stop if no improvement.

coloin wrote:That is very surprizing, though for clarity, it has been shown that 5 clues, one in each box B3B6B7B8B9 cant produce valid puzzles...

Which posts are you refering to?

JPF
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