Percent Sudoku

For fans of Killer Sudoku, Samurai Sudoku and other variants

Percent Sudoku

Postby 1to9only » Tue Oct 20, 2020 8:21 am

I've seen the Percent Sudokus before, and it's only recently that I've tried to generate one.
Here's one that is rated ED=2.8/1.2/1.2 (medium difficulty!):
Image
Code: Select all
....7.....978....62.6.....9....1..7..58....2.......4.....................2......8 ED=2.8/1.2/1.2

And a few more of varying difficulties for human solvers:
Code: Select all
.......9....23.6...3.7....5.....4........69........8...82..9....9.....2..1....... ED=2.0/1.2/1.2
...67...........8..........15..342....3.57.6..2...............8...9.6........2... ED=2.6/1.2/1.2
............9........41..2.7..2.5....48..7.....6..47.....8......7...........52... ED=3.0/1.2/1.2
..3...1..95..7....8...........3.6.1.....9.............1.......73..6..2...4....9.. ED=3.0/1.5/1.5
.9.........7.58.........972...5..29..........7.......8.5...3.......6.1..8.6....2. ED=3.4/1.2/1.2
...18..6...1.......62.7...9.....8...3...2.............5....7....4..3...1......... ED=3.4/1.5/1.5
2..6....1....5.......9......6.8..1...27...58.......4................6...5.9...... ED=4.2/1.2/1.2
.....4.....1........29..6....3....7............4.........16.....47.....9.58....2. ED=4.2/1.2/1.2
.......4...3..5..1...8........1........7..6.98..6.95.3......3..........4......... ED=4.4/1.2/1.2
......89....5......9..4.6.7......9............26.....1............8.24...8....76. ED=4.5/1.5/1.5

[Edit 22/10] Solutions - the ED ratings may be slightly different as I've now added Intersections for this variant!
Hidden Text: Show
Code: Select all
815679234497823516236145789942516873758934621361287495179458362684392157523761948 ED=2.8/1.2/1.2

875641293941235678236798145158924736723186954469573812582319467394867521617452389 ED=2.0/1.2/1.2
345678912672391584891425637156834279983257461427169853569743128238916745714582396 ED=2.6/1.2/1.2
491526378285973146367418925713285469948637512526194783152849637879361254634752891 ED=2.6/1.2/1.2
423569178951478632867213459798326514615894723234157896182945367379681245546732981 ED=2.6/1.5/1.5
491276835327958461568134972634581297289647513715329648152493786973862154846715329 ED=2.6/1.2/1.2
935182467781946235462375189154768392398421756276593814529817643847639521613254978 ED=2.6/1.5/1.5
258674931913258647674913258465827193327491586891365472146739825782546319539182764 ED=3.2/1.2/1.2
536784192971526834482913657863495271295671483714832965329167548647258319158349726 ED=4.2/1.2/1.2
981236745623475891457891236769153428532748619814629573298514367375962184146387952 ED=2.6/1.2/1.2
415627893768593214392148657134765928957281346826439571549376182671852439283914765 ED=4.5/1.5/1.5
Last edited by 1to9only on Thu Oct 22, 2020 8:43 am, edited 1 time in total.
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Re: Percent Sudoku

Postby creint » Tue Oct 20, 2020 6:30 pm

Can you make/solve one with 2 hollow boxes so it looks more like a percent?

Here is an example; rated easy two layers of locked singles:
Code: Select all
4 . . 1 . . 5 . 3
7 . 8 9 4 . 2 . .
. . . 7 . . . . .
. . . . . . . 9 .
. . . . . 8 . . .
. 7 . 5 . 9 . 3 .
6 . . 3 2 . . . .
. . 1 . . . . . .
9 . . . . . . . .
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Re: Percent Sudoku

Postby Hajime » Tue Oct 20, 2020 7:46 pm

creint wrote:Can you make/solve one with 2 hollow boxes so it looks more like a percent?

Where would you want the 9th cell positioned when it is out of the hollow box?
I placed them near the diagonal. The top-cell belongs to the top hollow box.
Percent.PNG
Percent.PNG (11.3 KiB) Viewed 152 times

Pretty difficult, I cannot determine an ER.
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Re: Percent Sudoku

Postby urhegyi » Tue Oct 20, 2020 9:34 pm

1to9only wrote:I've seen the Percent Sudokus before, and it's only recently that I've tried to generate one.
Here's one that is rated ED=2.8/1.2/1.2 (medium difficulty!):
Image
Code: Select all
....7.....978....62.6.....9....1..7..58....2.......4.....................2......8 ED=2.8/1.2/1.2

And a few more of varying difficulties for human solvers:
Code: Select all
.......9....23.6...3.7....5.....4........69........8...82..9....9.....2..1....... ED=2.0/1.2/1.2
...67...........8..........15..342....3.57.6..2...............8...9.6........2... ED=2.6/1.2/1.2
............9........41..2.7..2.5....48..7.....6..47.....8......7...........52... ED=3.0/1.2/1.2
..3...1..95..7....8...........3.6.1.....9.............1.......73..6..2...4....9.. ED=3.0/1.5/1.5
.9.........7.58.........972...5..29..........7.......8.5...3.......6.1..8.6....2. ED=3.4/1.2/1.2
...18..6...1.......62.7...9.....8...3...2.............5....7....4..3...1......... ED=3.4/1.5/1.5
2..6....1....5.......9......6.8..1...27...58.......4................6...5.9...... ED=4.2/1.2/1.2
.....4.....1........29..6....3....7............4.........16.....47.....9.58....2. ED=4.2/1.2/1.2
.......4...3..5..1...8........1........7..6.98..6.95.3......3..........4......... ED=4.4/1.2/1.2
......89....5......9..4.6.7......9............26.....1............8.24...8....76. ED=4.5/1.5/1.5

I tried your first four examples:
Code: Select all
815679234497823516236145789942516873758934621361287495179458362684392157523761948

Code: Select all
875641293941235678236798145158924736723186954469573812582319467394867521617452389

Code: Select all
345678912672391584891425637156834279983257461427169853569743128238916745714582396

Code: Select all
491526378285973146367418925713285469948637512526194783152849637879361254634752891
Last edited by urhegyi on Thu Oct 22, 2020 2:59 pm, edited 3 times in total.
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Re: Percent Sudoku

Postby 1to9only » Tue Oct 20, 2020 9:34 pm

Hajime's puzzle:
Code: Select all
.3....5..8.......3714...892...4............3...9...2...9.....8.2.........5....... ED=9.1/1.2/1.2
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Re: Percent Sudoku

Postby 1to9only » Tue Oct 20, 2020 9:40 pm

urhegyi wrote:I tried your first example:
Code: Select all
815679234497823516236145789942516873758934621361287495179458362684392157523761948

Yep. All good.
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Re: Percent Sudoku

Postby creint » Tue Oct 20, 2020 9:44 pm

Hajime wrote:
creint wrote:Can you make/solve one with 2 hollow boxes so it looks more like a percent?

Where would you want the 9th cell positioned when it is out of the hollow box?


It is not mandatory to use 9 cells, it's just that some solvers don't support it.
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Re: Percent Sudoku

Postby Hajime » Wed Oct 21, 2020 12:26 pm

1to9only wrote:Hajime's puzzle:
Code: Select all
.3....5..8.......3714...892...4............3...9...2...9.....8.2.........5....... ED=9.1/1.2/1.2

I think ED=9.1 is very high.
Beyond basic methods only Generalized Intersection, Turbot Crane (twice) and 2-string Kite (twice) are needed. I see that the Turbot Fish are generalized and make use of the jigsaws.
That leads to ED=4.0-4.3

Below a possible solution path:
Hidden Text: Show
Code: Select all
Solution:
#1//B4,JSB
936128574825947613714635892683412957572896431149573268497251386261389745358764129
.......21.222...1..2.2..1...222.1.......1.......1.333...1..3.3..1...333.13.......
Second line is the jigsaw patron.

J1e126789 means Jigsaw piece 1 elements 126789

Sol Step Grid Row Col Val Why
   1   1   1   1   1   9   HS in col
   2   1   1   9   8   2   HS in col
   3   1   1   4   8   5   HS in col
   4   1   1   2   3   5   HS in box
   5   1   1   2   4   9   HS in jigsaw
Naked/Hidden Pairs,Triplets,Quads  | NSS (134567)J1e126789 => (-1367)r4c6 (-1567)r5c5 | NSS (13467)J1e12789 => (-1367)r6c4 | NSS (356)b2e789 => (-6)r1c4 (-6)r1c5 (-6)r1c6 (-6)r2c5 (-6)r2c6 | NSS (5)c4r6 => (-5)r5c4 (-5)r7c4 (-5)r8c4 | NSS (29)b5e35 => (-29)r4c5 (-2)r5c4 (-29)r5c6 | NSS (259)b5e357 => (-5)r5c6 (-5)r6c5 | NSS (5)r6c4 => (-5)r6c1 | NSS (12346789)c6r12456789 => (-36)r3c6
   6   3   1   3   6   5   Naked Single
   7   3   1   6   4   5   Naked Single
   8   3   1   5   1   5   HS in row
Pointing, Claiming  | (8)J2r4 => (-8)r4c5 (-8)r4c9 | (9)J3r8 => (-9)r8c5 (-9)r8c9 | (8)c2b4 => (-8)r4c3 (-8)r5c3 | (8)J2c2 => (-8)r5c2 (-8)r6c2 | (3)J1b7 => (-3)r7c1 (-3)r8c3 (-3)r9c3
   9   5   1   4   2   8   HS in row
Generalized Intersection  | (2)J2r1c3b1 => (-2)r1c3 | (2)r1c5b2 => (-2)r2c5 | (2)r1c6b2 => (-2)r2c6 | (2)b1J2 => (-2)r4c3 | (6)b1r1J2 => (-6)r1c8 | (2)r2c2 => (-2)r5c2 | (2)r4J1 => (-2)r5c5 | (2)r4c6 => (-2)r1c6 | (3)r8c6b8J3 => (-3)r7c6 | (6)b1c3J2 => (-6)r4c3
   10   7   1   1   3   6   Naked Single
   11   7   1   1   8   7   Naked Single
   12   7   1   2   2   2   Naked Single
   13   7   1   4   3   3   Naked Single
   14   7   1   5   5   9   Naked Single
   15   7   1   3   5   3   HS in row
   16   7   1   3   4   6   HS in row
   17   7   1   4   6   2   HS in row
   18   7   1   5   3   2   HS in row
   19   7   1   6   6   3   HS in row
   20   7   1   8   4   3   HS in row
   21   7   1   9   1   3   HS in col
   22   7   1   7   7   3   HS in col
Naked/Hidden Pairs,Triplets,Quads  | NSS (178)b7e369 => (-1)r7c1 (-7)r8c2
   23   9   1   7   3   7   HS in jigsaw
Naked/Hidden Pairs,Triplets,Quads  | NSS (146)J3e348 => (-146)r8c6 (-146)r8c7 | NSS (79)r8c67 => (-7)r8c5 (-7)r8c9
Pointing, Claiming  | (1)J1b3 => (-1)r2c7
Generalized Intersection  | (6)J1r8c8 => (-6)r8c8
2-string-Kite,SkyScraper,TurbotFish  |
Turbot Crane (6) r6c8=r2c8-r8c2=r7c1 => (-6)r6c1 |
2-string Kite (6) r6c8=r7c6-r7c1=r4c1 => (-6)r6c2 |
Turbot Crane (6) r6c8=r7c6-r7c1=r8c2 => (-6)r2c8 |
2-string Kite (7) r5c4=r9c4-r8c6=r8c7 => (-7)r5c7
   24   14   1   2   7   6   HS in row
   25   14   1   6   8   6   HS in col
   26   14   1   8   2   6   HS in jigsaw
   27   15   1   7   1   4   Naked Single
   28   15   1   7   6   1   Naked Single
   29   15   1   8   8   4   Naked Single
   30   15   1   5   6   6   HS in row
   31   15   1   4   1   6   HS in col
   32   15   1   5   7   4   HS in col
   33   15   1   2   8   1   HS in col
   34   15   1   1   9   4   HS in col
   35   15   1   6   1   1   HS in box
   36   15   1   6   2   4   HS in box
   37   15   1   5   2   7   HS in box
   38   16   1   1   6   8   Naked Single
   39   16   1   7   4   2   Naked Single
   40   16   1   1   5   2   HS in row
   41   16   1   9   4   7   HS in col
   42   16   1   5   4   8   HS in col
   43   16   1   4   5   1   HS in col
   44   16   1   2   6   7   HS in col
   45   16   1   9   7   1   HS in col
   46   16   1   5   9   1   HS in col
   47   16   1   6   9   8   HS in col
   48   16   1   1   4   1   HS in box
   49   16   1   2   5   4   HS in box
   50   16   1   6   5   7   HS in box
   51   16   1   8   3   1   HS in box
   52   16   1   9   3   8   HS in box
   53   16   1   9   6   4   HS in box
   54   16   1   8   5   8   HS in box
   55   16   1   8   6   9   HS in box
   56   16   1   8   7   7   HS in box
   57   16   1   9   9   9   HS in box
   58   17   1   4   7   9   Naked Single
   59   17   1   4   9   7   Naked Single
   60   17   1   8   9   5   Naked Single
   61   17   1   9   5   6   Naked Single
   62   17   1   7   5   5   HS in row
   63   17   1   7   9   6   HS in row
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Re: Percent Sudoku

Postby Hajime » Wed Oct 21, 2020 3:16 pm

The last one of 1to9only with ed=4.5 solution is:

#1//B4,JSB
415627893768593214392148657134765928957281346826439571549376182671852439283914765
........1.222...1..222..1...222.1.......1.......1.333...1..333..1...333.1........

Two Nice Loops (X-chain) used.

A possible solution path is:
Hidden Text: Show
Code: Select all
NSS (2345)b6e2457 means:  a naked subset of candidates 2345 in box 6 element 2457
Generalized Intersection (1)r4c1J1 means: candidate 1 is locked in row4 intersecting with c1 and jigsaw 1

two X-Nice-loops used, the first makes use of a jigsaw.

Sol Step Grid Row Col Val Why
   1   1   1   7   6   6   HS in jigsaw
   2   1   1   6   6   9   HS in jigsaw
   3   2   1   2   5   9   HS in row
   4   2   1   8   1   6   HS in row
   5   2   1   6   8   7   HS in jigsaw
   6   2   1   7   8   8   HS in jigsaw
   7   3   1   2   2   6   HS in row
Naked/Hidden Pairs,Triplets,Quads  | NSS (2345)b6e2457 => (-2345)r4c9 (-2345)r5c9
Pointing, Claiming  | (8)J2c3 => (-8)r5c3 | (8)c5b5 => (-8)r4c6 (-8)r5c6 | (8)J1c5 => (-8)r4c5 (-8)r6c5 | (4)b6c8 => (-4)r2c8 | (2)b9c9 => (-2)r1c9 (-2)r2c9 | (9)J1b7 => (-9)r7c1 (-9)r8c3 (-9)r9c3
   8   6   1   6   1   8   HS in row
   9   6   1   8   9   9   HS in row
   10   6   1   5   5   8   HS in col
   11   6   1   4   9   8   HS in col
   12   6   1   5   9   6   HS in box
   13   7   1   4   5   6   HS in row
   14   7   1   6   4   4   HS in row
   15   7   1   1   4   6   HS in col
   16   7   1   1   5   2   HS in col
   17   7   1   9   6   4   HS in col
   18   7   1   2   9   4   HS in col
Pointing, Claiming  | (4)J2r4 => (-4)r4c1 (-4)r4c8 | (4)c8r5 => (-4)r5c1 (-4)r5c2 (-4)r5c3 | (1)c5b8 => (-1)r7c4 (-1)r9c4 | (5)b8c5 => (-5)r6c5 | (7)c5b8 => (-7)r7c4 | (7)b2c6 => (-7)r4c6 (-7)r5c6 | (7)J1b7 => (-7)r7c1 (-7)r7c2 (-7)r8c3
   19   9   1   6   5   3   Naked Single
   20   9   1   6   7   5   Naked Single
   21   9   1   5   8   4   HS in row
   22   9   1   3   8   5   HS in col
   23   10   1   1   9   3   Naked Single
Naked/Hidden Pairs,Triplets,Quads  | NSS (12)r2c78 => (-12)r2c1 (-12)r2c3 (-1)r2c6 | NSS (139)c4r379 => (-1)r4c4 (-1)r5c4 | NSS (2379)c4r4579 => (-3)r3c4 | NSS (157)c6r145 => (-7)r2c6 (-1)r3c6 | NSS (1358)c6r2345 => (-1)r1c6
   24   12   1   1   6   7   Naked Single
   25   12   1   3   4   1   Naked Single
Naked/Hidden Pairs,Triplets,Quads  | NSS (2347)r4c2348 => (-37)r4c1
Pointing, Claiming  | (7)r4J2 => (-7)r2c3 | (7)b1c1 => (-7)r5c1
   26   15   1   2   1   7   HS in row
Generalized Intersection  | (1)r4c1J1 => (-1)r9c1 | (5)r4c1J1 => (-5)r9c1 | (1)c8r8J1 => (-1)r8c2 | (3)J2c3b4 => (-3)r5c3
2-string Kite (2) r3c3=r4c4-r4c8=r2c8 => (-2)r7c3
Nice Loop [6] (2) r2c8-r4c8=r4c4-r3c3=r3c1-r9c1=r2c8 => (-2)r7c1 |
Nice Loop [4] (2) r3c3=r9c3-r9c1=r3c1-r3c3 => (-2)r9c9
   27   19   1   9   9   5   Naked Single
   28   19   1   7   9   2   HS in row
   29   20   1   9   5   1   Naked Single
Naked/Hidden Pairs,Triplets,Quads  | NSS (238)c3r239 => (-3)r4c3 (-3)r8c3 | NSS (157)r8c235 => (-1)r8c8 | NSS (57)r8c25 => (-5)r8c3 | NSS (23)c8r48 => (-2)r2c8 | NSS (3)c8r8 => (-3)r4c8 | NSS (3)b9e5 => (-3)r7c7
   30   22   1   2   8   1   Naked Single
   31   22   1   4   6   5   Naked Single
   32   22   1   4   8   2   Naked Single
   33   22   1   5   6   1   Naked Single
   34   22   1   5   7   3   Naked Single
   35   22   1   7   7   1   Naked Single
   36   22   1   8   2   7   Naked Single
   37   22   1   8   3   1   Naked Single
   38   22   1   8   5   5   Naked Single
   39   22   1   8   8   3   Naked Single
   40   22   1   2   7   2   HS in row
   41   22   1   4   1   1   HS in row
   42   22   1   4   2   3   HS in row
   43   22   1   4   3   4   HS in row
   44   22   1   4   4   7   HS in row
   45   22   1   5   4   2   HS in row
   46   22   1   5   3   7   HS in row
   47   22   1   5   1   9   HS in row
   48   22   1   7   5   7   HS in row
   49   22   1   9   4   9   HS in row
   50   22   1   1   2   1   HS in col
   51   22   1   7   2   4   HS in col
   52   22   1   5   2   5   HS in col
   53   22   1   9   3   3   HS in col
   54   22   1   1   3   5   HS in col
   55   22   1   7   3   9   HS in col
   56   22   1   7   4   3   HS in col
   57   22   1   3   1   3   HS in box
   58   22   1   1   1   4   HS in box
   59   22   1   2   6   3   HS in box
   60   22   1   3   6   8   HS in box
   61   22   1   9   1   2   HS in box
   62   22   1   7   1   5   HS in box
   63   22   1   3   3   2   HS in jigsaw
   64   22   1   2   3   8   HS in jigsaw
User avatar
Hajime
 
Posts: 231
Joined: 20 April 2018
Location: Netherlands

Re: Percent Sudoku

Postby 1to9only » Thu Oct 22, 2020 8:50 am

Hajime wrote:I think ED=9.1 is very high.

I modified SE 1.2.1.3 for this, the SE lack of newer solving methods will end up solving using chains, hence the high ED rating!
In post #1, I've now added the solutions to the puzzles.
1to9only
 
Posts: 2119
Joined: 04 April 2018

Re: Percent Sudoku

Postby urhegyi » Thu Oct 22, 2020 11:44 pm

I found one more percent sudoku I had a lot of difficulties to solve. Can you rate it please?
Code: Select all
.....3.5..2..8.......6.9.13...1.6....1.....2....9.8...28.7.5.......1..9..9.3.....
urhegyi
 
Posts: 96
Joined: 13 April 2020

Re: Percent Sudoku

Postby 1to9only » Fri Oct 23, 2020 7:10 am

urhegyi wrote:I found one more percent sudoku I had a lot of difficulties to solve. Can you rate it please?
Code: Select all
.....3.5..2..8.......6.9.13...1.6....1.....2....9.8...28.7.5.......1..9..9.3.....

My modified SE says the percent sudoku puzzle has multiple solutions.
1to9only
 
Posts: 2119
Joined: 04 April 2018

Re: Percent Sudoku

Postby urhegyi » Fri Oct 23, 2020 8:42 am

1to9only wrote:
urhegyi wrote:I found one more percent sudoku I had a lot of difficulties to solve. Can you rate it please?
Code: Select all
.....3.5..2..8.......6.9.13...1.6....1.....2....9.8...28.7.5.......1..9..9.3.....

My modified SE says the percent sudoku puzzle has multiple solutions.

I contacted the publisher. This should be the correct one(I will give it a second try):
Code: Select all
9....3.58.2..8.....7.6.9213..91.6...81.....29...9.81..2847.5.6.....1..9.19.3....2

This was very easy:
Code: Select all
961273458423581976578649213749126835815437629632958147284795361356812794197364582

I tried to make the original attempt work.
Now I have 4 hopefully correct percent sudokus.
Can you confirm uniqueness and give the rating?
Code: Select all
4....3.5..2..8.......6.9.13...1.6....1.....2....9.8.4728.7.5.......1..9..9.3.....

Code: Select all
7....3.5..2..8.......6.9.13...1.6....1.....2....9.8.4728.7.5.......1..9..9.3.....

Code: Select all
9....3.5..2..8.6.....6.9.13...1.6....1.....2....9.8.4728.7.5.......1..9..9.3.....

Code: Select all
9....3.5..2..8.9.....6.9.13...1.6....1.....2....9.8.4728.7.5.......1..9..9.3.....
Last edited by urhegyi on Fri Oct 23, 2020 11:13 pm, edited 2 times in total.
urhegyi
 
Posts: 96
Joined: 13 April 2020

Re: Percent Sudoku

Postby 1to9only » Fri Oct 23, 2020 9:22 am

After R2C1=6 and R2C3=3, the percent sudoku puzzle has no solution.
The republished percent sudoku is easy.
Code: Select all
9....3.58.2..8.....7.6.9213..91.6...81.....29...9.81..2847.5.6.....1..9.19.3....2 ED=1.5/1.2/1.2

Solution:
Code: Select all
961273458423581976578649213749126835815437629632958147284795361356812794197364582
1to9only
 
Posts: 2119
Joined: 04 April 2018

Re: Percent Sudoku

Postby urhegyi » Fri Oct 23, 2020 11:18 pm

I did some work to correct my percent sudokus from yesterday(with the multiple solutions).
Now I have 4 hopefully correct percent sudokus.
Can you confirm uniqueness and give the rating?
Code: Select all
4....3.5..2..8.......6.9.13...1.6....1.....2....9.8.4728.7.5.......1..9..9.3.....

Code: Select all
7....3.5..2..8.......6.9.13...1.6....1.....2....9.8.4728.7.5.......1..9..9.3.....

Code: Select all
9....3.5..2..8.6.....6.9.13...1.6....1.....2....9.8.4728.7.5.......1..9..9.3.....

Code: Select all
9....3.5..2..8.9.....6.9.13...1.6....1.....2....9.8.4728.7.5.......1..9..9.3.....
urhegyi
 
Posts: 96
Joined: 13 April 2020

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