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tarek
PostPosted: Sat Aug 16, 2008 10:04 am 
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I tested my solver on these, so I've got this non-single moves solutions file hanging around. I'll post it if there is a general interest.

breadth 1st solver Heirarchy:
1.Hidden singles
2.Naked singles
3.Intersections
4.Hidden doubles
5.Naked doubles
6.Naked triples
7.X-wings
8.Hidden triples
9.Naked quads.
10. Hidden quads.

tarek
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Børge
PostPosted: Sat Aug 16, 2008 11:47 am 
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tarek wrote:
I tested my solver on these, so I've got this non-single moves solutions file hanging around. I'll post it if there is a general interest.
I don't know about the general interest, but I am absolutely interested. Want to compare your lists of required techniques with the lists from the solvers I use.

The results are of course dependent on the hierarchy of the solvers and when you switch from one to the next:
  1. Each solver is completely exhausted in sequence, i.e. Hidden Singles - Naked Singles - ... - Hidden Quads - Hidden Singles - ...
  2. A solver is completely exhausted, but if at least one move was found you go back and start with Hidden Singles (unless the current solver is Hidden Singles).
  3. Immediately when a solver finds a single move, you start over with Hidden Singles (unless the current solver is Hidden Singles).

I presume that your solver is still under development and not yet public available?

tarek wrote:
breadth 1st solver Heirarchy:
1.Hidden singles
2.Naked singles
3.Intersections
4.Hidden doubles
5.Naked doubles
6.Naked triples
7.X-wings
8.Hidden triples
9.Naked quads.
10. Hidden quads.
Why have do you have "Hidden singles" before "Naked singles" and "Hidden doubles" before "Naked doubles"?

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tarek
PostPosted: Sat Aug 16, 2008 10:03 pm 
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Børge wrote:
I don't know about the general interest, but I am absolutely interested. Want to compare your lists of required techniques with the lists from the solvers I use.
Great, The next post will have that output.

Børge wrote:
I presume that your solver is still under development and not yet public available?
:lol: , The reason for me laughing is that it has been under development for more than 3 years now, no plans for making it vailable publicly. You just reminded me of how long the period since I started with all of this.

My older solver could solve: Vanilla, Samurai & Sudoku 3D but generate Vanilla only in addition to several operations targeting vanilla puzzles. Almost from scatch, I developed a new solver generator to solve & generate Sudoku variants. I am looking forward for it to be as powerful in solving as my old solver.

Børge wrote:
tarek wrote:
breadth 1st solver Heirarchy:
1.Hidden singles
2.Naked singles
3.Intersections
4.Hidden doubles
5.Naked doubles
6.Naked triples
7.X-wings
8.Hidden triples
9.Naked quads.
10. Hidden quads.
Why have do you have "Hidden singles" before "Naked singles" and "Hidden doubles" before "Naked doubles"?
If you are not using Pencilmarks Then Hidden singles would be much easier to spot than naked singles. The same with Hidden doubles Vs. Naked doubles. That is my limit without using pencilmarks. The idea is to mimic the human solver as much as possible. My question would then be to you, Why Naked singles before hidden singles & hidden doubles before naked doubles?
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tarek
PostPosted: Sat Aug 16, 2008 10:10 pm 
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Apprentice Level Regular Samurai Puzzle 1-15 non-single moves solutions
Code:
breadth 1st solver Heirarchy:
1.Hidden singles
2.Naked singles
3.Intersections
4.Hidden doubles
5.Naked doubles
6.Naked triples
7.X-wings
8.Hidden triples
9.Naked quads.
10. Hidden quads.


Non single moves per puzzle with solutions in line format:
Code:
Apprentice Regular Samurai #1
.78..4.....9.5.8..2..9.....1....62..5...7..98......5..8.539.............3........
.....9......2..4.5.....7.86.....8.7...4.3..6.5.3.........4...38.....12......7....
..............9.......4.........43...2...........8..17.....8......5.........2....
...................6.7.3...1..3.4...7.4..1.2....6.73.1..1.9...792......3.........
...8...1.....23.9........6813...8.....5..4....27.....1.6...7......1.27.3...4....9
3 forms an intersection in g3r1/g3b2
[g3r2c45][g3r3c46]<>3
6 forms an intersection in g3b3/g3r2
[g1r8c789][g3r2c45]<>6
6 forms an intersection in g3r9/g3b8
[g3r7c45][g3r8c56]<>6
4 forms an intersection in g3b3/g3r2
[g1r8c789]<>4
5 forms an intersection in g4b5/g4c5
[g4r123c5]<>5
8 forms an intersection in g4b5/g4c5
[g4r123c5]<>8
2 forms an intersection in g1b9/g1c9
[g1r12c9]<>2
3 forms an intersection in g3b7/g3c2
[g1r8c8][g3r6c2]<>3
5 forms an intersection in g3b3/g3r1
[g3r1c56]<>5
6 forms an intersection in g3b1/g3r1
[g3r1c56]<>6
6 forms an intersection in g3c5/g3b5
[g3r456c4][g3r56c6]<>6
1 forms an intersection in g4b8/g4c4
[g4r12c4]<>1
2 forms an intersection in g4b2/g4r1
[g4r1c13]<>2
4 forms an intersection in g4b7/g4c2
[g4r12c2]<>4
4 forms an intersection in g4b8/g4c4
[g4r12c4]<>4
4 forms an intersection in g4b9/g4c7
[g3r79c1]<>4
4 forms an intersection in g3b7/g3c3
[g1r7c9][g3r56c3]<>4
6 forms an intersection in g4b8/g4c6
[g4r12c6]<>6
7 forms an intersection in g5b3/g5c9
[g5r45c9]<>7
8 forms an intersection in g5b9/g5c8
[g5r56c8]<>8
8 forms an intersection in g5c3/g5b7
[g5r8c12]<>8
4 forms an intersection in g1b9/g1r7
[g1r7c2]<>4
4 forms an intersection in g1b8/g1c5
[g1r6c5]<>4
6 forms an intersection in g1b9/g1r7
[g1r7c2]<>6
8 forms an intersection in g3b9/g3r8
[g3r8c3]<>8
8 forms an intersection in g4b3/g4r3
[g4r3c13]<>8
9 forms an intersection in g4b6/g4r4
[g4r4c2]<>9
5 forms an intersection in g5b7/g5r8
[g5r8c8]<>5
37 is a hidden double in g5r5
[g5r5c4]<>2<>6 [g5r5c8]<>2
9 forms an intersection in g3b9/g3r9
[g3r9c1234]<>9
5 forms an intersection in g4r3/g4b3
[g3r7c123]<>5
5 forms an intersection in g3b5/g3r5
[g3r5c13]<>5
46 is a hidden double in g3c1
[g1r7c7]<>1 [g3r6c1]<>3<>9
58 is a hidden double in g3c1
[g3r4c1]<>1<>7 [g3r9c1]<>1
157 is a naked triple in g3c2
[g1r7c8]<>1 [g3r7c2]<>1<>7 [g3r8c2]<>7
Puzzle Solved
 Solution:
678234159439751826251968734193586247524173698786429513815397462962845371347612985
456189723987263415321547986219658374874932561563714892795426138648391257132875649
462831795371259648985647132857164329123795864649382517734918256296573481518426973
518269734473815296269743518156324879734981625892657341381592467925476183647138952
256879314481623597973541268134258976695714832827396451362987145549162783718435629


Apprentice Regular Samurai #2
...2.4...7.9.6......3..9586....4.....32..5.7..9.3....19.152.....2..9.............
...9.7.5......5..12..6..4.......91.8.8...2.46.694...7....53......................
....7................31.....78......2...5..9......7.81............6.........2....
39.........5.6....8..5.......9.2.....41.9...86..15..2......149...2.....5.........
....974.8...13.5...........8.2........6.5........438.92.13.........16.3..........
5 forms an intersection in g3b7/g3r7
[g3r7c789]<>5
1 forms an intersection in g3r8/g3b7
[g3r79c123]<>1
5 forms an intersection in g2r4/g2b4
[g2r5c13][g2r6c1]<>5
8 forms an intersection in g3b1/g3c1
[g3r78c1]<>8
4 forms an intersection in g1r7/g1b9
[g1r8c789][g1r9c79]<>4
4 forms an intersection in g3b1/g3r1
[g2r7c123][g3r1c6]<>4
9 forms an intersection in g3b3/g3c7
[g3r89c7]<>9
7 forms an intersection in g2r7/g2b9
[g2r89c79]<>7
8 forms an intersection in g1b9/g1c7
[g1r456c7]<>8
8 forms an intersection in g3b9/g3c9
[g2r789c3]<>8
9 forms an intersection in g3r7/g3b8
[g3r8c5][g3r9c46]<>9
9 forms an intersection in g4b2/g4r2
[g3r8c13]<>9
7 forms an intersection in g3b9/g3r9
[g3r9c134]<>7
7 forms an intersection in g5b5/g5r4
[g5r4c279]<>7
3 forms an intersection in g2b7/g2r8
[g2r8c79]<>3
5 forms an intersection in g2b7/g2r9
[g2r9c79]<>5
8 forms an intersection in g2b7/g2c1
[g2r12c1]<>8
2 forms an intersection in g5b8/g5r9
[g5r9c79]<>2
2 forms an intersection in g2b8/g2c4
[g2r2c4]<>2
9 forms an intersection in g2b7/g2c1
[g2r2c1]<>9
2 forms an intersection in g3b3/g3c9
[g3r4c9]<>2
4 forms an intersection in g5b4/g5c2
[g5r7c2]<>4
5 forms an intersection in g5b6/g5r4
[g5r4c2]<>5
7 forms an intersection in g5b6/g5r5
[g5r5c2]<>7
67 is a hidden double in g5r4
[g5r4c4]<>9
24 is a hidden double in g2c5
[g2r1c5]<>1<>8 [g2r2c5]<>8
1 forms an intersection in g2b2/g2r3
[g2r3c3]<>1
34 is a naked double in g2c2
[g2r2c2]<>3<>4 [g2r3c2]<>3 [g2r9c2]<>4
34 is a hidden double in g3c8
[g3r4c8]<>5
34 is a naked double in g3r4
[g3r4c4]<>4 [g3r4c5]<>4 [g3r4c6]<>3<>4 [g3r4c7]<>3 [g3r4c9]<>4
Puzzle Solved
 Solution:
168254793759863412243179586817942365432615978695387241971526834326498157584731629
631947852498325761275618493524769138783152946169483275912534687346871529857296314
834576912157982346629314857478169235216853794395247681542798163781635429963421578
396718542425963781817542963539826174241397658678154329753281496162479835984635217
163597428429138576578462913842679351396851742715243869251384697984716235637925184


Apprentice Regular Samurai #3
.........523......9....5.......9...32817....9.7...2.4...7.6.1......7.............
.......7..6...3.25....4.9...1...8...3..129.....9....68..8.5..........84..........
1..7....8............89....83.2.......9..5.7.2...4.1.....97...4.........9.2......
.8.........9......3..7..9.2..3.....9591..26......6.2....6..71...745......3..8....
..4...................8.1.9.....25..5.8...74...9..3.68..19....26...7............4
5 forms an intersection in g3r3/g3b1
[g1r7c89][g1r8c789]<>5
3 forms an intersection in g3b1/g3c1
[g3r78c1]<>3
2 forms an intersection in g1c9/g1b3
[g1r13c78]<>2
1 forms an intersection in g2b7/g2c3
[g2r123c3]<>1
2 forms an intersection in g3c8/g3b3
[g2r89c3]<>2
5 forms an intersection in g1b9/g1r9
[g1r9c234]<>5
6 forms an intersection in g1b1/g1r3
[g1r3c789]<>6
9 forms an intersection in g1b2/g1c4
[g1r789c4]<>9
1 forms an intersection in g1b1/g1c2
[g1r89c2]<>1
3 forms an intersection in g1b9/g1c7
[g1r13c7]<>3
4 forms an intersection in g1b4/g1r4
[g1r4c46]<>4
8 forms an intersection in g1b9/g1r8
[g1r8c46]<>8
9 forms an intersection in g1b9/g1c8
[g1r12c8]<>9
1 forms an intersection in g4b7/g4c1
[g4r12c1]<>1
3 forms an intersection in g4b3/g4c9
[g4r56c9]<>3
7 forms an intersection in g5b9/g5c8
[g5r12c8]<>7
3 forms an intersection in g3b3/g3c8
[g3r6c8]<>3
9 forms an intersection in g3b3/g3c8
[g3r6c8]<>9
6 forms an intersection in g5b9/g5c7
[g5r1c7]<>6
79 is a hidden double in g3c6
[g3r4c6]<>1<>6 [g3r6c6]<>3<>6<>8
6 forms an intersection in g4b3/g4r2
[g4r2c1246]<>6
6 forms an intersection in g1b9/g1r8
[g1r8c123]<>6
68 is a hidden double in g3c3
[g3r8c3]<>7
Puzzle Solved
 Solution:
714986532523417986968325417645198273281734659379652841857263194492571368136849725
843592671967813425152746983514678239386129754279435168628954317795361842431287596
194753628368421795725896431831267549649185273257349186513972864476538912982614357
487629513219358476365714982623175849591842637748963251856237194174596328932481765
864129357912537486357486129736842591528691743149753268471965832683274915295318674


Apprentice Regular Samurai #4
.8.4...2957.....1......74...5.9.2.....76...8......49...............28...64.......
..4.....6.8..9.2.....7.8..5.......3.157........2.4...1...6.1.7......9.6..........
....8.........2......9........4.69...6.1.8.5...9.25.4....2.........64............
3.6.......1.6.....87.4.1.....15...6.........7....2.8.37.4..52....3.1.6.........5.
......4.1...98...7.....1.....7...9...4...5.6....34.8...8..5..7.9..4..3..7........
2 forms an intersection in g2b7/g2r9
[g2r9c45689]<>2
3 forms an intersection in g1c2/g1b7
[g1r78c13]<>3
1 forms an intersection in g1b1/g1c1
[g1r78c1]<>1
4 forms an intersection in g2b2/g2r2
[g2r2c89]<>4
7 forms an intersection in g3b9/g3c8
[g2r89c2]<>7
8 forms an intersection in g2b7/g2r8
[g2r8c4579]<>8
3 forms an intersection in g2b3/g2c7
[g2r789c7]<>3
3 forms an intersection in g3b8/g3r7
[g3r7c789]<>3
6 forms an intersection in g5b1/g5r1
[g5r1c456]<>6
3 forms an intersection in g2b4/g2r6
[g2r6c46]<>3
9 forms an intersection in g2b7/g2r7
[g2r7c79]<>9
5 forms an intersection in g3b2/g3r2
[g2r8c13]<>5
6 forms an intersection in g4b7/g4c2
[g4r56c2]<>6
1 forms an intersection in g5b6/g5c8
[g5r89c8]<>1
1 forms an intersection in g5r8/g5b7
[g5r79c3][g5r9c2]<>1
6 forms an intersection in g5b5/g5r4
[g5r4c12]<>6
1 forms an intersection in g2b1/g2r3
[g2r3c5]<>1
5 forms an intersection in g4c3/g4b1
[g4r1c2]<>5
2 forms an intersection in g5b1/g5r2
[g5r2c8]<>2
3 forms an intersection in g5b1/g5r2
[g5r2c8]<>3
57 is a hidden double in g5c4
[g5r1c4]<>2 [g5r3c4]<>6
3 forms an intersection in g5b2/g5r1
[g5r1c8]<>3
15 is a hidden double in g5r8
[g5r8c2]<>2<>6 [g5r8c3]<>2<>6
17 is a hidden double in g3r1
[g3r1c6]<>3
19 is a naked double in g4r6
[g4r6c6]<>9
689 is a naked triple in g2r4
[g2r4c4]<>8<>9 [g2r4c5]<>6<>8 [g2r4c6]<>6 [g2r4c7]<>6<>8<>9
6 forms an intersection in g2r4/g2b4
[g2r6c12]<>6
26 is a hidden double in g2c2
[g2r3c2]<>1<>3<>9 [g2r9c2]<>1<>3
9 forms an intersection in g2b1/g2c1
[g2r46c1]<>9
58 is a hidden double in g3r9
[g3r9c4]<>7
Puzzle Solved
 Solution:
386415729574269318129387465853972146497631582261854973918546237735128694642793851
274315986583496217961728345649152738157863429832947651495631872318279564726584193
237681495694752318851943726512476983463198257789325641148237569975864132326519874
396257148412683975875491326931578462628349517547126893784965231253714689169832754
569732481132984657874561239317628945248195763695347812483259176951476328726813594


Apprentice Regular Samurai #5
.2..........1......5.8....77.8.9..1....7......69.4..8...7......64..23............
...5....36......2....37...1..8..9..7.1...2...9......6.....54.........5.8...8.....
.....3........4.......72...6.1.8..3.9...316...3.4.9.81.....5.....................
.....4.............9..8.....4...9.3.5...78.....9.6...1...1...5..526.......1......
.............19..........84.....4..648.1.....3296...4...1..3.......9.732.....689.
6 forms an intersection in g4r1/g4b1
[g4r2c123][g4r3c13]<>6
9 forms an intersection in g3c8/g3b3
[g2r789c3]<>9
8 forms an intersection in g1r8/g1b9
[g1r9c79]<>8
7 forms an intersection in g2b5/g2c4
[g2r78c4]<>7
1 forms an intersection in g3b1/g3c1
[g3r78c1]<>1
4 forms an intersection in g2b2/g2r2
[g2r2c2379]<>4
9 forms an intersection in g2b2/g2r2
[g2r2c2379]<>9
4 forms an intersection in g1b4/g1r5
[g1r5c789]<>4
4 forms an intersection in g2b3/g2c7
[g2r456c7]<>4
2 forms an intersection in g3b5/g3c4
[g3r789c4]<>2
4 forms an intersection in g3b3/g3r3
[g1r9c789]<>4
5 forms an intersection in g3b3/g3r3
[g1r9c789]<>5
3 forms an intersection in g4b3/g4c9
[g4r789c9]<>3
8 forms an intersection in g4b3/g4r1
[g4r1c123]<>8
2 forms an intersection in g1b2/g1c6
[g1r45c6]<>2
4 forms an intersection in g1b9/g1r7
[g1r7c46]<>4
1 forms an intersection in g2c6/g2b2
[g2r2c45]<>1
2 forms an intersection in g2r9/g2b9
[g2r7c79]<>2
2 forms an intersection in g3b1/g3r1
[g2r7c23]<>2
6 forms an intersection in g2b3/g2c7
[g2r79c7]<>6
7 forms an intersection in g2b7/g2r7
[g2r7c78]<>7
9 forms an intersection in g2b7/g2c2
[g2r13c2]<>9
5 forms an intersection in g3b5/g3c4
[g3r12c4]<>5
9 forms an intersection in g4b8/g4c5
[g4r12c5]<>9
2 forms an intersection in g5b7/g5r9
[g5r9c45]<>2
5 forms an intersection in g5b8/g5r9
[g5r9c13]<>5
5 forms an intersection in g5c1/g5b1
[g3r8c8][g3r9c9]<>5
7 forms an intersection in g5b7/g5r9
[g5r9c45]<>7
8 forms an intersection in g1b1/g1c1
[g1r9c1]<>8
9 forms an intersection in g1b1/g1c1
[g1r9c1]<>9
8 forms an intersection in g2b5/g2c5
[g2r2c5]<>8
5 forms an intersection in g3b9/g3c7
[g3r6c7]<>5
5 forms an intersection in g3r6/g3b4
[g3r45c2][g3r5c3]<>5
Puzzle Solved
 Solution:
826437591973152846451869237738295614514786923269341785397618452645923178182574369
479521683631948725582376491268439157715682934943715862897254316326197548154863279
452613897178954326369872154621587439984231675735469281893145762217396548546728913
167524893485936217293781546748219635516378924329465781674192358852643179931857462
762348519548219673913567284175984326486132957329675148891723465654891732237456891


Apprentice Regular Samurai #6
....72...6......58...5.971...1.....64.5..31..9..6.4...34..2.....1.............4..
............435.86.....631...7....6.1...4..7...2.91.......6.....2......9.9.2.....
............6.8.2.4......9..43....7.........8...4.12.......6.....9.3.......2.7...
..9.......3..4...9.2..9......7..8.....45..82.6..3.......5.8296..9..7.............
.......4....3....6...75............33....289.....6.1.4.2...6.5.8.9.1.....6.......
3 forms an intersection in g4b4/g4c1
[g4r789c1]<>3
4 forms an intersection in g4b3/g4c9
[g4r689c9]<>4
4 forms an intersection in g4r7/g4b7
[g4r89c1][g4r9c2]<>4
5 forms an intersection in g2b5/g2r4
[g2r4c1279]<>5
2 forms an intersection in g1b9/g1r9
[g1r9c123]<>2
3 forms an intersection in g1b2/g1r2
[g1r2c237]<>3
7 forms an intersection in g2b7/g2c1
[g2r123c1]<>7
8 forms an intersection in g2r8/g2b8
[g2r7c4][g2r9c56]<>8
1 forms an intersection in g3b1/g3c3
[g3r579c3]<>1
1 forms an intersection in g4c9/g4b9
[g4r8c78][g4r9c8]<>1
7 forms an intersection in g1b9/g1c9
[g1r56c9]<>7
1 forms an intersection in g2b2/g2r1
[g2r1c23]<>1
2 forms an intersection in g3b1/g3r3
[g3r3c56]<>2
3 forms an intersection in g3b5/g3r5
[g3r5c78]<>3
3 forms an intersection in g3c7/g3b3
[g2r7c23][g2r8c3]<>3
3 forms an intersection in g2b7/g2c1
[g2r146c1]<>3
5 forms an intersection in g3r9/g3b7
[g3r7c12]<>5
7 forms an intersection in g3b1/g3c3
[g3r56c3]<>7
5 forms an intersection in g4b3/g4r3
[g4r3c16]<>5
8 forms an intersection in g4r2/g4b1
[g4r13c1]<>8
8 forms an intersection in g5b1/g5c2
[g5r46c2]<>8
4 forms an intersection in g1b2/g1r2
[g1r2c3]<>4
5 forms an intersection in g1b5/g1r4
[g1r4c7]<>5
8 forms an intersection in g3b9/g3c8
[g2r7c2]<>8
8 forms an intersection in g2b7/g2c1
[g2r1346c1]<>8
9 forms an intersection in g3b2/g3r1
[g1r7c7]<>9
9 forms an intersection in g1b9/g1r8
[g1r8c345]<>9
1 forms an intersection in g5b2/g5c6
[g5r4c6]<>1
39 is a naked double in g1c8
[g1r5c8]<>9 [g1r6c8]<>3 [g1r9c8]<>3
3 forms an intersection in g1b9/g1r8
[g1r8c45]<>3
3 forms an intersection in g3b1/g3r2
[g2r8c1]<>3
38 is a hidden double in g2c1
[g2r7c1]<>4<>5<>7 [g2r9c1]<>5<>7
Puzzle Solved
 Solution:
154872639679341258823569714731258946465793182982614573347925861216487395598136427
634817295219435786578926314987352461153648972462791538345169827721583649896274153
861729345395648721427315896543862179712953468986471253234586917679134582158297634
179856234538241679426793158957428316314569827682317495745182963293674581861935742
917628345582394716634751289241987563356142897798563124423876951879415632165239478


Apprentice Regular Samurai #7
...74...8.2.1.............3.5...4....68.9.1..4.....5..5..26....6.........3.5.....
............869.4.2.....61......62....8..7....21...38........34....9........2.1..
...8........1..............43.....7..2..4...65..7.3.81.............81........9...
.....3...4..18.................7..82..2..9.....78....97..3.8....9...563.25.......
.............6.7.3....8..5.2....1....4...5.....684...1..5.26.........3..8...3.54.
1 forms an intersection in g2b7/g2r7
[g2r7c456]<>1
5 forms an intersection in g3b9/g3r8
[g3r8c234]<>5
1 forms an intersection in g1b3/g1c8
[g1r79c8]<>1
4 forms an intersection in g4c6/g4b5
[g4r45c4][g4r56c5]<>4
Puzzle Solved
 Solution:
315742968926183475847956213153624897768395124492817536571268349689431752234579681
456132879137869542289574613574386291398217456621945387712658934863491725945723168
349865712752194863681372945438516279127948356596723481215437698973681524864259137
876943215425186973931257864519674382382519746647832159764398521198425637253761498
698753214524169783137284659283691475941375862756842931375426198469518327812937546


Apprentice Regular Samurai #8
1.......4...27.9...2..5...7.57...........83...38....9..............47.....3..1...
.3............1...8...7..3.6.2.....1.59..7..2.....9..6....8.2......6.........4.8.
..............2..............4..5..2.....1..92.8.3.4.7.............43....7.29....
....9.........5...2.6..4.7......2.8...94.....56..7.2.4....3...7.51..84.3.3.1.....
............94........7.58...3....4..7.2...655...1.........16..4....9..2.69.5..7.
2 forms an intersection in g1b9/g1r7
[g1r7c1356]<>2
4 forms an intersection in g3r2/g3b3
[g2r7c23]<>4
9 forms an intersection in g3b1/g3c3
[g3r8c3]<>9
2 forms an intersection in g4b9/g4c8
[g3r8c2]<>2
8 forms an intersection in g3b3/g3r2
[g1r8c78][g3r2c45]<>8
1 forms an intersection in g5c8/g5b3
[g5r12c79]<>1
6 forms an intersection in g3c7/g3b6
[g3r456c8]<>6
3 forms an intersection in g2b6/g2c7
[g2r89c7]<>3
3 forms an intersection in g3b7/g3c1
[g3r45c1]<>3
3 forms an intersection in g3c9/g3b3
[g2r78c1]<>3
6 forms an intersection in g3b9/g3c9
[g2r79c3]<>6
6 forms an intersection in g2b7/g2c2
[g2r23c2]<>6
7 forms an intersection in g3b9/g3c7
[g2r78c1]<>7
7 forms an intersection in g2b7/g2c2
[g2r246c2]<>7
7 forms an intersection in g2b4/g2r6
[g2r6c78]<>7
8 forms an intersection in g3b5/g3r4
[g3r4c78]<>8
3 forms an intersection in g4b3/g4c7
[g4r45c7]<>3
7 forms an intersection in g5b8/g5c4
[g5r46c4]<>7
1 forms an intersection in g1b4/g1r5
[g1r5c5]<>1
5 forms an intersection in g1b3/g1c8
[g1r8c8]<>5
5 forms an intersection in g3b1/g3c1
[g3r5c1]<>5
1 forms an intersection in g3b6/g3c8
[g2r789c2][g3r789c8]<>1
3 forms an intersection in g3b4/g3c2
[g1r8c8]<>3
3 forms an intersection in g1b9/g1c9
[g1r2c9]<>3
2 forms an intersection in g4b8/g4r8
[g4r8c8]<>2
1 forms an intersection in g5b7/g5r8
[g5r8c7]<>1
7 forms an intersection in g5b1/g5c1
[g5r7c1]<>7
47 is a hidden double in g1c7
[g1r7c7]<>1<>5 [g1r9c7]<>5
1 forms an intersection in g1c7/g1b6
[g1r4c9]<>1
48 is a hidden double in g2r8
[g2r8c2]<>7<>9 [g2r8c3]<>1<>3
7 forms an intersection in g3r2/g3b2
[g3r13c456]<>7
8 forms an intersection in g5b7/g5r7
[g5r7c4]<>8
67 is a hidden double in g2c2
[g2r7c2]<>9 [g2r9c2]<>9
6 forms an intersection in g4b3/g4r2
[g4r2c45]<>6
Puzzle Solved
 Solution:
176893254385274916924156837657932148219468375438715692761589423892347561543621789
137896425495321678826475139642538791359617842718249356571983264984762513263154987
423869571561372984789154263194785632637421859258936417842617395916543728375298146
175693842843725916296814375417352689329486751568971234684539127751268493932147568
395186724728945316146372589613597248974238165582614937857421693431769852269853471


Apprentice Regular Samurai #9
35..2..........7..7..59..2....7.....8...1.3..24...38.6..........28..........4..5.
..951..3.4.....1.22............74...6.....8......913.......7..1.....5.7..........
....3........8.....5.1......1..26......4..1....5..9..7.....1..........9......27..
..........39..........7.....8...43..9..76......5.3.97..2........485.2.....1.....5
........1.9...4...7..2...3.4.7.....6.5..71.9..............57..4.....89....819..2.
8 forms an intersection in g2b5/g2c4
[g2r2378c4]<>8
6 forms an intersection in g2b5/g2c4
[g2r2378c4]<>6
2 forms an intersection in g4b4/g4r4
[g4r4c4589]<>2
6 forms an intersection in g5c5/g5b2
[g5r1c46][g5r2c4][g5r3c6]<>6
5 forms an intersection in g3b3/g3r1
[g3r1c46]<>5
4 forms an intersection in g4b3/g4r1
[g4r1c345]<>4
8 forms an intersection in g4b5/g4c6
[g4r1237c6]<>8
1 forms an intersection in g1b9/g1r7
[g1r7c123]<>1
2 forms an intersection in g1b6/g1c9
[g1r79c9]<>2
5 forms an intersection in g2b7/g2r7
[g2r7c78]<>5
7 forms an intersection in g2b6/g2c9
[g2r13c9]<>7
2 forms an intersection in g3b1/g3c1
[g3r56c1]<>2
2 forms an intersection in g5b3/g5r2
[g3r8c79]<>2
2 forms an intersection in g3b9/g3r7
[g3r7c23]<>2
26 is a hidden double in g3c3
[g3r5c3]<>8<>9 [g3r8c3]<>1<>8
1 forms an intersection in g1b6/g1c8
[g1r12c8]<>1
2 forms an intersection in g2b7/g2c3
[g2r46c3]<>2
8 forms an intersection in g5b1/g5c2
[g5r46c2]<>8
9 forms an intersection in g1b9/g1c7
[g1r1c7]<>9
6 forms an intersection in g2b7/g2c3
[g2r2c3]<>6
8 forms an intersection in g3r8/g3b8
[g3r7c4]<>8
47 is a hidden double in g2c3
[g2r6c3]<>8
26 is a naked double in g2r9
[g2r9c6]<>6 [g2r9c7]<>2<>6 [g2r9c8]<>2<>6 [g2r9c9]<>6
Puzzle Solved
 Solution:
359627184462831795781594623613782549895416372247953816534278961928165437176349258
769512438458736192231948765183674259694253817527891346845367921912485673376129584
961237845437685912258194376319726458672458139845319627584971263726843591193562784
176329584839145726254876193782954361913768452465231978527613849348592617691487235
263789541591364278784215639417932856356871492829546317932657184175428963648193725


Apprentice Regular Samurai #10
.83....9....19.64.......1...9........5.9..4.78....3..............8..5....65.2....
.....28.......4....6.7..5.4..7.4..9......3..26...9...3.....1......3...2....67....
...7.9........5.......4..........8.........69.42896........7..5............92....
.9.......6....8....7...6.........3...8..51.....63...49...4......5.....732...8.6..
..5.........7....1.....42..3.....8....293.6...74..81.....4...8.........9.4..5...2
9 forms an intersection in g2r7/g2b9
[g2r89c79]<>9
6 forms an intersection in g3r9/g3b9
[g3r78c7][g3r8c9]<>6
4 forms an intersection in g4b5/g4r4
[g4r4c123]<>4
9 forms an intersection in g5b6/g5c8
[g5r123c8]<>9
7 forms an intersection in g2b7/g2r8
[g2r8c79]<>7
2 forms an intersection in g3r1/g3b1
[g1r8c78]<>2
5 forms an intersection in g3b1/g3r1
[g2r7c12]<>5
5 forms an intersection in g2c6/g2b8
[g2r8c5]<>5
3 forms an intersection in g1b9/g1r8
[g1r8c1245]<>3
3 forms an intersection in g3c3/g3b4
[g3r45c2][g3r56c1]<>3
1 forms an intersection in g3b3/g3r3
[g1r9c89]<>1
9 forms an intersection in g3b7/g3r8
[g3r8c78]<>9
3 forms an intersection in g3b9/g3c8
[g3r6c8]<>3
9 forms an intersection in g2r3/g2b1
[g2r12c123]<>9
7 forms an intersection in g4r6/g4b5
[g4r4c56][g4r5c4]<>7
7 forms an intersection in g5b5/g5c6
[g5r789c6]<>7
6 forms an intersection in g1b9/g1r8
[g1r8c45]<>6
5 forms an intersection in g4b3/g4r3
[g4r3c34]<>5
7 forms an intersection in g4b3/g4r2
[g4r2c45]<>7
8 forms an intersection in g4b3/g4r1
[g4r1c13]<>8
8 forms an intersection in g4b9/g4r7
[g4r7c13]<>8
9 forms an intersection in g4b3/g4r2
[g4r2c45]<>9
3 forms an intersection in g5b1/g5c2
[g5r78c2]<>3
5 forms an intersection in g5c7/g5b9
[g5r7c9][g5r8c8]<>5
6 forms an intersection in g5b4/g5r4
[g5r4c46]<>6
2 forms an intersection in g4b6/g4r5
[g4r5c4]<>2
34 is a hidden double in g4r5
[g4r5c1]<>7<>9 [g4r5c3]<>7<>9
2 forms an intersection in g4c4/g4b2
[g4r1c6][g4r2c5]<>2
7 forms an intersection in g4b4/g4r4
[g4r4c9]<>7
29 is a hidden double in g5c8
[g5r4c8]<>5<>7 [g5r6c8]<>3<>5
48 is a hidden double in g4r8
[g4r8c1]<>1<>9 [g4r8c3]<>1<>9
29 is a hidden double in g2r3
[g2r3c1]<>1 [g2r3c3]<>1<>3
68 is a hidden double in g3r7
[g3r7c2]<>1<>2 [g3r7c3]<>1
79 is a hidden double in g4c1
[g4r7c1]<>1
1 forms an intersection in g4b7/g4c3
[g4r123c3]<>1
12 is a naked double in g3r4
[g3r4c2]<>1 [g3r4c3]<>1 [g3r4c4]<>1
15 is a naked double in g4c9
[g3r8c3]<>1 [g4r7c9]<>1
5 forms an intersection in g3b6/g3r6
[g3r6c1]<>5
Puzzle Solved
 Solution:
183456792572198643649237185297514836356982417814673259731869524928745361465321978
143952876758164239269738514837246195495813762612597483386421957974385621521679348
524719386361285974978643521659371842813452769742896153286137495197564238435928617
193745286645238197872196435729864351384951762516327849961473528458612973237589614
495312768238765941617894235369541827182937654574628193921473586753286419846159372


Apprentice Regular Samurai #11
..5..2...9.8...........6.18...2.7.......1.7.41.74...6......3...8.4......69...4...
.4.65......7.8..........8.9..4..1..2....9.4.56.93....1.....85..........7...4..2..
.....5......27..............1.7..6.87.9.3.5.......1..9............3.........17...
..2......1...2......6..4...4.....19....3.72....5.1.......23..5..79..5.......7...8
...4..9.....6...8..............645...2.35...4......87.9.......1.74.1...8.....7.3.
4 forms an intersection in g3b1/g3r1
[g2r7c1][g3r1c45]<>4
7 forms an intersection in g3c9/g3b9
[g3r78c7]<>7
9 forms an intersection in g3b9/g3c8
[g2r79c2]<>9
2 forms an intersection in g2r1/g2b1
[g2r23c1][g2r3c23]<>2
3 forms an intersection in g3r1/g3b3
[g2r89c3][g2r9c12]<>3
5 forms an intersection in g5c1/g5b7
[g5r79c23]<>5
6 forms an intersection in g5c1/g5b7
[g5r79c23]<>6
8 forms an intersection in g1c6/g1b5
[g1r46c5][g1r5c4]<>8
2 forms an intersection in g3b3/g3r1
[g1r7c789]<>2
3 forms an intersection in g5b6/g5c9
[g5r123c9]<>3
9 forms an intersection in g5b5/g5r6
[g5r6c239]<>9
1 forms an intersection in g1b1/g1c2
[g1r78c2]<>1
2 forms an intersection in g1b9/g1r9
[g1r9c35]<>2
6 forms an intersection in g1b1/g1c2
[g1r45c2]<>6
2 forms an intersection in g2b7/g2r7
[g2r7c45]<>2
2 forms an intersection in g3b7/g3r9
[g3r9c79]<>2
9 forms an intersection in g3b7/g3c1
[g1r78c7]<>9
9 forms an intersection in g1b9/g1c8
[g1r145c8]<>9
4 forms an intersection in g4r7/g4b7
[g4r9c23]<>4
5 forms an intersection in g4b6/g4c9
[g3r89c3]<>5
5 forms an intersection in g3b7/g3c1
[g1r89c7][g3r46c1]<>5
1 forms an intersection in g5b1/g5r2
[g5r2c67]<>1
1 forms an intersection in g5b5/g5r6
[g5r6c23]<>1
8 forms an intersection in g5b1/g5c1
[g5r49c1]<>8
3 forms an intersection in g2b7/g2r7
[g2r7c5]<>3
2 forms an intersection in g5b5/g5r6
[g5r6c9]<>2
9 forms an intersection in g5b1/g5c2
[g5r4c2]<>9
56 is a hidden double in g5c1
[g5r8c1]<>2<>3 [g5r9c1]<>1<>2
2 forms an intersection in g5b7/g5c3
[g3r78c9]<>2
3 forms an intersection in g3c9/g3b9
[g3r79c78]<>3
5 forms an intersection in g1r9/g1b8
[g1r7c45][g1r8c456]<>5
5 forms an intersection in g1b9/g1r8
[g1r8c2]<>5
3 forms an intersection in g4b7/g4r9
[g4r9c7]<>3
4 forms an intersection in g4b9/g4c7
[g4r6c7]<>4
6 forms an intersection in g4b3/g4r2
[g4r2c6]<>6
8 forms an intersection in g4b7/g4r7
[g4r7c6]<>8
16 is a hidden double in g1c2
[g1r1c2]<>3<>4<>7 [g1r2c2]<>2<>3<>4<>7
2 forms an intersection in g1b1/g1r3
[g1r3c7]<>2
69 is a hidden double in g1c3
[g1r4c3]<>3 [g1r5c3]<>2<>3
26 is a hidden double in g3b5
[g3r6c5]<>4<>5
268 is a naked triple in g3c2
[g1r7c8]<>8 [g3r6c2]<>2<>6
26 is a hidden double in g3r6
[g3r6c1]<>4
267 is a hidden triple in g1r8
[g1r8c2]<>3 [g1r8c4]<>1<>9 [g1r8c5]<>9
Puzzle Solved
 Solution:
715382649968541372432796518549267831386915724127438965251873496874629153693154287
248659173397182654165734829574861392813297465629345781732918546486523917951476238
496185732153279486287463951315794628729836514648521379571948263864352197932617845
942683571153729864786154932427568193618397245395412687864231759279845316531976428
263485917197632485845179326381764592729358164456291873938526741674913258512847639


Apprentice Regular Samurai #12
3...1...2..9..........2.93..2..37..8......5..51..8..9.1....6..7..6..1.....5.....9
..........82...7..4.....9.1..7...235.....1...96..2..7...............54....34..6.2
..79.........7......9.....3............62.....96...54....8..........3....6379....
.....1...95..7......24...6389.............7...3.98....2.95...........4.7.75.4..3.
....9...4..............76....6.....1...539.7.......2....7...9.8.2...3......27..1.
2 forms an intersection in g3b1/g3r2
[g2r8c12][g3r2c6]<>2
3 forms an intersection in g5b9/g5r9
[g5r9c123]<>3
4 forms an intersection in g5b9/g5c7
[g5r45c7]<>4
2 forms an intersection in g1b9/g1r8
[g1r8c4]<>2
4 forms an intersection in g5b1/g5c1
[g5r456789c1]<>4
4 forms an intersection in g1b9/g1r8
[g1r8c1245]<>4
7 forms an intersection in g3c9/g3b6
[g3r45c78]<>7
9 forms an intersection in g2b1/g2r1
[g2r1c456]<>9
9 forms an intersection in g2b7/g2r8
[g2r8c589]<>9
8 forms an intersection in g3b3/g3c7
[g3r459c7]<>8
8 forms an intersection in g5b1/g5r3
[g5r3c458]<>8
4 forms an intersection in g1c9/g1b6
[g1r5c8][g1r6c7]<>4
1 forms an intersection in g2b1/g2r1
[g2r1c45]<>1
5 forms an intersection in g2b7/g2c2
[g2r13c2]<>5
7 forms an intersection in g2b7/g2r9
[g2r9c56]<>7
5 forms an intersection in g3b3/g3c8
[g3r78c8]<>5
6 forms an intersection in g3b3/g3c7
[g3r78c7]<>6
1 forms an intersection in g5b5/g5r6
[g5r6c12]<>1
3 forms an intersection in g5b1/g5r1
[g5r1c48]<>3
4 forms an intersection in g5r5/g5b4
[g5r46c2]<>4
5 forms an intersection in g5b1/g5c3
[g5r89c3]<>5
6 forms an intersection in g5b1/g5c2
[g5r79c2]<>6
9 forms an intersection in g5b1/g5r2
[g5r2c89]<>9
3 forms an intersection in g1b7/g1c2
[g1r5c2]<>3
7 forms an intersection in g1b2/g1c4
[g1r8c4]<>7
2 forms an intersection in g3b3/g3r1
[g3r1c6]<>2
4 forms an intersection in g3b1/g3r2
[g3r2c6]<>4
6 forms an intersection in g4b2/g4c4
[g4r5c4]<>6
2 forms an intersection in g5b5/g5r4
[g5r4c1]<>2
37 is a hidden double in g2r8
[g2r8c5]<>1<>6<>8 [g2r8c9]<>8
Puzzle Solved
 Solution:
368419752259763841471825936924537168683192574517684293142956387896371425735248619
791362548582194763436857921147986235325741896968523174254678319619235487873419652
387916254425378619619452873734589126158624937296137548972845361841263795563791482
483651972956273841712498563891764325624315798537982614249537186368129457175846239
361892754795346182482157639856724391214539876973681245137465928528913467649278513


Apprentice Regular Samurai #13
4...8.9....2....717.....8.....94.....3.....14.2....3...6.5.7...2.9.1......1..9...
.6...5.....1...643....2....4......8...2..1.....356..1.....1.47....7....1...4..2.9
.....3........1..............4.1..7.7..4..8...8..79..1...9...................6...
.2..3.............83...1...2....7.4....6.41....1..2..3.1529......7.....4......9..
.....89.......7..........52...3...1.......5....67..4...7....39..2.9.5.6.4..63..2.
3 forms an intersection in g3b1/g3c2
[g3r458c2]<>3
3 forms an intersection in g2r7/g2b8
[g2r89c56]<>3
8 forms an intersection in g2r9/g2b8
[g2r7c46][g2r8c56]<>8
9 forms an intersection in g2b7/g2r8
[g2r8c56]<>9
5 forms an intersection in g2c7/g2b6
[g2r4c9][g2r5c8]<>5
5 forms an intersection in g2b3/g2r3
[g2r3c123]<>5
9 forms an intersection in g5c1/g5b4
[g5r45c23][g5r6c2]<>9
5 forms an intersection in g4b5/g4c5
[g4r2389c5]<>5
8 forms an intersection in g4b5/g4c5
[g4r289c5]<>8
5 forms an intersection in g4c7/g4b6
[g4r45c9][g4r56c8]<>5
7 forms an intersection in g4b3/g4c8
[g4r5679c8]<>7
7 forms an intersection in g4r3/g4b2
[g4r12c4][g4r2c5]<>7
3 forms an intersection in g1b9/g1c8
[g1r13c8]<>3
2 forms an intersection in g3r2/g3b2
[g3r1c5][g3r3c4]<>2
3 forms an intersection in g3b3/g3c8
[g3r56c8]<>3
6 forms an intersection in g4b7/g4r9
[g4r9c89]<>6
9 forms an intersection in g4c3/g4b1
[g4r1c1][g4r2c2]<>9
4 forms an intersection in g5b1/g5c2
[g5r45c2]<>4
5 forms an intersection in g5b5/g5c5
[g5r12c5]<>5
6 forms an intersection in g5b2/g5c5
[g5r45c5]<>6
7 forms an intersection in g4b8/g4r9
[g4r9c9]<>7
8 forms an intersection in g5b8/g5r7
[g5r7c9]<>8
46 is a hidden double in g3c8
[g3r7c8]<>5 [g3r8c8]<>5<>9
6 forms an intersection in g3b1/g3c2
[g3r78c2]<>6
6 forms an intersection in g4b3/g4c9
[g4r47c9]<>6
47 is a hidden double in g4r9
[g4r9c4]<>1<>5<>8
5 forms an intersection in g4b8/g4c6
[g4r12c6]<>5
5 forms an intersection in g3c6/g3b5
[g3r46c4]<>5
Puzzle Solved
 Solution:
416782953382695471795134826157943682938256714624871395863527149249318567571469238
368145927521978643749623158415297386672831594893564712286319475934752861157486239
149753286567281934238694157924815673713462895685379421851947362376128549492536718
729436851154829376836571492268317549973654128541982763415298637397165284682743915
362518947549267831718493652987354216234186579156729483671842395823975164495631728


Apprentice Regular Samurai #14
....8.........158..3...97...9...6.....73...12..5.7........47............6.1......
.8.....4...78...3......3.......1....46..2.38........29...4.........7...6..1.9...8
.............95......2....1.....71...72........5..92......5.......3.....9....6..8
.....8........7...1...6.9......1.....3.7.5.9.7.2.....8.....3...3......6.41.69....
.....1........72....8....9.1....2.8..7.5....1.6.4...2....8....56.9........7...9.6
4 forms an intersection in g5b2/g5r3
[g5r3c9]<>4
4 forms an intersection in g3r1/g3b2
[g3r2c4][g3r3c56]<>4
1 forms an intersection in g3b4/g3c1
[g1r78c7]<>1
5 forms an intersection in g2c5/g2b2
[g2r1c46][g2r2c6][g2r3c4]<>5
6 forms an intersection in g2c5/g2b2
[g2r1c46][g2r2c6][g2r3c4]<>6
5 forms an intersection in g2c9/g2b3
[g2r12c7][g2r3c8]<>5
6 forms an intersection in g2b7/g2c1
[g2r123c1]<>6
3 forms an intersection in g1r9/g1b8
[g1r8c56]<>3
5 forms an intersection in g1b1/g1r1
[g1r1c46]<>5
8 forms an intersection in g1b4/g1c1
[g1r78c1]<>8
9 forms an intersection in g1c7/g1b6
[g1r6c89]<>9
2 forms an intersection in g2b9/g2c7
[g2r12c7]<>2
7 forms an intersection in g2b7/g2c2
[g2r46c2]<>7
7 forms an intersection in g2c9/g2b3
[g2r1c7][g2r3c8]<>7
7 forms an intersection in g2r5/g2b5
[g2r46c4]<>7
9 forms an intersection in g2b7/g2r7
[g2r7c78]<>9
3 forms an intersection in g3b3/g3r2
[g1r8c78]<>3
3 forms an intersection in g1b9/g1r7
[g1r7c13]<>3
9 forms an intersection in g3b3/g3r1
[g1r7c89]<>9
9 forms an intersection in g1b9/g1r9
[g1r9c45]<>9
9 forms an intersection in g3b4/g3r4
[g3r4c89]<>9
6 forms an intersection in g3b3/g3c7
[g3r5c7]<>6
17 is a hidden double in g3r2
[g3r2c4]<>6
6 forms an intersection in g3r2/g3b1
[g1r7c78]<>6
Puzzle Solved
 Solution:
752483196946721583138569724294816375867354912315972648529647831483195267671238459
386251947157849632294763815932518764465927381718634529529486173843175296671392458
831764529267195843459283671398527164672841395145639287716958432584372916923416758
543928716269137584187564923854219637631785492792346158976853241325471869418692375
432981657916357248758246193193672584274598361865413729321869475649735812587124936


Apprentice Regular Samurai #15
...9..2.5..9.3.7...8.1..6....3.18.....7....4.2......63.........4...2..7...16.9...
..31......5....2.8...8....6.....7.....1...62....5148...............3...2..8..2.59
...3.8....7.2.............8....6...27.3.9...58...3.......94.............1........
.4...5....9.............1.....5.239..2...8...6...1....1.....8....576...34......5.
....3...7....8........7.1.8...7........2..6.49...5......2........53..79.6...9435.
8 forms an intersection in g5b5/g5r6
[g5r6c278]<>8
Puzzle Solved
 Solution:
174986235659234781382157694963418527517362849248795163725843916496521378831679452
283156794659473218417829536835267941741398625962514873524981367196735482378642159
916378524378254196452619378591467832723891645864532917637945281245183769189726453
842195637391876245576423189718542396924638571653917428137259864285764913469381752
281435967769182435453976128126743589538219674974658213392567841845321796617894352

tarek
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Børge
PostPosted: Sun Aug 17, 2008 7:51 pm 
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Joined: Mon Apr 21, 2008 10:32 am
Posts: 868
tarek wrote:
If you are not using Pencilmarks Then Hidden singles would be much easier to spot than naked singles. The same with Hidden doubles Vs. Naked doubles. My question would then be to you, Why Naked singles before hidden singles & hidden doubles before naked doubles?
I beg to differ. Cross Hatching will locate Hidden-Singles, but I often do it differently:
For each empty cell I go through all numbers and see which digits fits to find Naked-Singles, Pairs and Triplets, which I scribble down. Hope this answers your question.

tarek wrote:
Non single moves per puzzle with solutions in line format:
Oops, not exactly what I had in mind. Do you have summaries only? I.e.:
xx Hidden singles
yy Naked singles
zz Intersections
etc.

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tarek
PostPosted: Sun Aug 17, 2008 8:49 pm 
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Posts: 251
Børge wrote:
For each empty cell I go through all numbers and see which digits fits to find Naked-Singles, Pairs and Triplets, which I scribble down. Hope this answers your question.
yes :ok:, each person solves differently. To me finding hidden singles & hidden doubles is easier than finding a naked single. From what I've seen with helping people solve puzzles on the forums, more experience in solving without pencilmarks makes spotting naked stuff easier - to a level equal to their hidden counterparts.

Børge wrote:
Do you have summaries only? I.e.:
xx Hidden singles
yy Naked singles
zz Intersections
etc.
Unfortunately not :oops:
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