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

### Results after processing nearly 9300 puzzles

After processing nearly 9300 puzzles here are the puzzles that stand out:

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`TTHsieh-0003ER = 5.4Requires 2 Hidden quadsFully symmetric & minimalDoesn't solve with FNBHTW+-------+-------+-------+| . . . | . . . | . . . || . . 1 | 2 . 3 | 4 . . || . 2 . | 1 . 4 | . 5 . |+-------+-------+-------+| . 1 3 | . . . | 5 4 . || . . . | . . . | . . . || . 6 7 | . . . | 1 2 . |+-------+-------+-------+| . 5 . | 6 . 2 | . 8 . || . . 6 | 7 . 8 | 3 . . || . . . | . . . | . . . |+-------+-------+-------+`

Code: Select all
`Pure 1 Hidden quadSolve with FNBHTWStable with X cyclesSymmetric & minimalER = 5.4.....1..2.2..3.4....526..7...8.....5.46...28.3.....1...6..849....9.2..3.8..9.....#champagne-0365.....1..2.3..2.4....253..6...6.....3.24...78.5.....9...5..748....7.8..9.8..6.....#champagne-0369.....1..2.3..2.4....253..6...6.....3.24...78.9.....1...5..748....7.8..5.8..6.....#champagne-0376...1..2...3.4.5.......26..517.....5...6...1...4.....388..56.......3.8.4...9..2...#champagne-0525...1..2...3.4.5.......67..515.....3...6...1...4.....878..57.......3.6.4...9..2...#champagne-0526...1..2...1.3.4.......25..675.....6...8...9...3.....458..21.......6.3.7...9..7...#champagne-0528...1..2...3.4.2.......56..715.....6...2...8...9.....746..38.......6.5.3...1..9...#champagne-0548.....9.87....8.654...6..39...2..7..6.4.....1.5..4..9...25..3...817.9....43.2.....#champagne-0577.....9.87....6.543...5..69...3..6..5.8.....2.2..7..9...67..1...348.9....12.6.....#champagne-0594.....9.87....7.654...6..39...2..4..6.7.....2.5..7..9...83..1...954.8....12.3.....#champagne-0596.....9.87....6.543...5..29...7..1..5.4.....6.2..3..9...62..4...784.9....35.8.....#champagne-0598.....9.87....8.654...6..93...3..2..6.4.....2.5..1..8...95..7...834.2....71.9.....#champagne-0608.....9.87....6.543...5..29...2..6..5.3.....6.4..7..9...24..1...983.4....51.2.....#champagne-0623.....9.87....6.549...8..36...3..2..5.5.....9.4..5..7...35..4...894.1....62.3.....#champagne-0625.....9.87....8.654...6..39...2..5..8.4.....2.5..7..9...37..1...485.9....12.3.....#champagne-0627.....9.87....7.654...6..39...3..2..6.2.....4.4..1..9...35..7...842.5....17.3.....#champagne-0628.....9.87....6.543...5..69...7..2..5.8.....2.4..3..8...69..1...874.9....31.6.....#champagne-0633.....9.87....6.543...8..69...2..4..5.5.....7.3..2..9...61..8...834.2....27.1.....#champagne-0655.....1..2.3..4.5.....63..79..4.....8.73...64.8.....1..65..79.....9.6..5.4..8.....#champagne-6773.....1..212..3.4.....26..7...3.....8.76...23.9.....1...4..76.....1.2..437..9.....#champagne-7706.....1.23...4..15.....5.6.7.2.1.83....7..2...9..54.....726....843.......6.9...7..#champagne-9372`

tarek

tarek

Posts: 3537
Joined: 05 January 2006

i filtered for "superior plus"
(i.e. discarding any which need XY-Wing, XYZ-Wing, Unique rectangles and loops)

= 6,545 puzzles, rather more than i'd try solving

the following puzzles are likely to be interesting --
(most are from champagne, except the 2 noted)

.....1....29.3.4....452..6...7.......62...38.9.....2...8..635....5.8..4.7..9.....
.....1....2..3.45...452..61..7.......62...38.9.....2...8..635....5.8..4.7..9.....

.....1...23..4.5..8.162..3...6.....7.28...49.1.....2......946....3.8..5.9..7.....
.....1..2.2..3.4....452..6...7.....1.62...38.9.....2...8..635....5.8..4.7..9.....
.....1.32.2..3.4....452..6...7...6.1.62...38.9.........8..635....5.8..4.7..9.....
.....1..2.2..3.4....45.9.6...7.....1.62...38.9.....2...8..635....5.8..4.7..9.....
.....1.3..2..3.4....452..6...7.....1.62...38.9.....2...8..635....5.8..4.7..9.....
.....1....2..3.45...452..6...7.......62...38.9.....2...8..635....5.8..437..9.....
.....1....2..3.45...452..6...7.......62...38.9.....2...8..635...95.8..4.7..9.....
.....1..2.2..3.4.8..562..7.........9.72...36.9.....7...4..785......6..4.5..9....6
.....1.23...2..45.....6.1.7.3.8.72....4..6...7..49.....839....294.......1.7...9.. # dobrichev

.....1..2.3..4.5.....62.13...6.....7.28...49.1.....2...85.94.....3.8..5.9..7.....
.....1..2.31.4.5.....62..3...6.....7.28...49.1.....2...85.94.....3.8..5.9..7.....
.....1....3..4.5.68.162..3...6.....7.28...49.1.....2......946....3.8..5.9..7.....
.....1..2.2..3.4.....62..7...6.....3.38...21.7.....9...4..895.7..9.1..4.8..54....
....41..2.2..3......452..6...7.....1.62...38.9.....2...8..635....5.8..4.7..9.....
.....1..2.3..2.4....564..3...7.....8.42...51.9.....2..5...18.....3.5.16.7..9.....
....81..2.1..3.4....2.6..7...8.....6.36...79.7.....2.8.4..759....5.9..4....3.....
.....1..2.2..3.4..6.452......7.....1.62...38.9......7..8..635....5.8..4.7..9.....
....41..2.2..3......452..6...7...2.1.62...38.9.........8..635....5.8..4.7..9.....
.....1...12..3.4....452..6...7.......62...38.9.....2...8..635....5.8..4.7..9..8..
....41.3..2..3......452..6...7.....1.62...38.9.....2...8..635....5.8..4.7..9.....

.....1..2.3..2.49...1.5..3...6.......57...12.8.....96..6..187....3.7..5.7..6.....

.....1..2.2..3.4...9526..7...3.....8.76...23.9.....1...4..7.5......2..4.7..9.....
.....1....3..4.5....162..3...6.....7.28...49.1.....2...85.946....3.8..5.9..7.....
.....1..2.2..3.4....562..7...6.....3.38...21.......9...42.89....59.1..4.8..5.....
.....1..2.3..4.5....162..3..96.....7.28...49.1.....2...8..946....378..5..........
.....1..2.3..4.5..4.162..3...6....7..28...49.1.....2...8..946....3.8....9..7.....
.....1..2.3..4......162.53...6.....7.28...49.1.7...2......946....3.8..5.9..7.....

8..3.1..2...........7.4.9..1.......9..6.5.7..2.......4..8.9.6...........3..4.8..1 # gsf # 24 # 43 { <-- edit: found it }

Pat

Posts: 3880
Joined: 18 July 2005

Pat wrote:8..3.1..2...........7.4.9..1.......9..6.5.7..2.......4..8.9.6...........3..4.8..1 # this one from who? i need to track it down---

This one is on the list as posted by gsf

tarek

Posts: 3537
Joined: 05 January 2006

### from Layout 289 of the Patterns Game

this puzzle only needs "basic" moves

5....78...1..8..2...46....7..34.6...............2.86..1....59...5..6..4...23....1
Pat # 289 # (258812) #

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` 5 . . | . . 7 | 8 . .  . 1 . | . 8 . | . 2 .  . . 4 | 6 . . | . . 7 -------+-------+------ . . 3 | 4 . 6 | . . .  . . . | . . . | . . .  . . . | 2 . 8 | 6 . . -------+-------+------ 1 . . | . . 5 | 9 . .  . 5 . | . 6 . | . 4 .  . . 2 | 3 . . | . . 1 `

Pat

Posts: 3880
Joined: 18 July 2005

Hi all,

is there anybody here who knows he's/she's able to program Hidden Quad search easily?

My solver search naked single, hidden single, naked pair, hidden pair, naked triplet, hidden triplet, naked quad, hidden quad and then other techniques.

R. Jamil
rjamil

Posts: 539
Joined: 15 October 2014
Location: Karachi, Pakistan

rjamil, following your <earlier query>, where Blue showed my algorithm missed some locked set instances, I eventually wrote a different version for my Excel spreadsheet. It runs through the possible positions for 1 to 4 cells for set 1 and accumulates the digits they hold. Set 2 is the complementary set for which the digits are also accumulated. If set 1 isn't a naked set, the digits common to both sets are removed and it is tested to see if it is a hidden set.

The same code therefore tests for all locked sets that can exist in a house.

I should explain I call the binary representation of the digits 'BitValues' which are treated as integers [0..511] in my code allowing them to be used with logical AND and OR operators.
The code contains calls to a 'BitCount' function which returns how many bits are set = number of digits or cells involved.

Code: Select all
`Function FindLSet(VDomain As Range, VMask As Integer, PMask As Integer) As Integer'Returns the bitvalue of a locked set, either naked or hidden, found in a house'VDomain: bivalue array of the digit values by position in the house'VMask, PMask: bitvalues of unsolved values & positions in the houseDim x As Single                              'General purpose loop counterDim xbv As Integer                           'The bitvalue of xDim PC As Single                             'Unsolved Position counterDim Pbv(9) As Integer                        'Array of the Bitvalues of the unsolved positionsDim P1 As Single, P2 As Single, P3 As Single 'Loop counters for test positionsDim P4 As Single                             ' "     "       "   "     "Dim S1P As Integer                           'Set 1 cell positions as bitvaluesDim S1PC As Single                           'Set1 Position Count (will be 1 to 4 )Dim S1V As Integer, S2V As Integer           'Bitvalues of the digit values in sets 1 & 2Dim CommonV As Integer                       'Bitvalue of the digit values in both sets'Shortlist the unsolved positions to avoid repeated testing.For x = 1 To 9                               'collect the unsolved positions  xbv = 2 ^ (x - 1)                          'the bitvalue of x  If (xbv And PMask) > 0 Then                'the position is unsolved    PC = PC + 1                              'increment the count    Pbv(PC) = xbv                            'store the position as bitvalue in array  End IfNext x'VBasic returns 0 for a false condition and -1 for a true one. 'As a zero value is a null entry, these nested loops give a search order of 'singles, doubles, triples, quads either naked or hidden.For P1 = 0 To (3 - PC) * (PC > 7)                   'if PC <8 this loop never operates  For P2 = P1 + 1 + (P1 = 0) To (2 - PC) * (PC > 5) 'if PC <6 this loop never operates    For P3 = P2 + 1 + (P2 = 0) To PC - 1            'this posn (starts at 0 if P2=0, else it is P2+1)      For P4 = P3 + 1 To PC                         'highest posn        S1P = Pbv(P1) + Pbv(P2) + Pbv(P3) + Pbv(P4) 'bitvalue of the test positions        S1PC = BitCount(S1P)                        'set1 position count        S1V = 0                                     'reset values in set1        S2V = 0                                     'reset values in set2        For x = 1 To 9                              'loop through all positions          If ((2 ^ (x - 1)) And S1P) <> 0 Then      'the cell position is in set1            S1V = S1V Or VDomain(x)                 'add its values to set1          Else            S2V = S2V Or VDomain(x)                 'add its values to set2          End If        Next x        S2V = S2V And VMask                         'remove known digit values from set2        CommonV = S1V And S2V                       'values in both sets        If CommonV <> 0 Then                        'when common=0 there are no eliminations          If BitCount(S1V) = S1PC Then              'set1 = naked set, set2 = hidden set            FindLSet = S1V          Else            S1V = S1V And (511 - CommonV)           'reduce set1 to locked values            If BitCount(S1V) = S1PC Then              FindLSet = S2V                        'set1 = hidden set, set2 = naked set            End If          End If          If FindLSet <> 0 Then Exit Function        End If      Next P4    Next P3  Next P2Next P1End Function`

Even if you can't translate the code, it should be enough to demonstrate the approach I came up with.

DPB
David P Bird
2010 Supporter

Posts: 1043
Joined: 16 September 2008
Location: Middle England

Hi,

Checked:
Code: Select all
`21.....7..39.7.......28.......6...2.8.........6..587...4.......1..9..6....5.41.89`
It solved with one hidden pair, one hidden quad and all naked / hidden singles.

R. Jamil

Edit 20170823: Find below steps to solve the puzzle:
Code: Select all
`21.....7..39.7.......28.......6...2.8.........6..587...4.......1..9..6....5.41.89 Moderate0) Apply Hidden Single Cell Value 8 from Values 468 at Cell 21) Apply Hidden Single Cell Value 1 from Values 145 at Cell 122) Apply Hidden Single Cell Value 2 from Values 1234 at Cell 473) Apply Hidden Single Cell Value 9 from Values 3679 at Cell 544) Apply Hidden Single Cell Value 9 from Values 1349 at Cell 525) Apply Hidden Single Cell Value 1 from Values 134 at Cell 536) Apply Hidden Single Cell Value 8 from Values 3578 at Cell 577) Apply Hidden Single Cell Value 5 from Values 345 at Cell 38) Apply Hidden Single Cell Value 8 from Values 278 at Cell 649) Apply Hidden Single Cell Value 6 from Values 367 at Cell 7210) Apply Hidden Single Cell Value 6 from Values 467 at Cell 2011) Apply Hidden Single Cell Value 2 from Values 27 at Cell 7312) Apply Naked Single Cell Value 3 from Values 3 at Cell 7813) Apply Naked Single Cell Value 7 from Values 7 at Cell 7534) Found Hidden pair Cell Values 28 at Unit 1 Cells 15 17181) Found Hidden quad Cell Values 1279 at Unit 4 Cells 37 38 40 4114) Apply Hidden Single Cell Value 4 from Values 1347 at Cell 2915) Apply Naked Single Cell Value 3 from Values 3 at Cell 4516) Apply Naked Single Cell Value 4 from Values 4 at Cell 4817) Apply Naked Single Cell Value 3 from Values 3 at Cell 3918) Apply Hidden Single Cell Value 1 from Values 19 at Cell 3119) Apply Hidden Single Cell Value 3 from Values 358 at Cell 3520) Apply Hidden Single Cell Value 8 from Values 58 at Cell 3321) Apply Naked Single Cell Value 2 from Values 2 at Cell 1522) Apply Naked Single Cell Value 8 from Values 8 at Cell 1723) Apply Hidden Single Cell Value 1 from Values 17 at Cell 3824) Apply Hidden Single Cell Value 3 from Values 1345 at Cell 2525) Apply Hidden Single Cell Value 1 from Values 1459 at Cell 2426) Apply Naked Single Cell Value 5 from Values 5 at Cell 6027) Apply Naked Single Cell Value 4 from Values 4 at Cell 4228) Apply Naked Single Cell Value 9 from Values 9 at Cell 629) Apply Naked Single Cell Value 1 from Values 1 at Cell 6130) Apply Naked Single Cell Value 4 from Values 4 at Cell 7031) Apply Hidden Single Cell Value 9 from Values 49 at Cell 2332) Apply Naked Single Cell Value 7 from Values 7 at Cell 3233) Apply Naked Single Cell Value 5 from Values 5 at Cell 2734) Apply Naked Single Cell Value 9 from Values 9 at Cell 2835) Apply Naked Single Cell Value 4 from Values 4 at Cell 936) Apply Naked Single Cell Value 7 from Values 7 at Cell 3737) Apply Naked Single Cell Value 6 from Values 6 at Cell 1438) Apply Naked Single Cell Value 3 from Values 3 at Cell 439) Apply Naked Single Cell Value 4 from Values 4 at Cell 540) Apply Naked Single Cell Value 6 from Values 6 at Cell 841) Apply Naked Single Cell Value 5 from Values 5 at Cell 4442) Apply Naked Single Cell Value 6 from Values 6 at Cell 4343) Apply Naked Single Cell Value 2 from Values 2 at Cell 6744) Apply Naked Single Cell Value 9 from Values 9 at Cell 4045) Apply Naked Single Cell Value 6 from Values 6 at Cell 5846) Apply Naked Single Cell Value 3 from Values 3 at Cell 5947) Apply Naked Single Cell Value 7 from Values 7 at Cell 5648) Apply Naked Single Cell Value 3 from Values 3 at Cell 6549) Apply Naked Single Cell Value 2 from Values 2 at Cell 6250) Apply Naked Single Cell Value 5 from Values 5 at Cell 6851) Apply Naked Single Cell Value 2 from Values 2 at Cell 4152) Apply Naked Single Cell Value 7 from Values 7 at Cell 7153) Apply Naked Single Cell Value 5 from Values 5 at Cell 1654) Apply Naked Single Cell Value 4 from Values 4 at Cell 2655) Apply Naked Single Cell Value 5 from Values 5 at Cell 1956) Apply Naked Single Cell Value 7 from Values 7 at Cell 181) 218534976439176258756289134594617823871392465362458791947863512183925647625741389 # S19 # N37 # H20 # G0 # D0 # 0.000000`
Last edited by rjamil on Wed Aug 23, 2017 12:10 pm, edited 1 time in total.
rjamil

Posts: 539
Joined: 15 October 2014
Location: Karachi, Pakistan

... or the hidden pair 14c3 alone ...
eleven

Posts: 2376
Joined: 10 February 2008

Regarding this puzzle "21.....7..39.7.......28.......6...2.8.........6..587...4.......1..9..6....5.41.89" , my solver solves it at line-box stage before testing for locked sets:
3s at r46c1 only ones in column => -3 r45c3.
3s at r56c4 only ones in column => -3 r45c56.
4s at r45c3 only ones in column => -4 r46c1.
solved!

No need for locked sets, hidden or otherwise.
In box 5, there is a naked quin and it's complementary hidden quad.
Personally I find it simpler to code naked quins, but each to his/her own.
Phil
pjb
2014 Supporter

Posts: 2169
Joined: 11 September 2011
Location: Sydney, Australia

Hi,

pjb wrote:Personally I find it simpler to code naked quins, but each to his/her own.

That's why I asked again for hidden quad (or tuples) searching routine whether simple or still complicated for one to code.

pjb wrote:Here's a nice example from a set published by Champage: ".....1..2.2..3.4....562..7...6.....3.38...21.7.....9...4..895....9.1..4.8..5....."
In box 5, there is a naked quin and it's complementary hidden quad.

Here is steps to solve the puzzle by my solver:
Code: Select all
`.....1..2.2..3.4....562..7...6.....3.38...21.7.....9...4..895....9.1..4.8..5.....154) Found Hidden quad Cell Values 1238 at Unit 22 Cells 30 32 48 5089) Found Row wise Sword Fish for Value 4 at r349c1567) Found Hidden pair Cell Values 24 at Unit 21 Cells 27 4731) Found Pointing and Claiming Intersection Removal Value 1 at Cells 28 37 4622) Found XY-Wings Type 1 in Cells 32 27 23 Values 248 remove 4 from Cell 180) Apply Hidden Single Cell Value 4 from Values 347 at Cell 21) Apply Naked Single Cell Value 2 from Values 2 at Cell 472) Apply Naked Single Cell Value 4 from Values 4 at Cell 273) Apply Hidden Single Cell Value 4 from Values 48 at Cell 234) Apply Hidden Single Cell Value 4 from Values 479 at Cell 395) Apply Hidden Single Cell Value 4 from Values 4568 at Cell 536) Apply Hidden Single Cell Value 4 from Values 467 at Cell 7627) Found Pointing and Claiming Intersection Removal Value 3 at Cells 0 9 1836) Found Box-Line Reduction Intersection Removal Value 9 at Cells 3 12 2140) Found Box-Line Reduction Intersection Removal Value 6 at Cells 31 40 4950) Found Row wise Sword Fish for Value 5 at r146c2587) Apply Hidden Single Cell Value 5 from Values 256 at Cell 638) Apply Naked Single Cell Value 9 from Values 9 at Cell 369) Apply Hidden Single Cell Value 9 from Values 579 at Cell 3110) Apply Hidden Single Cell Value 7 from Values 78 at Cell 3311) Apply Hidden Single Cell Value 2 from Values 126 at Cell 5412) Apply Hidden Single Cell Value 2 from Values 2369 at Cell 7913) Apply Hidden Single Cell Value 9 from Values 1679 at Cell 8014) Apply Hidden Single Cell Value 9 from Values 89 at Cell 1915) Apply Hidden Single Cell Value 8 from Values 378 at Cell 116) Apply Hidden Single Cell Value 7 from Values 17 at Cell 115) Found Naked pair Cell Values 36 at Unit 0 Cells 0 617) Apply Hidden Single Cell Value 3 from Values 36 at Cell 6118) Apply Naked Single Cell Value 1 from Values 1 at Cell 5619) Apply Naked Single Cell Value 7 from Values 7 at Cell 5720) Apply Naked Single Cell Value 9 from Values 9 at Cell 321) Apply Naked Single Cell Value 8 from Values 8 at Cell 1222) Apply Naked Single Cell Value 5 from Values 5 at Cell 1423) Apply Naked Single Cell Value 7 from Values 7 at Cell 424) Apply Naked Single Cell Value 6 from Values 6 at Cell 4025) Apply Naked Single Cell Value 7 from Values 7 at Cell 4126) Apply Naked Single Cell Value 5 from Values 5 at Cell 4427) Apply Naked Single Cell Value 8 from Values 8 at Cell 3428) Apply Naked Single Cell Value 2 from Values 2 at Cell 3229) Apply Naked Single Cell Value 1 from Values 1 at Cell 3030) Apply Naked Single Cell Value 3 from Values 3 at Cell 4831) Apply Naked Single Cell Value 5 from Values 5 at Cell 4932) Apply Naked Single Cell Value 1 from Values 1 at Cell 4633) Apply Naked Single Cell Value 8 from Values 8 at Cell 5034) Apply Naked Single Cell Value 6 from Values 6 at Cell 5235) Apply Naked Single Cell Value 9 from Values 9 at Cell 1636) Apply Naked Single Cell Value 5 from Values 5 at Cell 2837) Apply Naked Single Cell Value 6 from Values 6 at Cell 6238) Apply Naked Single Cell Value 2 from Values 2 at Cell 6639) Apply Naked Single Cell Value 8 from Values 8 at Cell 6940) Apply Naked Single Cell Value 7 from Values 7 at Cell 7141) Apply Naked Single Cell Value 6 from Values 6 at Cell 6442) Apply Naked Single Cell Value 3 from Values 3 at Cell 6843) Apply Naked Single Cell Value 7 from Values 7 at Cell 7344) Apply Naked Single Cell Value 3 from Values 3 at Cell 7445) Apply Naked Single Cell Value 5 from Values 5 at Cell 746) Apply Naked Single Cell Value 6 from Values 6 at Cell 7747) Apply Naked Single Cell Value 1 from Values 1 at Cell 7848) Apply Naked Single Cell Value 3 from Values 3 at Cell 2449) Apply Naked Single Cell Value 6 from Values 6 at Cell 650) Apply Naked Single Cell Value 3 from Values 3 at Cell 051) Apply Naked Single Cell Value 1 from Values 1 at Cell 1752) Apply Naked Single Cell Value 8 from Values 8 at Cell 2653) Apply Naked Single Cell Value 6 from Values 6 at Cell 954) Apply Naked Single Cell Value 1 from Values 1 at Cell 181) 384971652627835491195624378456192783938467215712358964241789536569213847873546129 # S1 # N40 # H15 # G0 # D0 # 0.000000`

R. Jamil

pjb wrote:Personally I find it simpler to code naked quins, but each to his/her own.

Will you report beyond naked quad as its complementary hidden tuple or just naked tuples?
rjamil

Posts: 539
Joined: 15 October 2014
Location: Karachi, Pakistan

You don't need to look beyond the examples in my post at the top this page.

Tarek

tarek

Posts: 3537
Joined: 05 January 2006

Hi,
tarek wrote:You don't need to look beyond the examples in my post at the top this page.

However my question is that, if someone's solver detect naked tuples only, will he/she report naked quintuple, sextuple and septuplet search as hidden quad, triple and pair accordingly?

R. Jamil
rjamil

Posts: 539
Joined: 15 October 2014
Location: Karachi, Pakistan

see next ..
Last edited by eleven on Tue Sep 12, 2017 9:03 pm, edited 1 time in total.
eleven

Posts: 2376
Joined: 10 February 2008

I don't care, how you implement it, but you should know, that for a manual non-pencilmark solver the 2 quads of the first sample jump into her eyes before starting to look for singles and pairs.
Code: Select all
` +-------+-------+-------+ | . . . | . . . | . . . | | . . 1 |*2 . 3 | 4 . . | | . 2 . |*1 . 4 | . 5 . | +-------+-------+-------+ | . 1 3 | . x x | 5 4 . | | . . . | . x x | . . . | | .*6*7 | . . . |*1*2 . | +-------+-------+-------+ | . 5 . |*6 . 2 | . 8 . | | . . 6 |*7 . 8 | 3 . . | | . . . | . . . | . . . | +-------+-------+-------+ +-------+-------+-------+ | . . . | . . . | . . x | | . .*1 |*2 . 3 |*4 . . | | .*2 . |*1 . 4 | .*5 . | +-------+-------+-------+ | . 1 3 | . . . |*5*4 . | | . . . | . . . | . . . | | . 6 7 | . . . |*1*2 . | +-------+-------+-------+ | . 5 . | 6 . 2 | . 8 x | | . . 6 | 7 . 8 | 3 . x | | . . . | . . . | . . x | +-------+-------+-------+`
Last edited by eleven on Tue Sep 12, 2017 9:04 pm, edited 1 time in total.
eleven

Posts: 2376
Joined: 10 February 2008

I like how eleven emphasises the point! I agree with you eleven btw!!!

Pencil & paper solvers will always spot the hidden stuff first (tried & tested)

PM grid solvers tend to spot naked stuff first (generaly)

Experienced solvers will have a mix of both

When I designed a solver I always thought that looking at x number of cells is always easier than looking at x+y number of cells

Tarek

tarek

Posts: 3537
Joined: 05 January 2006

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