The New Sudoku Players' Forum

by **Pat** » Wed Jun 07, 2006 8:18 am

--- super-shorthand could add to my confusion ---

Ruud (2006.May.26) wrote:Techniques:
NS (N)
HS (F)

gsf (2006.Mar.22) wrote:method:
F: naked-single
N: hidden-single

by **gsf** » Wed Jun 07, 2006 3:11 pm

Pat wrote:--- super-shorthand could add to my confusion ---

Ruud (2006.May.26) wrote:Techniques:
NS (N)
HS (F)

gsf (2006.Mar.22) wrote:method:
F: naked-single
N: hidden-single

yeah
FN come from when I clean-room coded over a year ago
based on the actual coding
F: forced value -- the only possible value in a cell
N: numerated value -- only possible value in row/col/box by counting
too late for this horse to change

by **gsf** » Wed Jun 07, 2006 3:14 pm

tarek wrote:I've just analysed the log & I think I found the problem
here the log for the 2nd step from the first puzzle
Code: Select all
*--------------------------------------------------------------------------* | 789 56789 6789 | 235679 1 234589 | 2789 2489 2 | | 1 56789 2 | 5679 456789 4589 | 3 1489 14 | | 4 3 1789 | 279 789 289 | 12789 5 6 | |------------------------+------------------------+------------------------| | 5 289 1389 | 4 39 6 | 128 1238 7 | | 789 4789 34789 | 12359 359 12359 | 568 3468 345 | | 6 24 134 | 8 35 7 | 125 1234 9 | |------------------------+------------------------+------------------------| | 3 1 469 | 569 4569 459 | 2 7 8 | | 2 26789 5 | 13679 36789 1389 | 4 1369 13 | | 789 46789 46789 | 135679 2 134589 | 1569 1369 135 | *--------------------------------------------------------------------------* Eliminating 1 From r3c3 (Box 4 & Column 3 Box-Line interaction)

this step is strange
the previous step made the [21]=1 placement
why would a placement not immediately remove the candidate from the remainder of its row/col/box cells?

by **tarek** » Wed Jun 07, 2006 10:32 pm

You're right.........

the single elimination has to start after a placement, I thought that we agreed that the 1st step would be box-line interaction (pointing pairs), that is why it did a box-line eliminaton 1st, where if left the single elimination would have done it in the same step.........At the end of the day it doesn't make a difference as the step count remains the same.The only difference is that it shows you more possible pointing pairs, I therfore see no other reason for the pointing pairs to be before single eliminations as the results are the same eventually

tarek

by **gsf** » Wed Jun 07, 2006 11:41 pm

can you post all of the steps for that first puzzle?

by **gsf** » Thu Jun 08, 2006 6:37 am

tarek wrote:I therfore see no other reason for the pointing pairs to be before single eliminations as the results are the same eventually

the step count could be different because of the grouping
what do you get for this puzzle

Code: Select all: ...9.4....34...51.8..1.7..27.25.31.9..97.68...........5.......3.78...49..4.3.1.5. # box-line first 1 [1] B11 [17][18][19]^7 [85]^5 [32]^9 [81]^1 [51][61]^3 [48][58][68]^4 N12 [13][29]=7 [21][37][72]=9 [38][45]=4 [58][81][63]=3 [89]=1 [86]=5 2 B16 [15][64][65][66][95][97][11]^2 [15]^3 [11][12][15]^6 [15][62]^8 [12][32]^5 [65]^9 N12 [12][55][91]=2 [17][35]=3 [15][33]=5 [42]=8 [66][95]=9 [73]=1 [74]=4 3 B13 [67][68][69][97][99][62]^6 [61][62][51]^1 [77][78]^7 [78]^8 [76]^2 N16 [11][52][65]=1 [32][48][61][93][77][19]=6 [75][97][68]=7 [84][26]=2 [99][18]=8 4 B4 [59]^4 [69]^5 [25]^6 [24]^8 N11 [24][85]=6 [25][64][76]=8 [51][69]=4 [59][62]=5 [67][78]=2 S # hidden-single first 1 [1] N9 [29][13]=7 [21][37]=9 [38]=4 [81][63]=3 [86]=5 [89]=1 B12 [15]^2 [15][18]^3 [11][12][15]^6 [15]^8 [12][32]^5 [75][76]^9 [72]^1 2 N10 [17][35][58]=3 [15][33]=5 [45]=4 [73]=1 [72][95][66]=9 B11 [62][78]^8 [64][65][97][11]^2 [97][99][91]^6 [77][78]^7 3 N13 [12][55][91]=2 [32][93][61]=6 [42][99][18]=8 [74]=4 [75][97][68]=7 B6 [59]^4 [62][51]^1 [76][77]^2 [78]^6 4 N13 [11][52][65]=1 [19][48][77]=6 [51][69]=4 [67][78][84][26]=2 [76]=8 B2 [25]^6 [24]^8 5 N6 [24][85]=6 [25][64]=8 [59][62]=5 S

by **tarek** » Thu Jun 08, 2006 8:56 am

Oh, what I was referring to by single elimination is single eliminations that follow placements......

The misunderstanding probably stems from terms used by us collectively which are interpreted differently individually.....

Hidden singles to me means PLACMENT of that single.....No eliminations at all

Naked single to me also means PLACEMNT of that single........No eliminations at all

Single eliminations is the elimination of candidates following a placement

In the Ulterior thread...... A placement can only be achieved by Hidden singles, Therefore a cell which is still uncovered which has one candidate can be uncivered using NAKED SINGLES but this is not allowed, therefore single eliminations stemming from that cell are not allowed until it is uncovered as a hidden single (a degenerate hidden single)

I used to attach single eliminations to the Naked singles algorithm, but because of this thread now I have 3 algorithms (one for naked singles, one for hidden singles & one for single eliminations), I'll post the logs for that puyzzle shortly.

I#m visiting a friend in Germanzy, & I'm finding using the kezyboard there a bit frustrating.

tarek

by **tarek** » Thu Jun 08, 2006 11:23 am

Here is the log for the 24 stepper Ocean has posted
Ive tried to mark eliminations resulting in degenerate hidden singles with %%%%%

Fruitful Pointing pairs with &&&&&&&&

you can also notice the repition of some pointing pair elimination following single elimination to demonstrate that the pointing pair algorithm IMO does need to be 1st

Code: Select all: . . . | . 1 . | . . . . . 2 | . . . | 3 . . 4 3 . | . . . | . 5 6 -------+-------+------ 5 . . | 4 . 6 | . . 7 . . . | . . . | . . . 6 . . | 8 . 7 | . . 9 -------+-------+------ 3 1 . | . . . | . 7 8 . . 5 | . . . | 4 . . . . . | . 2 . | . . . Eliminating 1 From r1c4 (Single in Box 2) Eliminating 1 From r1c6 (Single in Box 2) Eliminating 1 From r2c4 (Single in Box 2) Eliminating 1 From r2c5 (Single in Box 2) Eliminating 1 From r2c6 (Single in Box 2) Eliminating 1 From r3c4 (Single in Box 2) Eliminating 1 From r3c5 (Single in Box 2) Eliminating 1 From r3c6 (Single in Box 2) Eliminating 1 From r1c1 (Single in Row 1) Eliminating 1 From r1c2 (Single in Row 1) Eliminating 1 From r1c3 (Single in Row 1) Eliminating 1 From r1c7 (Single in Row 1) Eliminating 1 From r1c8 (Single in Row 1) Eliminating 1 From r1c9 (Single in Row 1) Eliminating 1 From r4c5 (Single in Column 5) Eliminating 1 From r5c5 (Single in Column 5) Eliminating 1 From r6c5 (Single in Column 5) Eliminating 1 From r7c5 (Single in Column 5) Eliminating 1 From r8c5 (Single in Column 5) Eliminating 2 From r1c1 (Single in Box 1) Eliminating 2 From r1c2 (Single in Box 1) Eliminating 2 From r1c3 (Single in Box 1) Eliminating 2 From r2c1 (Single in Box 1) Eliminating 2 From r2c2 (Single in Box 1) Eliminating 2 From r3c3 (Single in Box 1) Eliminating 2 From r2c4 (Single in Row 2) Eliminating 2 From r2c5 (Single in Row 2) Eliminating 2 From r2c6 (Single in Row 2) Eliminating 2 From r2c8 (Single in Row 2) Eliminating 2 From r2c9 (Single in Row 2) Eliminating 2 From r4c3 (Single in Column 3) Eliminating 2 From r5c3 (Single in Column 3) Eliminating 2 From r6c3 (Single in Column 3) Eliminating 2 From r7c3 (Single in Column 3) Eliminating 2 From r9c3 (Single in Column 3) Eliminating 3 From r1c7 (Single in Box 3) Eliminating 3 From r1c8 (Single in Box 3) Eliminating 3 From r1c9 (Single in Box 3) Eliminating 3 From r2c8 (Single in Box 3) Eliminating 3 From r2c9 (Single in Box 3) Eliminating 3 From r3c7 (Single in Box 3) Eliminating 3 From r2c1 (Single in Row 2) Eliminating 3 From r2c2 (Single in Row 2) Eliminating 3 From r2c4 (Single in Row 2) Eliminating 3 From r2c5 (Single in Row 2) Eliminating 3 From r2c6 (Single in Row 2) Eliminating 3 From r4c7 (Single in Column 7) Eliminating 3 From r5c7 (Single in Column 7) Eliminating 3 From r6c7 (Single in Column 7) Eliminating 3 From r7c7 (Single in Column 7) Eliminating 3 From r9c7 (Single in Column 7) Eliminating 4 From r1c1 (Single in Box 1) Eliminating 4 From r1c2 (Single in Box 1) Eliminating 4 From r1c3 (Single in Box 1) Eliminating 4 From r2c1 (Single in Box 1) Eliminating 4 From r2c2 (Single in Box 1) Eliminating 4 From r3c3 (Single in Box 1) Eliminating 4 From r3c4 (Single in Row 3) Eliminating 4 From r3c5 (Single in Row 3) Eliminating 4 From r3c6 (Single in Row 3) Eliminating 4 From r3c7 (Single in Row 3) Eliminating 4 From r5c1 (Single in Column 1) Eliminating 4 From r8c1 (Single in Column 1) Eliminating 4 From r9c1 (Single in Column 1) Eliminating 3 From r1c1 (Single in Box 1) Eliminating 3 From r1c2 (Single in Box 1) Eliminating 3 From r1c3 (Single in Box 1) Eliminating 3 From r3c3 (Single in Box 1) Eliminating 3 From r3c4 (Single in Row 3) Eliminating 3 From r3c5 (Single in Row 3) Eliminating 3 From r3c6 (Single in Row 3) Eliminating 3 From r4c2 (Single in Column 2) Eliminating 3 From r5c2 (Single in Column 2) Eliminating 3 From r6c2 (Single in Column 2) Eliminating 3 From r8c2 (Single in Column 2) Eliminating 3 From r9c2 (Single in Column 2) Eliminating 5 From r1c7 (Single in Box 3) Eliminating 5 From r1c8 (Single in Box 3) Eliminating 5 From r1c9 (Single in Box 3) Eliminating 5 From r2c8 (Single in Box 3) Eliminating 5 From r2c9 (Single in Box 3) Eliminating 5 From r3c7 (Single in Box 3) Eliminating 5 From r3c3 (Single in Row 3) Eliminating 5 From r3c4 (Single in Row 3) Eliminating 5 From r3c5 (Single in Row 3) Eliminating 5 From r3c6 (Single in Row 3) Eliminating 5 From r4c8 (Single in Column 8) Eliminating 5 From r5c8 (Single in Column 8) Eliminating 5 From r6c8 (Single in Column 8) Eliminating 5 From r8c8 (Single in Column 8) Eliminating 5 From r9c8 (Single in Column 8) Eliminating 6 From r1c7 (Single in Box 3) Eliminating 6 From r1c8 (Single in Box 3) Eliminating 6 From r1c9 (Single in Box 3) Eliminating 6 From r2c8 (Single in Box 3) Eliminating 6 From r2c9 (Single in Box 3) Eliminating 6 From r3c7 (Single in Box 3) Eliminating 6 From r3c3 (Single in Row 3) Eliminating 6 From r3c4 (Single in Row 3) Eliminating 6 From r3c5 (Single in Row 3) Eliminating 6 From r3c6 (Single in Row 3) Eliminating 6 From r5c9 (Single in Column 9) Eliminating 6 From r8c9 (Single in Column 9) Eliminating 6 From r9c9 (Single in Column 9) Eliminating 5 From r4c2 (Single in Box 4) Eliminating 5 From r4c3 (Single in Box 4) Eliminating 5 From r5c1 (Single in Box 4) Eliminating 5 From r5c2 (Single in Box 4) Eliminating 5 From r5c3 (Single in Box 4) Eliminating 5 From r6c2 (Single in Box 4) Eliminating 5 From r6c3 (Single in Box 4) Eliminating 5 From r4c5 (Single in Row 4) Eliminating 5 From r4c7 (Single in Row 4) Eliminating 5 From r1c1 (Single in Column 1) Eliminating 5 From r2c1 (Single in Column 1) Eliminating 5 From r8c1 (Single in Column 1) Eliminating 5 From r9c1 (Single in Column 1) Eliminating 4 From r4c5 (Single in Box 5) Eliminating 4 From r5c4 (Single in Box 5) Eliminating 4 From r5c5 (Single in Box 5) Eliminating 4 From r5c6 (Single in Box 5) Eliminating 4 From r6c5 (Single in Box 5) Eliminating 4 From r4c2 (Single in Row 4) Eliminating 4 From r4c3 (Single in Row 4) Eliminating 4 From r4c7 (Single in Row 4) Eliminating 4 From r4c8 (Single in Row 4) Eliminating 4 From r1c4 (Single in Column 4) Eliminating 4 From r2c4 (Single in Column 4) Eliminating 4 From r7c4 (Single in Column 4) Eliminating 4 From r8c4 (Single in Column 4) Eliminating 4 From r9c4 (Single in Column 4) Eliminating 6 From r4c5 (Single in Box 5) Eliminating 6 From r5c4 (Single in Box 5) Eliminating 6 From r5c5 (Single in Box 5) Eliminating 6 From r5c6 (Single in Box 5) Eliminating 6 From r6c5 (Single in Box 5) Eliminating 6 From r4c2 (Single in Row 4) Eliminating 6 From r4c3 (Single in Row 4) Eliminating 6 From r4c7 (Single in Row 4) Eliminating 6 From r4c8 (Single in Row 4) Eliminating 6 From r1c6 (Single in Column 6) Eliminating 6 From r2c6 (Single in Column 6) Eliminating 6 From r7c6 (Single in Column 6) Eliminating 6 From r8c6 (Single in Column 6) Eliminating 6 From r9c6 (Single in Column 6) Eliminating 7 From r4c7 (Single in Box 6) Eliminating 7 From r4c8 (Single in Box 6) Eliminating 7 From r5c7 (Single in Box 6) Eliminating 7 From r5c8 (Single in Box 6) Eliminating 7 From r5c9 (Single in Box 6) Eliminating 7 From r6c7 (Single in Box 6) Eliminating 7 From r6c8 (Single in Box 6) Eliminating 7 From r4c2 (Single in Row 4) Eliminating 7 From r4c3 (Single in Row 4) Eliminating 7 From r4c5 (Single in Row 4) Eliminating 7 From r1c9 (Single in Column 9) Eliminating 7 From r2c9 (Single in Column 9) Eliminating 7 From r8c9 (Single in Column 9) Eliminating 7 From r9c9 (Single in Column 9) Eliminating 6 From r5c1 (Single in Box 4) Eliminating 6 From r5c2 (Single in Box 4) Eliminating 6 From r5c3 (Single in Box 4) Eliminating 6 From r6c2 (Single in Box 4) Eliminating 6 From r6c3 (Single in Box 4) Eliminating 6 From r6c7 (Single in Row 6) Eliminating 6 From r6c8 (Single in Row 6) Eliminating 6 From r1c1 (Single in Column 1) Eliminating 6 From r2c1 (Single in Column 1) Eliminating 6 From r8c1 (Single in Column 1) Eliminating 6 From r9c1 (Single in Column 1) Eliminating 8 From r4c5 (Single in Box 5) Eliminating 8 From r5c4 (Single in Box 5) Eliminating 8 From r5c5 (Single in Box 5) Eliminating 8 From r5c6 (Single in Box 5) Eliminating 8 From r6c5 (Single in Box 5) Eliminating 8 From r6c2 (Single in Row 6) Eliminating 8 From r6c3 (Single in Row 6) Eliminating 8 From r6c7 (Single in Row 6) Eliminating 8 From r6c8 (Single in Row 6) Eliminating 8 From r1c4 (Single in Column 4) Eliminating 8 From r2c4 (Single in Column 4) Eliminating 8 From r3c4 (Single in Column 4) Eliminating 8 From r7c4 (Single in Column 4) Eliminating 8 From r8c4 (Single in Column 4) Eliminating 8 From r9c4 (Single in Column 4) Eliminating 7 From r5c4 (Single in Box 5) Eliminating 7 From r5c5 (Single in Box 5) Eliminating 7 From r5c6 (Single in Box 5) Eliminating 7 From r6c5 (Single in Box 5) Eliminating 7 From r6c2 (Single in Row 6) Eliminating 7 From r6c3 (Single in Row 6) Eliminating 7 From r1c6 (Single in Column 6) Eliminating 7 From r2c6 (Single in Column 6) Eliminating 7 From r3c6 (Single in Column 6) Eliminating 7 From r7c6 (Single in Column 6) Eliminating 7 From r8c6 (Single in Column 6) Eliminating 7 From r9c6 (Single in Column 6) Eliminating 9 From r4c7 (Single in Box 6) Eliminating 9 From r4c8 (Single in Box 6) Eliminating 9 From r5c7 (Single in Box 6) Eliminating 9 From r5c8 (Single in Box 6) Eliminating 9 From r5c9 (Single in Box 6) Eliminating 9 From r6c7 (Single in Box 6) Eliminating 9 From r6c8 (Single in Box 6) Eliminating 9 From r6c2 (Single in Row 6) Eliminating 9 From r6c3 (Single in Row 6) Eliminating 9 From r6c5 (Single in Row 6) Eliminating 9 From r1c9 (Single in Column 9) Eliminating 9 From r2c9 (Single in Column 9) Eliminating 9 From r8c9 (Single in Column 9) Eliminating 9 From r9c9 (Single in Column 9) Eliminating 3 From r7c3 (Single in Box 7) Eliminating 3 From r8c1 (Single in Box 7) Eliminating 3 From r9c1 (Single in Box 7) Eliminating 3 From r9c3 (Single in Box 7) Eliminating 3 From r7c4 (Single in Row 7) Eliminating 3 From r7c5 (Single in Row 7) Eliminating 3 From r7c6 (Single in Row 7) Eliminating 3 From r5c1 (Single in Column 1) Eliminating 1 From r7c3 (Single in Box 7) Eliminating 1 From r8c1 (Single in Box 7) Eliminating 1 From r8c2 (Single in Box 7) Eliminating 1 From r9c1 (Single in Box 7) Eliminating 1 From r9c2 (Single in Box 7) Eliminating 1 From r9c3 (Single in Box 7) Eliminating 1 From r7c4 (Single in Row 7) Eliminating 1 From r7c6 (Single in Row 7) Eliminating 1 From r7c7 (Single in Row 7) Eliminating 1 From r2c2 (Single in Column 2) Eliminating 1 From r4c2 (Single in Column 2) Eliminating 1 From r5c2 (Single in Column 2) Eliminating 1 From r6c2 (Single in Column 2) Eliminating 7 From r7c7 (Single in Box 9) Eliminating 7 From r8c8 (Single in Box 9) Eliminating 7 From r9c7 (Single in Box 9) Eliminating 7 From r9c8 (Single in Box 9) Eliminating 7 From r7c3 (Single in Row 7) Eliminating 7 From r7c4 (Single in Row 7) Eliminating 7 From r7c5 (Single in Row 7) Eliminating 7 From r1c8 (Single in Column 8) Eliminating 7 From r2c8 (Single in Column 8) Eliminating 8 From r7c7 (Single in Box 9) Eliminating 8 From r8c8 (Single in Box 9) Eliminating 8 From r8c9 (Single in Box 9) Eliminating 8 From r9c7 (Single in Box 9) Eliminating 8 From r9c8 (Single in Box 9) Eliminating 8 From r9c9 (Single in Box 9) Eliminating 8 From r7c3 (Single in Row 7) Eliminating 8 From r7c5 (Single in Row 7) Eliminating 8 From r7c6 (Single in Row 7) Eliminating 8 From r1c9 (Single in Column 9) Eliminating 8 From r2c9 (Single in Column 9) Eliminating 8 From r5c9 (Single in Column 9) Eliminating 5 From r7c3 (Single in Box 7) Eliminating 5 From r8c2 (Single in Box 7) Eliminating 5 From r9c2 (Single in Box 7) Eliminating 5 From r9c3 (Single in Box 7) Eliminating 5 From r8c4 (Single in Row 8) Eliminating 5 From r8c5 (Single in Row 8) Eliminating 5 From r8c6 (Single in Row 8) Eliminating 5 From r8c9 (Single in Row 8) Eliminating 5 From r1c3 (Single in Column 3) Eliminating 4 From r7c7 (Single in Box 9) Eliminating 4 From r8c8 (Single in Box 9) Eliminating 4 From r8c9 (Single in Box 9) Eliminating 4 From r9c7 (Single in Box 9) Eliminating 4 From r9c8 (Single in Box 9) Eliminating 4 From r9c9 (Single in Box 9) Eliminating 4 From r8c2 (Single in Row 8) Eliminating 4 From r8c5 (Single in Row 8) Eliminating 4 From r8c6 (Single in Row 8) Eliminating 4 From r1c7 (Single in Column 7) Eliminating 4 From r5c7 (Single in Column 7) Eliminating 4 From r6c7 (Single in Column 7) Eliminating 2 From r7c4 (Single in Box 8) Eliminating 2 From r7c5 (Single in Box 8) Eliminating 2 From r7c6 (Single in Box 8) Eliminating 2 From r8c4 (Single in Box 8) Eliminating 2 From r8c5 (Single in Box 8) Eliminating 2 From r8c6 (Single in Box 8) Eliminating 2 From r9c4 (Single in Box 8) Eliminating 2 From r9c6 (Single in Box 8) Eliminating 2 From r9c1 (Single in Row 9) Eliminating 2 From r9c2 (Single in Row 9) Eliminating 2 From r9c7 (Single in Row 9) Eliminating 2 From r9c8 (Single in Row 9) Eliminating 2 From r9c9 (Single in Row 9) Eliminating 2 From r3c5 (Single in Column 5) Eliminating 2 From r4c5 (Single in Column 5) Eliminating 2 From r5c5 (Single in Column 5) Eliminating 2 From r6c5 (Single in Column 5) *--------------------------------------------------------------------------* | 789 56789 6789 | 235679 1 234589 | 2789 2489 24 | | 1789 56789 2 | 5679 456789 4589 | 3 1489 14 | | 4 3 1789 | 279 789 289 | 12789 5 6 | |------------------------+------------------------+------------------------| | 5 289 1389 | 4 39 6 | 128 1238 7 | | 12789 24789 134789 | 12359 359 12359 | 12568 123468 12345 | | 6 24 134 | 8 35 7 | 125 1234 9 | |------------------------+------------------------+------------------------| | 3 1 469 | 569 4569 459 | 2569 7 8 | | 2789 26789 5 | 13679 36789 1389 | 4 12369 123 | | 789 46789 46789 | 135679 2 134589 | 1569 1369 135 | *--------------------------------------------------------------------------* Eliminating 1 From r5c1 (Box 5 & Row 5 Box-Line interaction) Eliminating 1 From r5c3 (Box 5 & Row 5 Box-Line interaction) Eliminating 1 From r5c7 (Box 5 & Row 5 Box-Line interaction) Eliminating 1 From r5c8 (Box 5 & Row 5 Box-Line interaction) Eliminating 1 From r5c9 (Box 5 & Row 5 Box-Line interaction) Eliminating 2 From r5c1 (Box 5 & Row 5 Box-Line interaction) Eliminating 2 From r5c2 (Box 5 & Row 5 Box-Line interaction) Eliminating 2 From r5c7 (Box 5 & Row 5 Box-Line interaction) Eliminating 2 From r5c8 (Box 5 & Row 5 Box-Line interaction) Eliminating 2 From r5c9 (Box 5 & Row 5 Box-Line interaction) Eliminating 2 From r8c8 (Box 7 & Row 8 Box-Line interaction) Eliminating 2 From r8c9 (Box 7 & Row 8 Box-Line interaction) r2c1 value MUST be 1 (Hidden Single in Column 1)&&&&&&&&&&&&& r8c1 value MUST be 2 (Hidden Single in Column 1)&&&&&&&&&&&& r1c9 value MUST be 2 (Hidden Single in Column 9)&&&&&&&&&&& r7c7 value MUST be 2 (Hidden Single in Row 7) End of Step 1 *--------------------------------------------------------------------------* | 789 56789 6789 | 235679 1 234589 | 2789 2489 2 | | 1 56789 2 | 5679 456789 4589 | 3 1489 14 | | 4 3 1789 | 279 789 289 | 12789 5 6 | |------------------------+------------------------+------------------------| | 5 289 1389 | 4 39 6 | 128 1238 7 | | 789 4789 34789 | 12359 359 12359 | 568 3468 345 | | 6 24 134 | 8 35 7 | 125 1234 9 | |------------------------+------------------------+------------------------| | 3 1 469 | 569 4569 459 | 2 7 8 | | 2 26789 5 | 13679 36789 1389 | 4 1369 13 | | 789 46789 46789 | 135679 2 134589 | 1569 1369 135 | *--------------------------------------------------------------------------* Eliminating 1 From r3c3 (Box 4 & Column 3 Box-Line interaction) Eliminating 2 From r8c2 (Box 4 & Column 2 Box-Line interaction) Eliminating 5 From r9c4 (Box 9 & Row 9 Box-Line interaction) Eliminating 5 From r9c6 (Box 9 & Row 9 Box-Line interaction) Eliminating 2 From r1c7 (Single in Box 3) Eliminating 2 From r1c8 (Single in Box 3) Eliminating 2 From r3c7 (Single in Box 3) Eliminating 2 From r1c4 (Single in Row 1) Eliminating 2 From r1c6 (Single in Row 1) Eliminating 1 From r3c3 (Single in Box 1) Eliminating 1 From r2c8 (Single in Row 2) Eliminating 1 From r2c9 (Single in Row 2)%%% Eliminating 2 From r4c7 (Single in Column 7) Eliminating 2 From r6c7 (Single in Column 7) Eliminating 2 From r8c2 (Single in Box 7) *--------------------------------------------------------------------------* | 789 56789 6789 | 35679 1 34589 | 789 489 2 | | 1 56789 2 | 5679 456789 4589 | 3 489 4 | | 4 3 789 | 279 789 289 | 1789 5 6 | |------------------------+------------------------+------------------------| | 5 289 1389 | 4 39 6 | 18 1238 7 | | 789 4789 34789 | 12359 359 12359 | 568 3468 345 | | 6 24 134 | 8 35 7 | 15 1234 9 | |------------------------+------------------------+------------------------| | 3 1 469 | 569 4569 459 | 2 7 8 | | 2 6789 5 | 13679 36789 1389 | 4 1369 13 | | 789 46789 46789 | 135679 2 134589 | 1569 1369 135 | *--------------------------------------------------------------------------* $$$$$$$Eliminating 5 From r9c4 (Box 9 & Row 9 Box-Line interaction) $$$$$$$Eliminating 5 From r9c6 (Box 9 & Row 9 Box-Line interaction) r3c7 value MUST be 1 (Hidden Single in Row 3) End of Step 2 *--------------------------------------------------------------------------* | 789 56789 6789 | 35679 1 34589 | 789 489 2 | | 1 56789 2 | 5679 456789 4589 | 3 489 4 | | 4 3 789 | 279 789 289 | 1 5 6 | |------------------------+------------------------+------------------------| | 5 289 1389 | 4 39 6 | 18 1238 7 | | 789 4789 34789 | 12359 359 12359 | 568 3468 345 | | 6 24 134 | 8 35 7 | 15 1234 9 | |------------------------+------------------------+------------------------| | 3 1 469 | 569 4569 459 | 2 7 8 | | 2 6789 5 | 13679 36789 1389 | 4 1369 13 | | 789 46789 46789 | 13679 2 13489 | 1569 1369 135 | *--------------------------------------------------------------------------* Eliminating 1 From r4c7 (Single in Column 7)%%% Eliminating 1 From r6c7 (Single in Column 7)%%% Eliminating 1 From r9c7 (Single in Column 7) *--------------------------------------------------------------------------* | 789 56789 6789 | 35679 1 34589 | 789 489 2 | | 1 56789 2 | 5679 456789 4589 | 3 489 4 | | 4 3 789 | 279 789 289 | 1 5 6 | |------------------------+------------------------+------------------------| | 5 289 1389 | 4 39 6 | 8 1238 7 | | 789 4789 34789 | 12359 359 12359 | 568 3468 345 | | 6 24 134 | 8 35 7 | 5 1234 9 | |------------------------+------------------------+------------------------| | 3 1 469 | 569 4569 459 | 2 7 8 | | 2 6789 5 | 13679 36789 1389 | 4 1369 13 | | 789 46789 46789 | 13679 2 13489 | 569 1369 135 | *--------------------------------------------------------------------------* Eliminating 1 From r8c8 (Box 6 & Column 8 Box-Line interaction) Eliminating 1 From r9c8 (Box 6 & Column 8 Box-Line interaction) r1c7 value MUST be 7 (Hidden Single in Column 7) End of Step 3 *--------------------------------------------------------------------------* | 789 56789 6789 | 35679 1 34589 | 7 489 2 | | 1 56789 2 | 5679 456789 4589 | 3 489 4 | | 4 3 789 | 279 789 289 | 1 5 6 | |------------------------+------------------------+------------------------| | 5 289 1389 | 4 39 6 | 8 1238 7 | | 789 4789 34789 | 12359 359 12359 | 568 3468 345 | | 6 24 134 | 8 35 7 | 5 1234 9 | |------------------------+------------------------+------------------------| | 3 1 469 | 569 4569 459 | 2 7 8 | | 2 6789 5 | 13679 36789 1389 | 4 369 13 | | 789 46789 46789 | 13679 2 13489 | 569 369 135 | *--------------------------------------------------------------------------* Eliminating 8 From r4c8 (Box 3 & Column 8 Box-Line interaction) Eliminating 8 From r5c8 (Box 3 & Column 8 Box-Line interaction) Eliminating 9 From r8c8 (Box 3 & Column 8 Box-Line interaction) Eliminating 9 From r9c8 (Box 3 & Column 8 Box-Line interaction) Eliminating 7 From r1c1 (Single in Row 1) Eliminating 7 From r1c2 (Single in Row 1) Eliminating 7 From r1c3 (Single in Row 1) Eliminating 7 From r1c4 (Single in Row 1) *--------------------------------------------------------------------------* | 89 5689 689 | 3569 1 34589 | 7 489 2 | | 1 56789 2 | 5679 456789 4589 | 3 489 4 | | 4 3 789 | 279 789 289 | 1 5 6 | |------------------------+------------------------+------------------------| | 5 289 1389 | 4 39 6 | 8 1238 7 | | 789 4789 34789 | 12359 359 12359 | 568 3468 345 | | 6 24 134 | 8 35 7 | 5 1234 9 | |------------------------+------------------------+------------------------| | 3 1 469 | 569 4569 459 | 2 7 8 | | 2 6789 5 | 13679 36789 1389 | 4 369 13 | | 789 46789 46789 | 13679 2 13489 | 569 369 135 | *--------------------------------------------------------------------------* $$$$$$$Eliminating 8 From r4c8 (Box 3 & Column 8 Box-Line interaction) $$$$$$$Eliminating 8 From r5c8 (Box 3 & Column 8 Box-Line interaction) $$$$$$$Eliminating 9 From r8c8 (Box 3 & Column 8 Box-Line interaction) $$$$$$$Eliminating 9 From r9c8 (Box 3 & Column 8 Box-Line interaction) r9c7 value MUST be 9 (Hidden Single in Column 7) End of Step 4 *--------------------------------------------------------------------------* | 89 5689 689 | 3569 1 34589 | 7 489 2 | | 1 56789 2 | 5679 456789 4589 | 3 489 4 | | 4 3 789 | 279 789 289 | 1 5 6 | |------------------------+------------------------+------------------------| | 5 289 1389 | 4 39 6 | 8 123 7 | | 789 4789 34789 | 12359 359 12359 | 568 346 345 | | 6 24 134 | 8 35 7 | 5 1234 9 | |------------------------+------------------------+------------------------| | 3 1 469 | 569 4569 459 | 2 7 8 | | 2 6789 5 | 13679 36789 1389 | 4 36 13 | | 789 46789 46789 | 13679 2 13489 | 9 36 135 | *--------------------------------------------------------------------------* Eliminating 6 From r5c8 (Box 9 & Column 8 Box-Line interaction) Eliminating 9 From r9c1 (Single in Row 9) Eliminating 9 From r9c2 (Single in Row 9) Eliminating 9 From r9c3 (Single in Row 9) Eliminating 9 From r9c4 (Single in Row 9) Eliminating 9 From r9c6 (Single in Row 9) *--------------------------------------------------------------------------* | 89 5689 689 | 3569 1 34589 | 7 489 2 | | 1 56789 2 | 5679 456789 4589 | 3 489 4 | | 4 3 789 | 279 789 289 | 1 5 6 | |------------------------+------------------------+------------------------| | 5 289 1389 | 4 39 6 | 8 123 7 | | 789 4789 34789 | 12359 359 12359 | 568 346 345 | | 6 24 134 | 8 35 7 | 5 1234 9 | |------------------------+------------------------+------------------------| | 3 1 469 | 569 4569 459 | 2 7 8 | | 2 6789 5 | 13679 36789 1389 | 4 36 13 | | 78 4678 4678 | 1367 2 1348 | 9 36 135 | *--------------------------------------------------------------------------* $$$$$$$Eliminating 6 From r5c8 (Box 9 & Column 8 Box-Line interaction) r5c7 value MUST be 6 (Hidden Single in Column 7) r9c9 value MUST be 5 (Hidden Single in Row 9) End of Step 5 *--------------------------------------------------------------------------* | 89 5689 689 | 3569 1 34589 | 7 489 2 | | 1 56789 2 | 5679 456789 4589 | 3 489 4 | | 4 3 789 | 279 789 289 | 1 5 6 | |------------------------+------------------------+------------------------| | 5 289 1389 | 4 39 6 | 8 123 7 | | 789 4789 34789 | 12359 359 12359 | 6 34 345 | | 6 24 134 | 8 35 7 | 5 1234 9 | |------------------------+------------------------+------------------------| | 3 1 469 | 569 4569 459 | 2 7 8 | | 2 6789 5 | 13679 36789 1389 | 4 36 13 | | 78 4678 4678 | 1367 2 1348 | 9 36 5 | *--------------------------------------------------------------------------* Eliminating 5 From r5c9 (Single in Column 9) r6c7 value MUST be 5 (Hidden Single in Column 7) r4c7 value MUST be 8 (Hidden Single in Column 7) r8c9 value MUST be 1 (Hidden Single in Column 9) End of Step 6 *--------------------------------------------------------------------------* | 89 5689 689 | 3569 1 34589 | 7 489 2 | | 1 56789 2 | 5679 456789 4589 | 3 489 4 | | 4 3 789 | 279 789 289 | 1 5 6 | |------------------------+------------------------+------------------------| | 5 289 1389 | 4 39 6 | 8 123 7 | | 789 4789 34789 | 12359 359 12359 | 6 34 34 | | 6 24 134 | 8 35 7 | 5 1234 9 | |------------------------+------------------------+------------------------| | 3 1 469 | 569 4569 459 | 2 7 8 | | 2 6789 5 | 13679 36789 1389 | 4 36 1 | | 78 4678 4678 | 1367 2 1348 | 9 36 5 | *--------------------------------------------------------------------------* Eliminating 3 From r4c8 (Box 9 & Column 8 Box-Line interaction) Eliminating 3 From r5c8 (Box 9 & Column 8 Box-Line interaction) Eliminating 3 From r6c8 (Box 9 & Column 8 Box-Line interaction) Eliminating 8 From r4c2 (Single in Row 4) Eliminating 8 From r4c3 (Single in Row 4) Eliminating 5 From r6c5 (Single in Row 6) Eliminating 1 From r8c4 (Single in Row 8) Eliminating 1 From r8c6 (Single in Row 8) *--------------------------------------------------------------------------* | 89 5689 689 | 3569 1 34589 | 7 489 2 | | 1 56789 2 | 5679 456789 4589 | 3 489 4 | | 4 3 789 | 279 789 289 | 1 5 6 | |------------------------+------------------------+------------------------| | 5 29 139 | 4 39 6 | 8 123 7 | | 789 4789 34789 | 12359 359 12359 | 6 34 34 | | 6 24 134 | 8 3 7 | 5 1234 9 | |------------------------+------------------------+------------------------| | 3 1 469 | 569 4569 459 | 2 7 8 | | 2 6789 5 | 3679 36789 389 | 4 36 1 | | 78 4678 4678 | 1367 2 1348 | 9 36 5 | *--------------------------------------------------------------------------* $$$$$$$Eliminating 3 From r4c8 (Box 9 & Column 8 Box-Line interaction) $$$$$$$Eliminating 3 From r5c8 (Box 9 & Column 8 Box-Line interaction) $$$$$$$Eliminating 3 From r6c8 (Box 9 & Column 8 Box-Line interaction) r5c9 value MUST be 3 (Hidden Single in Column 9) End of Step 7 *--------------------------------------------------------------------------* | 89 5689 689 | 3569 1 34589 | 7 489 2 | | 1 56789 2 | 5679 456789 4589 | 3 489 4 | | 4 3 789 | 279 789 289 | 1 5 6 | |------------------------+------------------------+------------------------| | 5 29 139 | 4 39 6 | 8 12 7 | | 789 4789 34789 | 12359 359 12359 | 6 4 3 | | 6 24 134 | 8 3 7 | 5 124 9 | |------------------------+------------------------+------------------------| | 3 1 469 | 569 4569 459 | 2 7 8 | | 2 6789 5 | 3679 36789 389 | 4 36 1 | | 78 4678 4678 | 1367 2 1348 | 9 36 5 | *--------------------------------------------------------------------------* Eliminating 4 From r1c8 (Box 6 & Column 8 Box-Line interaction) Eliminating 4 From r2c8 (Box 6 & Column 8 Box-Line interaction) Eliminating 3 From r5c3 (Single in Row 5) Eliminating 3 From r5c4 (Single in Row 5) Eliminating 3 From r5c5 (Single in Row 5) Eliminating 3 From r5c6 (Single in Row 5) *--------------------------------------------------------------------------* | 89 5689 689 | 3569 1 34589 | 7 489 2 | | 1 56789 2 | 5679 456789 4589 | 3 489 4 | | 4 3 789 | 279 789 289 | 1 5 6 | |------------------------+------------------------+------------------------| | 5 29 139 | 4 39 6 | 8 12 7 | | 789 4789 4789 | 1259 59 1259 | 6 4 3 | | 6 24 134 | 8 3 7 | 5 124 9 | |------------------------+------------------------+------------------------| | 3 1 469 | 569 4569 459 | 2 7 8 | | 2 6789 5 | 3679 36789 389 | 4 36 1 | | 78 4678 4678 | 1367 2 1348 | 9 36 5 | *--------------------------------------------------------------------------* Eliminating 3 From r8c5 (Box 5 & Column 5 Box-Line interaction) $$$$$$$Eliminating 4 From r1c8 (Box 6 & Column 8 Box-Line interaction) $$$$$$$Eliminating 4 From r2c8 (Box 6 & Column 8 Box-Line interaction) r2c9 value MUST be 4 (Hidden Single in Column 9)&&&&&&&& r1c6 value MUST be 4 (Hidden Single in Row 1) End of Step 8 *--------------------------------------------------------------------------* | 89 5689 689 | 3569 1 4 | 7 89 2 | | 1 56789 2 | 5679 456789 4589 | 3 89 4 | | 4 3 789 | 279 789 289 | 1 5 6 | |------------------------+------------------------+------------------------| | 5 29 139 | 4 39 6 | 8 12 7 | | 789 4789 4789 | 1259 59 1259 | 6 4 3 | | 6 24 134 | 8 3 7 | 5 124 9 | |------------------------+------------------------+------------------------| | 3 1 469 | 569 4569 459 | 2 7 8 | | 2 6789 5 | 3679 6789 389 | 4 36 1 | | 78 4678 4678 | 1367 2 1348 | 9 36 5 | *--------------------------------------------------------------------------* Eliminating 4 From r2c5 (Single in Box 2) Eliminating 4 From r2c6 (Single in Box 2) Eliminating 4 From r7c6 (Single in Column 6) Eliminating 4 From r9c6 (Single in Column 6) *-----------------------------------------------------------------* | 89 5689 689 | 3569 1 4 | 7 89 2 | | 1 56789 2 | 5679 56789 589 | 3 89 4 | | 4 3 789 | 279 789 289 | 1 5 6 | |---------------------+---------------------+---------------------| | 5 29 139 | 4 39 6 | 8 12 7 | | 789 4789 4789 | 1259 59 1259 | 6 4 3 | | 6 24 134 | 8 3 7 | 5 124 9 | |---------------------+---------------------+---------------------| | 3 1 469 | 569 4569 59 | 2 7 8 | | 2 6789 5 | 3679 6789 389 | 4 36 1 | | 78 4678 4678 | 1367 2 138 | 9 36 5 | *-----------------------------------------------------------------* r7c5 value MUST be 4 (Hidden Single in Column 5) r1c4 value MUST be 3 (Hidden Single in Row 1) End of Step 9 *-----------------------------------------------------------------* | 89 5689 689 | 3 1 4 | 7 89 2 | | 1 56789 2 | 5679 56789 589 | 3 89 4 | | 4 3 789 | 279 789 289 | 1 5 6 | |---------------------+---------------------+---------------------| | 5 29 139 | 4 39 6 | 8 12 7 | | 789 4789 4789 | 1259 59 1259 | 6 4 3 | | 6 24 134 | 8 3 7 | 5 124 9 | |---------------------+---------------------+---------------------| | 3 1 469 | 569 4 59 | 2 7 8 | | 2 6789 5 | 3679 6789 389 | 4 36 1 | | 78 4678 4678 | 1367 2 138 | 9 36 5 | *-----------------------------------------------------------------* Eliminating 5 From r2c2 (Box 2 & Row 2 Box-Line interaction) Eliminating 6 From r2c2 (Box 2 & Row 2 Box-Line interaction) Eliminating 3 From r8c4 (Single in Column 4) Eliminating 3 From r9c4 (Single in Column 4) Eliminating 4 From r7c3 (Single in Row 7) *-----------------------------------------------------------------* | 89 5689 689 | 3 1 4 | 7 89 2 | | 1 56789 2 | 5679 56789 589 | 3 89 4 | | 4 3 789 | 279 789 289 | 1 5 6 | |---------------------+---------------------+---------------------| | 5 29 139 | 4 39 6 | 8 12 7 | | 789 4789 4789 | 1259 59 1259 | 6 4 3 | | 6 24 134 | 8 3 7 | 5 124 9 | |---------------------+---------------------+---------------------| | 3 1 69 | 569 4 59 | 2 7 8 | | 2 6789 5 | 679 6789 389 | 4 36 1 | | 78 4678 4678 | 167 2 138 | 9 36 5 | *-----------------------------------------------------------------* $$$$$$$Eliminating 5 From r2c2 (Box 2 & Row 2 Box-Line interaction) $$$$$$$Eliminating 6 From r2c2 (Box 2 & Row 2 Box-Line interaction) r1c2 value MUST be 5 (Hidden Single in Column 2) End of Step 10 *-----------------------------------------------------------------* | 89 5 689 | 3 1 4 | 7 89 2 | | 1 789 2 | 5679 56789 589 | 3 89 4 | | 4 3 789 | 279 789 289 | 1 5 6 | |---------------------+---------------------+---------------------| | 5 29 139 | 4 39 6 | 8 12 7 | | 789 4789 4789 | 1259 59 1259 | 6 4 3 | | 6 24 134 | 8 3 7 | 5 124 9 | |---------------------+---------------------+---------------------| | 3 1 69 | 569 4 59 | 2 7 8 | | 2 6789 5 | 679 6789 389 | 4 36 1 | | 78 4678 4678 | 167 2 138 | 9 36 5 | *-----------------------------------------------------------------* r1c3 value MUST be 6 (Hidden Single in Row 1) End of Step 11 *-----------------------------------------------------------------* | 89 5 6 | 3 1 4 | 7 89 2 | | 1 789 2 | 5679 56789 589 | 3 89 4 | | 4 3 789 | 279 789 289 | 1 5 6 | |---------------------+---------------------+---------------------| | 5 29 139 | 4 39 6 | 8 12 7 | | 789 4789 4789 | 1259 59 1259 | 6 4 3 | | 6 24 134 | 8 3 7 | 5 124 9 | |---------------------+---------------------+---------------------| | 3 1 69 | 569 4 59 | 2 7 8 | | 2 6789 5 | 679 6789 389 | 4 36 1 | | 78 4678 4678 | 167 2 138 | 9 36 5 | *-----------------------------------------------------------------* Eliminating 6 From r7c3 (Single in Column 3)%%%%%%% Eliminating 6 From r9c3 (Single in Column 3) *-----------------------------------------------------------------* | 89 5 6 | 3 1 4 | 7 89 2 | | 1 789 2 | 5679 56789 589 | 3 89 4 | | 4 3 789 | 279 789 289 | 1 5 6 | |---------------------+---------------------+---------------------| | 5 29 139 | 4 39 6 | 8 12 7 | | 789 4789 4789 | 1259 59 1259 | 6 4 3 | | 6 24 134 | 8 3 7 | 5 124 9 | |---------------------+---------------------+---------------------| | 3 1 9 | 569 4 59 | 2 7 8 | | 2 6789 5 | 679 6789 389 | 4 36 1 | | 78 4678 478 | 167 2 138 | 9 36 5 | *-----------------------------------------------------------------* r7c4 value MUST be 6 (Hidden Single in Row 7) End of Step 12 *-----------------------------------------------------------------* | 89 5 6 | 3 1 4 | 7 89 2 | | 1 789 2 | 5679 56789 589 | 3 89 4 | | 4 3 789 | 279 789 289 | 1 5 6 | |---------------------+---------------------+---------------------| | 5 29 139 | 4 39 6 | 8 12 7 | | 789 4789 4789 | 1259 59 1259 | 6 4 3 | | 6 24 134 | 8 3 7 | 5 124 9 | |---------------------+---------------------+---------------------| | 3 1 9 | 6 4 59 | 2 7 8 | | 2 6789 5 | 679 6789 389 | 4 36 1 | | 78 4678 478 | 167 2 138 | 9 36 5 | *-----------------------------------------------------------------* Eliminating 6 From r8c4 (Single in Box 8) Eliminating 6 From r8c5 (Single in Box 8) Eliminating 6 From r9c4 (Single in Box 8) Eliminating 6 From r2c4 (Single in Column 4) *-----------------------------------------------------------------* | 89 5 6 | 3 1 4 | 7 89 2 | | 1 789 2 | 579 56789 589 | 3 89 4 | | 4 3 789 | 279 789 289 | 1 5 6 | |---------------------+---------------------+---------------------| | 5 29 139 | 4 39 6 | 8 12 7 | | 789 4789 4789 | 1259 59 1259 | 6 4 3 | | 6 24 134 | 8 3 7 | 5 124 9 | |---------------------+---------------------+---------------------| | 3 1 9 | 6 4 59 | 2 7 8 | | 2 6789 5 | 79 789 389 | 4 36 1 | | 78 4678 478 | 17 2 138 | 9 36 5 | *-----------------------------------------------------------------* r2c5 value MUST be 6 (Hidden Single in Column 5) r7c6 value MUST be 5 (Hidden Single in Row 7) End of Step 13 *--------------------------------------------------------* | 89 5 6 | 3 1 4 | 7 89 2 | | 1 789 2 | 579 6 589 | 3 89 4 | | 4 3 789 | 279 789 289 | 1 5 6 | |------------------+------------------+------------------| | 5 29 139 | 4 39 6 | 8 12 7 | | 789 4789 4789 | 1259 59 1259 | 6 4 3 | | 6 24 134 | 8 3 7 | 5 124 9 | |------------------+------------------+------------------| | 3 1 9 | 6 4 5 | 2 7 8 | | 2 6789 5 | 79 789 389 | 4 36 1 | | 78 4678 478 | 17 2 138 | 9 36 5 | *--------------------------------------------------------* Eliminating 9 From r8c2 (Box 8 & Row 8 Box-Line interaction) Eliminating 5 From r2c6 (Single in Column 6) Eliminating 5 From r5c6 (Single in Column 6) *--------------------------------------------------------* | 89 5 6 | 3 1 4 | 7 89 2 | | 1 789 2 | 579 6 89 | 3 89 4 | | 4 3 789 | 279 789 289 | 1 5 6 | |------------------+------------------+------------------| | 5 29 139 | 4 39 6 | 8 12 7 | | 789 4789 4789 | 1259 59 129 | 6 4 3 | | 6 24 134 | 8 3 7 | 5 124 9 | |------------------+------------------+------------------| | 3 1 9 | 6 4 5 | 2 7 8 | | 2 6789 5 | 79 789 389 | 4 36 1 | | 78 4678 478 | 17 2 138 | 9 36 5 | *--------------------------------------------------------* $$$$$$$Eliminating 9 From r8c2 (Box 8 & Row 8 Box-Line interaction) r5c5 value MUST be 5 (Hidden Single in Column 5) r2c4 value MUST be 5 (Hidden Single in Row 2) r7c3 value MUST be 9 (Hidden Single in Row 7) End of Step 14 *--------------------------------------------------------* | 89 5 6 | 3 1 4 | 7 89 2 | | 1 789 2 | 5 6 89 | 3 89 4 | | 4 3 789 | 279 789 289 | 1 5 6 | |------------------+------------------+------------------| | 5 29 139 | 4 39 6 | 8 12 7 | | 789 4789 4789 | 1259 5 129 | 6 4 3 | | 6 24 134 | 8 3 7 | 5 124 9 | |------------------+------------------+------------------| | 3 1 9 | 6 4 5 | 2 7 8 | | 2 678 5 | 79 789 389 | 4 36 1 | | 78 4678 478 | 17 2 138 | 9 36 5 | *--------------------------------------------------------* Eliminating 7 From r3c3 (Box 2 & Row 3 Box-Line interaction) Eliminating 5 From r5c4 (Single in Column 4) Eliminating 9 From r3c3 (Single in Column 3) Eliminating 9 From r4c3 (Single in Column 3) Eliminating 9 From r5c3 (Single in Column 3) *--------------------------------------------------------* | 89 5 6 | 3 1 4 | 7 89 2 | | 1 789 2 | 5 6 89 | 3 89 4 | | 4 3 78 | 279 789 289 | 1 5 6 | |------------------+------------------+------------------| | 5 29 13 | 4 39 6 | 8 12 7 | | 789 4789 478 | 129 5 129 | 6 4 3 | | 6 24 134 | 8 3 7 | 5 124 9 | |------------------+------------------+------------------| | 3 1 9 | 6 4 5 | 2 7 8 | | 2 678 5 | 79 789 389 | 4 36 1 | | 78 4678 478 | 17 2 138 | 9 36 5 | *--------------------------------------------------------* $$$$$$$Eliminating 7 From r3c3 (Box 2 & Row 3 Box-Line interaction) r2c2 value MUST be 7 (Hidden Single in Row 2) End of Step 15 *--------------------------------------------------------* | 89 5 6 | 3 1 4 | 7 89 2 | | 1 7 2 | 5 6 89 | 3 89 4 | | 4 3 8 | 279 789 289 | 1 5 6 | |------------------+------------------+------------------| | 5 29 13 | 4 39 6 | 8 12 7 | | 789 4789 478 | 129 5 129 | 6 4 3 | | 6 24 134 | 8 3 7 | 5 124 9 | |------------------+------------------+------------------| | 3 1 9 | 6 4 5 | 2 7 8 | | 2 678 5 | 79 789 389 | 4 36 1 | | 78 4678 478 | 17 2 138 | 9 36 5 | *--------------------------------------------------------* Eliminating 7 From r5c2 (Single in Column 2) Eliminating 7 From r8c2 (Single in Column 2) Eliminating 7 From r9c2 (Single in Column 2) *-----------------------------------------------* | 89 5 6 | 3 1 4 | 7 89 2 | | 1 7 2 | 5 6 89 | 3 89 4 | | 4 3 8 | 279 789 289 | 1 5 6 | |---------------+---------------+---------------| | 5 29 13 | 4 39 6 | 8 12 7 | | 789 489 478 | 129 5 129 | 6 4 3 | | 6 24 134 | 8 3 7 | 5 124 9 | |---------------+---------------+---------------| | 3 1 9 | 6 4 5 | 2 7 8 | | 2 68 5 | 79 789 389 | 4 36 1 | | 78 468 478 | 17 2 138 | 9 36 5 | *-----------------------------------------------* Eliminating 7 From r9c4 (Box 7 & Row 9 Box-Line interaction) r1c1 value MUST be 9 (Hidden Single in Box 1) End of Step 16 *-----------------------------------------------* | 9 5 6 | 3 1 4 | 7 89 2 | | 1 7 2 | 5 6 89 | 3 89 4 | | 4 3 8 | 279 789 289 | 1 5 6 | |---------------+---------------+---------------| | 5 29 13 | 4 39 6 | 8 12 7 | | 789 489 478 | 129 5 129 | 6 4 3 | | 6 24 134 | 8 3 7 | 5 124 9 | |---------------+---------------+---------------| | 3 1 9 | 6 4 5 | 2 7 8 | | 2 68 5 | 79 789 389 | 4 36 1 | | 78 468 478 | 1 2 138 | 9 36 5 | *-----------------------------------------------* Eliminating 9 From r1c8 (Single in Row 1)%%%%%%%%%%%% Eliminating 9 From r5c1 (Single in Column 1) *-----------------------------------------------* | 9 5 6 | 3 1 4 | 7 8 2 | | 1 7 2 | 5 6 89 | 3 89 4 | | 4 3 8 | 279 789 289 | 1 5 6 | |---------------+---------------+---------------| | 5 29 13 | 4 39 6 | 8 12 7 | | 78 489 478 | 129 5 129 | 6 4 3 | | 6 24 134 | 8 3 7 | 5 124 9 | |---------------+---------------+---------------| | 3 1 9 | 6 4 5 | 2 7 8 | | 2 68 5 | 79 789 389 | 4 36 1 | | 78 468 478 | 1 2 138 | 9 36 5 | *-----------------------------------------------* r2c8 value MUST be 9 (Hidden Single in Column 8) r1c8 value MUST be 8 (Hidden Single in Row 1) r3c3 value MUST be 8 (Hidden Single in Box 1) End of Step 17 *-----------------------------------------------* | 9 5 6 | 3 1 4 | 7 8 2 | | 1 7 2 | 5 6 89 | 3 9 4 | | 4 3 8 | 279 789 289 | 1 5 6 | |---------------+---------------+---------------| | 5 29 13 | 4 39 6 | 8 12 7 | | 78 489 478 | 129 5 129 | 6 4 3 | | 6 24 134 | 8 3 7 | 5 124 9 | |---------------+---------------+---------------| | 3 1 9 | 6 4 5 | 2 7 8 | | 2 68 5 | 79 789 389 | 4 36 1 | | 78 468 478 | 1 2 138 | 9 36 5 | *-----------------------------------------------* Eliminating 9 From r2c6 (Single in Row 2)%%%%%%%%%%%%%%% Eliminating 8 From r3c5 (Single in Row 3) Eliminating 8 From r3c6 (Single in Row 3) Eliminating 8 From r5c3 (Single in Column 3) Eliminating 8 From r9c3 (Single in Column 3) *-----------------------------------------------* | 9 5 6 | 3 1 4 | 7 8 2 | | 1 7 2 | 5 6 8 | 3 9 4 | | 4 3 8 | 279 79 29 | 1 5 6 | |---------------+---------------+---------------| | 5 29 13 | 4 39 6 | 8 12 7 | | 78 489 47 | 129 5 129 | 6 4 3 | | 6 24 134 | 8 3 7 | 5 124 9 | |---------------+---------------+---------------| | 3 1 9 | 6 4 5 | 2 7 8 | | 2 68 5 | 79 789 389 | 4 36 1 | | 78 468 47 | 1 2 138 | 9 36 5 | *-----------------------------------------------* r8c5 value MUST be 8 (Hidden Single in Column 5) r2c6 value MUST be 8 (Hidden Single in Row 2) End of Step 18 *-----------------------------------------------* | 9 5 6 | 3 1 4 | 7 8 2 | | 1 7 2 | 5 6 8 | 3 9 4 | | 4 3 8 | 279 79 29 | 1 5 6 | |---------------+---------------+---------------| | 5 29 13 | 4 39 6 | 8 12 7 | | 78 489 47 | 129 5 129 | 6 4 3 | | 6 24 134 | 8 3 7 | 5 124 9 | |---------------+---------------+---------------| | 3 1 9 | 6 4 5 | 2 7 8 | | 2 68 5 | 79 8 389 | 4 36 1 | | 78 468 47 | 1 2 138 | 9 36 5 | *-----------------------------------------------* Eliminating 8 From r8c6 (Single in Column 6) Eliminating 8 From r9c6 (Single in Column 6) Eliminating 8 From r8c2 (Single in Row 8)%%%%%%%%%%%% *-----------------------------------------------* | 9 5 6 | 3 1 4 | 7 8 2 | | 1 7 2 | 5 6 8 | 3 9 4 | | 4 3 8 | 279 79 29 | 1 5 6 | |---------------+---------------+---------------| | 5 29 13 | 4 39 6 | 8 12 7 | | 78 489 47 | 129 5 129 | 6 4 3 | | 6 24 134 | 8 3 7 | 5 124 9 | |---------------+---------------+---------------| | 3 1 9 | 6 4 5 | 2 7 8 | | 2 6 5 | 79 8 39 | 4 36 1 | | 78 468 47 | 1 2 13 | 9 36 5 | *-----------------------------------------------* r3c5 value MUST be 7 (Hidden Single in Column 5) r8c4 value MUST be 7 (Hidden Single in Row 8) End of Step 19 *-----------------------------------------------* | 9 5 6 | 3 1 4 | 7 8 2 | | 1 7 2 | 5 6 8 | 3 9 4 | | 4 3 8 | 279 7 29 | 1 5 6 | |---------------+---------------+---------------| | 5 29 13 | 4 39 6 | 8 12 7 | | 78 489 47 | 129 5 129 | 6 4 3 | | 6 24 134 | 8 3 7 | 5 124 9 | |---------------+---------------+---------------| | 3 1 9 | 6 4 5 | 2 7 8 | | 2 6 5 | 7 8 39 | 4 36 1 | | 78 468 47 | 1 2 13 | 9 36 5 | *-----------------------------------------------* Eliminating 7 From r3c4 (Single in Box 2) r4c5 value MUST be 9 (Hidden Single in Column 5) r8c6 value MUST be 9 (Hidden Single in Row 8) End of Step 20 *-----------------------------------------------* | 9 5 6 | 3 1 4 | 7 8 2 | | 1 7 2 | 5 6 8 | 3 9 4 | | 4 3 8 | 29 7 29 | 1 5 6 | |---------------+---------------+---------------| | 5 29 13 | 4 9 6 | 8 12 7 | | 78 489 47 | 129 5 129 | 6 4 3 | | 6 24 134 | 8 3 7 | 5 124 9 | |---------------+---------------+---------------| | 3 1 9 | 6 4 5 | 2 7 8 | | 2 6 5 | 7 8 9 | 4 36 1 | | 78 468 47 | 1 2 13 | 9 36 5 | *-----------------------------------------------* Eliminating 9 From r5c4 (Single in Box 5) Eliminating 9 From r5c6 (Single in Box 5) Eliminating 9 From r4c2 (Single in Row 4)%%%%%%%%%%%%%% Eliminating 9 From r3c6 (Single in Column 6)%%%%%%%%%%%%%% *-----------------------------------------------* | 9 5 6 | 3 1 4 | 7 8 2 | | 1 7 2 | 5 6 8 | 3 9 4 | | 4 3 8 | 29 7 2 | 1 5 6 | |---------------+---------------+---------------| | 5 2 13 | 4 9 6 | 8 12 7 | | 78 489 47 | 12 5 12 | 6 4 3 | | 6 24 134 | 8 3 7 | 5 124 9 | |---------------+---------------+---------------| | 3 1 9 | 6 4 5 | 2 7 8 | | 2 6 5 | 7 8 9 | 4 36 1 | | 78 468 47 | 1 2 13 | 9 36 5 | *-----------------------------------------------* r5c2 value MUST be 9 (Hidden Single in Column 2) r3c4 value MUST be 9 (Hidden Single in Column 4) r6c5 value MUST be 3 (Hidden Single in Column 5) r9c6 value MUST be 3 (Hidden Single in Column 6) r4c3 value MUST be 3 (Hidden Single in Row 4) r8c8 value MUST be 3 (Hidden Single in Row 8) End of Step 21 *-----------------------------------------------* | 9 5 6 | 3 1 4 | 7 8 2 | | 1 7 2 | 5 6 8 | 3 9 4 | | 4 3 8 | 9 7 2 | 1 5 6 | |---------------+---------------+---------------| | 5 2 3 | 4 9 6 | 8 12 7 | | 78 9 47 | 12 5 12 | 6 4 3 | | 6 24 134 | 8 3 7 | 5 124 9 | |---------------+---------------+---------------| | 3 1 9 | 6 4 5 | 2 7 8 | | 2 6 5 | 7 8 9 | 4 3 1 | | 78 468 47 | 1 2 3 | 9 36 5 | *-----------------------------------------------* Eliminating 3 From r6c3 (Single in Box 4) Eliminating 3 From r9c8 (Single in Box 9)%%%%%%%%%% *-----------------------------------------------* | 9 5 6 | 3 1 4 | 7 8 2 | | 1 7 2 | 5 6 8 | 3 9 4 | | 4 3 8 | 9 7 2 | 1 5 6 | |---------------+---------------+---------------| | 5 2 3 | 4 9 6 | 8 12 7 | | 78 9 47 | 12 5 12 | 6 4 3 | | 6 24 14 | 8 3 7 | 5 124 9 | |---------------+---------------+---------------| | 3 1 9 | 6 4 5 | 2 7 8 | | 2 6 5 | 7 8 9 | 4 3 1 | | 78 468 47 | 1 2 3 | 9 6 5 | *-----------------------------------------------* r9c2 value MUST be 8 (Hidden Single in Column 2) r6c3 value MUST be 1 (Hidden Single in Column 3) r5c4 value MUST be 2 (Hidden Single in Column 4) r5c6 value MUST be 1 (Hidden Single in Column 6) r9c8 value MUST be 6 (Hidden Single in Column 8) r3c6 value MUST be 2 (Hidden Single in Row 3) r4c8 value MUST be 1 (Hidden Single in Row 4) r5c1 value MUST be 8 (Hidden Single in Row 5) r8c2 value MUST be 6 (Hidden Single in Row 8) r9c4 value MUST be 1 (Hidden Single in Row 9) End of Step 22 *-----------------------------------------------* | 9 5 6 | 3 1 4 | 7 8 2 | | 1 7 2 | 5 6 8 | 3 9 4 | | 4 3 8 | 9 7 2 | 1 5 6 | |---------------+---------------+---------------| | 5 2 3 | 4 9 6 | 8 1 7 | | 8 9 47 | 2 5 1 | 6 4 3 | | 6 24 1 | 8 3 7 | 5 124 9 | |---------------+---------------+---------------| | 3 1 9 | 6 4 5 | 2 7 8 | | 2 6 5 | 7 8 9 | 4 3 1 | | 78 8 47 | 1 2 3 | 9 6 5 | *-----------------------------------------------* Eliminating 1 From r6c8 (Single in Box 6) Eliminating 8 From r9c1 (Single in Column 1)%%%%%%%%%%% *--------------------------------------* | 9 5 6 | 3 1 4 | 7 8 2 | | 1 7 2 | 5 6 8 | 3 9 4 | | 4 3 8 | 9 7 2 | 1 5 6 | |------------+------------+------------| | 5 2 3 | 4 9 6 | 8 1 7 | | 8 9 47 | 2 5 1 | 6 4 3 | | 6 24 1 | 8 3 7 | 5 24 9 | |------------+------------+------------| | 3 1 9 | 6 4 5 | 2 7 8 | | 2 6 5 | 7 8 9 | 4 3 1 | | 7 8 47 | 1 2 3 | 9 6 5 | *--------------------------------------* r9c1 value MUST be 7 (Hidden Single in Column 1) r6c2 value MUST be 4 (Hidden Single in Column 2) r6c8 value MUST be 2 (Hidden Single in Column 8) r4c2 value MUST be 2 (Hidden Single in Row 4) r5c3 value MUST be 7 (Hidden Single in Row 5) r9c3 value MUST be 4 (Hidden Single in Row 9) End of Step 23 *-----------------------------* | 9 5 6 | 3 1 4 | 7 8 2 | | 1 7 2 | 5 6 8 | 3 9 4 | | 4 3 8 | 9 7 2 | 1 5 6 | |---------+---------+---------| | 5 2 3 | 4 9 6 | 8 1 7 | | 8 9 7 | 2 5 1 | 6 4 3 | | 6 4 1 | 8 3 7 | 5 2 9 | |---------+---------+---------| | 3 1 9 | 6 4 5 | 2 7 8 | | 2 6 5 | 7 8 9 | 4 3 1 | | 7 8 4 | 1 2 3 | 9 6 5 | *-----------------------------* r5c8 value MUST be 4 (Hidden Single in Column 8) End of Step 24 *-----------------------------* | 9 5 6 | 3 1 4 | 7 8 2 | | 1 7 2 | 5 6 8 | 3 9 4 | | 4 3 8 | 9 7 2 | 1 5 6 | |---------+---------+---------| | 5 2 3 | 4 9 6 | 8 1 7 | | 8 9 7 | 2 5 1 | 6 4 3 | | 6 4 1 | 8 3 7 | 5 2 9 | |---------+---------+---------| | 3 1 9 | 6 4 5 | 2 7 8 | | 2 6 5 | 7 8 9 | 4 3 1 | | 7 8 4 | 1 2 3 | 9 6 5 | *-----------------------------* Step Count: 040101010203010202010101020301010302020206100601

look at the non PM grid after the end of step 22 before the start of step 23 compared to the PM grid

Code: Select all: *-----------------------------* | 9 5 6 | 3 1 4 | 7 8 2 | | 1 7 2 | 5 6 8 | 3 9 4 | | 4 3 8 | 9 7 2 | 1 5 6 | |---------+---------+---------| | 5 . 3 | 4 9 6 | 8 1 7 | | 8 9 . | 2 5 1 | 6 . 3 | | 6 . 1 | 8 3 7 | 5 . 9 | |---------+---------+---------| | 3 1 9 | 6 4 5 | 2 7 8 | | 2 6 5 | 7 8 9 | 4 3 1 | | . 8 . | 1 2 3 | 9 6 5 | *-----------------------------* *-----------------------------------------------* | 9 5 6 | 3 1 4 | 7 8 2 | | 1 7 2 | 5 6 8 | 3 9 4 | | 4 3 8 | 9 7 2 | 1 5 6 | |---------------+---------------+---------------| | 5 2 3 | 4 9 6 | 8 1 7 | | 8 9 47 | 2 5 1 | 6 4 3 | | 6 24 1 | 8 3 7 | 5 124 9 | |---------------+---------------+---------------| | 3 1 9 | 6 4 5 | 2 7 8 | | 2 6 5 | 7 8 9 | 4 3 1 | | 78 8 47 | 1 2 3 | 9 6 5 | *-----------------------------------------------*

looking at r5c8 clearly it can only be 4, that is a naked single & many players would make the placement that way, however this thread & several öther players dont. The same goes for r4c2 however at this step the question of where would you place 2 in row 4 is

by **ronk** » Thu Jun 08, 2006 12:24 pm

tarek wrote:I used to attach single eliminations to the Naked singles algorithm, but because of this thread now I have 3 algorithms (one for naked singles, one for hidden singles & one for single eliminations) ...

I must be missing something. If "single eliminations" were attached to both naked singles and hidden singles, wouldn't disallowance of naked singles then also disallow "single eliminations" due to naked singles?

If so, then your log could be a lot shorter.

by **tarek** » Thu Jun 08, 2006 1:18 pm

ronk wrote:I must be missing something. If "single eliminations" were attached to both naked singles and hidden singles, wouldn't disallowance of naked singles then also disallow "single eliminations" due to naked singles?.

You are right, there are no naked singles in my log & therefore no single eliminations following naked singles.... the single eliminations follow only hidden singles.... the part that follows the log should make things a bit clearer, naked singles detection is turned off, therefore single eliminations in step 23 are blind to the fact that r5c8 is a naked single

tarek

by **gsf** » Thu Jun 08, 2006 4:55 pm

tarek wrote:Here is the log for the 24 stepper Ocean has posted

thanks
I finally reach step count convergence
here's my (terse) log, B:box-line, N:hidden-single

Code: Select all: 1 [1] B12 [51][53][57][58][59]^1 [51][52][57][58][59][88][89]^2 N4 [77][81][19]=2 [21]=1 2 B2 [94][96]^5 N1 [37]=1 3 B2 [88][98]^1 N1 [17]=7 4 B4 [48][58]^8 [88][98]^9 N1 [97]=9 5 B1 [58]^6 N2 [57]=6 [99]=5 6 N3 [67]=5 [47]=8 [89]=1 7 B3 [48][58][68]^3 N1 [59]=3 8 B3 [85]^3 [18][28]^4 N2 [16][29]=4 9 N2 [14]=3 [75]=4 10 B2 [22]^5 [22]^6 N1 [12]=5 11 N1 [13]=6 12 N1 [74]=6 13 N2 [25]=6 [76]=5 14 B1 [82]^9 N3 [24][55]=5 [73]=9 15 B1 [33]^7 N1 [22]=7 16 B1 [94]^7 N1 [11]=9 17 N3 [18][33]=8 [28]=9 18 N2 [26][85]=8 19 N2 [84][35]=7 20 N2 [86][45]=9 21 N6 [34][52]=9 [43][88][65][96]=3 22 N10 [36][54]=2 [48][94][63][56]=1 [51][92]=8 [82][98]=6 23 N6 [42][68]=2 [53][91]=7 [93][62]=4 24 N1 [58]=4 S

by **tarek** » Fri Jun 09, 2006 5:46 am

Fantastic gsf,

i see that you also went ahead to put the algorithms in the following order...

1. single elimination
2. Box line (pointing pairs)
3. Hidden singles

I will be doing that shortly......

So if the methods converged...........WHERE ARE THE PUZZLES

tarek

by **gsf** » Fri Jun 09, 2006 7:08 am

tarek wrote:Fantastic gsf,

i see that you also went ahead to put the algorithms in the following order...

1. single elimination
2. Box line (pointing pairs)
3. Hidden singles

by way of command line options
I don't want to reprogram this again
for ulterior the constraint order and grouping is specified as

Code: Select all: {B2:N}

(use only box-line and hidden single in that order, count both as one step,
commit moves between each -- ab's rules)
and for inferior its

Code: Select all: {FN}

(use only naked and hidden singles in that order, count both as one step,
commit moves after both applied)

here's the first batch in the format ocean uses for the low stepper thread
sorted by symmetry type, steps, clues and (symmetric) minimal
a double check on step count would be good

code wrote:#!sudoku -c5,SYMMETRY,STEPS,CLUES,MINIMAL,PUZZLE,SUBMITTER,SEQUENCE
I,2,40,SM,000567000013408750050903080831000429200000008764000531080104060079605340000239000,gsf,2006-06-09
I,3,32,SM,001708600000305000609000305970030084000902000230050016506000409000509000007106800,gsf,2006-06-09
II,2,36,SM,063900010810700094000010005000259047004607200920134000500020000490003061070006480,gsf,2006-06-09
II,3,32,SM,000000300005837000203500760090080630080903010016070020034001502000728900008000000,gsf,2006-06-09
II,22,25,SM,001009000040010230050000006300080000080341060000090008800000050064070020000400800,gsf,2006-06-09
III,3,32,SM,000879000604000809300605007042000710000402000036000490900107008705000906000963000,gsf,2006-06-09
III,20,28,SM,090000070201709304000000000023905740000000000057608120000000000605302409040000080,gsf,2006-06-09
III,21,28,SM,010803070008706500060000030074000210000000000092000680050000040003908100040201090,gsf,2006-06-09
IV,3,30,SM,000970280000405001000800609694000010500000002010000574807002000400306000051094000,gsf,2006-06-09
IV,20,26,SM,060500009904600000050004000230060700000109000009020048000700010000002603700001020,gsf,2006-06-09
IV,22,24,SM,000007400050040700000000012000690001040201080500078000790000000003060090002400000,gsf,2006-06-09
V,20,24,M,000000004100008300400120060056030000000701000000060490090045008005900006300000000,gsf,2006-06-09
V,21,24,SM,040320010010007000090000600400001308000000000507800004002000090000100070060032080,gsf,2006-06-09
V,21,25,M,200000000030400000097001030304050700002070600009020308040700180000009050000000002,gsf,2006-06-09
V,22,24,M,008050000000004720000000051050000017302000406410000090260000000075900000000040200,gsf,2006-06-09
V,23,26,SM,000450076000000500400070008903008200080000060004200109100030002007000000630027000,gsf,2006-06-09
V,24,27,SM,102030000009004050050010007900206500000090000006407003300060040020800600000020709,gsf,2006-06-09
V,25,26,SM,005000200300000060080005009750004800004809300009700014100500070040000002006000100,gsf,2006-06-09
VI,20,24,M,007208006000000500094500200800020000000003070200090000018700900000000600005102008,gsf,2006-06-09
VI,21,24,SM,300000008400030009006704500000010000000607000500000002050000080200803004040209060,gsf,2006-06-09
VI,21,25,M,083000650700000004006000200050302090001708400000000000000409000004165800002000100,gsf,2006-06-09
VI,22,25,SM,000000000120000047800306002510000039000408000000000000064000590200090004907000806,gsf,2006-06-09
VI,23,24,M,006010400000504000470000086600803001050000030090020050700000005020000010003000700,gsf,2006-06-09
VI,24,25,SM,000302000051000480300000006000000000060508040093040520605000701000705000009000800,gsf,2006-06-09
VI,25,28,SM,070609080580000072000000000800000009003000700090304010600201007001000200930806051,gsf,2006-06-09
VI,26,26,SM,009000300280706045000509000402000507700000002090020010800000006000601000040070030,gsf,2006-06-09
VII,3,32,SM,080473002703000001020900005809006013400000029300700840000009000000824000958610000,gsf,2006-06-09
VII,20,23,SM,406000100050009000000001206000000530079100000800250000000010003080040050000800001,gsf,2006-06-09
VII,20,24,M,000540010000000209906000070004700000060800003700013008005001600010070000000400300,gsf,2006-06-09
VII,21,24,M,000000300010900020000307604065004000000001000003790500708002090040000750006000000,gsf,2006-06-09
VII,22,25,M,000000084009004500060100200001000760000001300030020090013570000400908000900000006,gsf,2006-06-09
VII,23,24,M,004000300000900020500380604065004000009001000000790500708002090040000700006000000,gsf,2006-06-09
VII,24,25,SM,029601040050008003000000800000102036700000000100009004096000001004000027000950000,gsf,2006-06-09
VII,25,28,SM,000000008040068090000950700003000004015000607070000130002035010060009200300210006,gsf,2006-06-09
VII,26,25,M,000041903000008600000050000000000000702000001190000480450009160000005804900070020,gsf,2006-06-09

by **gsf** » Sat Jun 10, 2006 5:29 am

here's a symmetry I symmetrically minimal 48 clue 1 stepper

Code: Select all: #I,1,48,SM,017209430503106207490307086879000521000000000235000864320705048906803702058402910,gsf,2006-06-10 . 1 7 2 . 9 4 3 . 5 . 3 1 . 6 2 . 7 4 9 . 3 . 7 . 8 6 8 7 9 . . . 5 2 1 . . . . . . . . . 2 3 5 . . . 8 6 4 3 2 . 7 . 5 . 4 8 9 . 6 8 . 3 7 . 2 . 5 8 4 . 2 9 1 .

by **Pat** » Sun Jun 11, 2006 11:19 am

tarek (2006.Jun.4) wrote:
Pat (2006.Jun.4) wrote:
RW (2006.May.29) wrote:[ 6 ulterior puzzles ]

#3
-

nice puzzle — does seem to need 4 exclusions from box to line

You are solving it Pat in the method which this thread does not employ.
We employ ab's method, "hidden singles" & box-line at the same time.
Pat's method, is exhausting "hidden singles" before going to box-line.

hey tarek, i'm not a computer — i don't always find all "hidden singles" before the box-line interactions.

i was proposing an additional method of rating the puzzles — by the needed box-line interactions.

consider this example of solving by multi-stage box-line interactions, posted by RW (2006.May.29):

Code: Select all: -----|-----|* | * * X X|. . .|X | X * X X|. . .|X | X -----+-----+----- | X X|. . .|X | * | * *|-----|--|-- | X X|. . .|X | * -----+-----+----- | . .|. . .|. | . | . .|. . .|. | . | . .|. . .|. A .

it would be a great joy to solve a puzzle this way;
but then i'd have to ask, was it all actually needed??

if the puzzle needs this complex deduction,
then the puzzle deserves a high rating;

but suppose all this wasn't needed,
suppose i missed some "hidden single"
— then all the joy i got from my comlex solution
is merely my fault for missing an easier way,
and the puzzle in my opinion does not deserve a high rating.

~ Pat

The New Sudoku Players' Forum

Ulterior Puzzles

shorthand

Re: shorthand

re: _needed_ box-line interactions