The New Sudoku Players' Forum

[Luke]

The first chain will crack the puzzle, but its presence in the second chain is what caught my attention. The second chain allows two different values to be assigned to cell [r2c7] without any contradiction in the logic -- I think. Is the second chain a valid chain?

I'm not gettin' it, so what's new...both chains can be viewed as type 3 discontinuous nice loops, with the weak links eliminated from the start cells. I can see why the first loop makes the second redundant, but how does the second impact r2c7?

[daj95376]

The first chain will crack the puzzle, but its presence in the second chain is what caught my attention. The second chain allows two different values to be assigned to cell [r2c7] without any contradiction in the logic -- I think. Is the second chain a valid chain?

I'm not gettin' it, so what's new...both chains can be viewed as type 3 discontinuous nice loops, with the weak links eliminated from the start cells. I can see why the first loop makes the second redundant, but how does the second impact r2c7?

The emphasis of my original question was in regards to the steps in a chain being allowed to assign two different values to a cell. Like you, hobiwan and ronk were more interested in other aspects of my chains. Fortunately, they did answer my question as well.

Here's everything that's important about these two cells -- using hobiwan's suggested perspective of a forcing chain.

Code: Select all

[r2c2]=5                       =>  [r2c2]<>3, [r2c7]<>5
[r2c2]<>5  => ... => [r2c7]=3  =>  [r2c2]<>3, [r2c7]<>5


[daj95376]

A question on Eureka/AIC notation:

Would you use (1=1)r58c8 to represent a strong link in [c8] for <1>?

[ronk]

A question on Eureka/AIC notation:

Would you use (1=1)r58c8 to represent a strong link in [c8] for <1>?

I asked José ... he said 'no way'.

[daj95376]

This puzzle has multiple solutions, but none of the solutions have any U4s to my knowledge.

Code: Select all

8....6..2..295..7..9.........4..8..5.8.....9.9..1..8.........1..7..394..3..6....9

 +-----------------------------------------------------------------------+
 |  8      1345   1357   |  347    147    6      |  9      345    2      |
 |  146    1346   2      |  9      5      134    |  136    7      8      |
 |  14567  9      13567  |  23478  12478  12347  |  1356   3456   134    |
 |-----------------------+-----------------------+-----------------------|
 |  1267   1236   4      |  237    9      8      |  12367  236    5      |
 |  12567  8      13567  |  23457  2467   23457  |  12367  9      1347   |
 |  9      2356   3567   |  1      2467   23457  |  8      2346   347    |
 |-----------------------+-----------------------+-----------------------|
 |  2456   2456   9      |  24578  2478   2457   |  2357   1      37     |
 |  125    7      158    |  25     3      9      |  4      258    6      |
 |  3      245    58     |  6      1247   12457  |  257    258    9      |
 +-----------------------------------------------------------------------+
 # 148 eliminations remain


Is there a larger unavoidable, or is there something else that I'm missing? TIA!!!

[dobrichev]

Is there a larger unavoidable, or is there something else that I'm missing?

It has 770 solutions. List of the unavoidables not hit for first 2 and last solution follows. Entire list size is 2.8MB.

Hidden Text: Show

Code: Select all

8....6..2..295..7..9.........4..8..5.8.....9.9..1..8.........1..7..394..3..6....9   24   770   #pattern,nClues,nSolutions

815376942462951378793842561134798625287563194956124837629485713571239486348617259   1   16   #solution,sNumber,nUnavoidables
.....................84..................................48......................   4   n
......................42.........................24..............................   4   n
........................56.......62...........................................25.   6   n
..........6....3....3....6..3....6.............6....3............................   8   n
....................................2.756...4.56.24..7.2.4.5...5..2..............   15   n
.15........................13.....2.2.756...4.56.24.37...4.5...5.1...............   20   n
.1.37.........13..7.3.....113.7.......7..31.4.....4..7......7.3.............17...   21   n
.15.7....46...1...7...4.............2.75......5..24...62...57..5..2.........172..   23   n
..5.7..4..........7...4.5.1.3.....2.2.75..1.4.5...4.3..2.4.5...5..2...........25.   24   n
...37..4..6....3..7.3.42.6..3.7..62.2.7..3.......2..3762....7.3..................   24   n
.1537..4......13..7...4...113.7.......75.31.4.5...4.3..2.4.57............4..172..   29   n
..53...4......13....3.4.5.1.3.....2.2..5.31.4.5...4.3..2.4.57..5..2......4..1725.   30   n
.1537..4.46...13..7...4..6.13....62.2.7563....56.2..3.62.4.57............4..172..   34   n
.1537..4..6...13..7...4..6.13.7..62.2.75.31...5..24.3.62.4.57..5..2.........172..   35   n
.1537.....6...13..7.3....6.13.7..62.2.75.31.4.5..24.3762...57..5..2.........172..   35   n
.15....4.46...13..7.3.4.5.113.....2.2.75.31.4.....4.3.62.4.57..5.12...8..48.1725.   38   y

815376942462951378793482561134798625287563194956124837629845713571239486348617259   2   17   #solution,sNumber,nUnavoidables
.....................48..................................84......................   4   n
........................56.......62...........................................25.   6   n
..........6....3....3....6..3....6.............6....3............................   8   n
....................................2..5......5..24....2..45...5..2..............   10   n
.....................4.2............2.756...4.56.24..7.2...5...5..2..............   16   n
.1.37.........13..7.3.....113.7.......7..31.4.....4..7......7.3.............17...   21   n
..........6....3..7.3....6..3....62.2.75.3.......24.3.62..45...5..2..............   21   n
.153...4..........7.34..5.113.....2.2.7..31.4.....4.3..........5.1............25.   23   n
..53...4............34.25.1.3.....2.2..5.31.4.5...4.3..2...5...5..2...........25.   24   n
..5.7..4..........7..4.25.1.3.....2.2.75..1.4.5...4.3..2..457..5..2......4...725.   28   n
.1537..4..6...13..7..4...6.13.7..62.2.7.631...56.2..3.62....................17...   29   n
.1.37....4....1...7.34.2...13.7.....2.75.3..4.5..24..7.2...57..5..2.........172..   29   n
.1537..4..6...13..7..4.2.6..3....62.2.7563....56.2..3.62...5...5..2.........17...   31   n
.1537..4..6...13..7..4...6..3.7..62.2.7.63..4.56.24.3762....7.3.............17...   32   n
.1537.....6...13..7.3....6.13.7..62.2.75.31.4.5..24.3762...57..5..2.........172..   35   n
.1537..4..6...13..7..4...6.13.7..62.2.75.31.4.5..24.3762...57..5..2.........172..   36   n
.15.7..4.46...13..7.34.25.113.....2.2.75.31.4.....4.3.62..457..5.12...8..48.1725.   40   n

...

857416932412953678693782154134298765786345291925167843569824317271539486348671529   770   81   #solution,sNumber,nUnavoidables
..74...3............37....4.........................43...........................   8   n
.....................7.2....3.2..7............2...7..3......3.7..................   10   n
........................154.3.2........3..2.1.2.....43........................52.   13   n
.5.....3............3....5..3.2.......6345....25.6....5...24...2..5..............   18   n
.57.1.....1...3...6.37.2....3.2.....7.63......25..7.........................71...   19   n
.5741.....1...3.....37.2....3.2.......634.....25.67.........................71...   20   n
.57.1.....1....6..6..7.21.....2..7..7....52....5..7...56....................71...   20   n
.5.....3..1....6..6.3...15.13....7..7....5.....5..7..356....3.7..................   20   n
.574...3............37..154.3.2.......634.2.1.25.6..4.........................52.   22   n
.5.....3.41.........3....5.13....7..7...45.....5..7..35....43.7..........4..7.5..   22   n
.5741.....1....6..6..7821...........7...45.....5..7...56.824................71...   23   n
.5.41..3..1...3...6.3....54.3.....6...634........67.4356....................71...   23   n
.574.....41...3.....37.....13....7..7..345.....5..7..35....43.7..........4..7.5..   25   n
.57.1.....1....6..6..7821.....2..7..7.....2...25..7...56.82....2..5.........71...   25   n
.5.4...3.41...3...6.3....5.13....7..7.634.........7..35....43.7..........4..7.5..   25   n
.5.....3..........6.3...15413....76.7.6.45..1..5.67.4356....3.7..................   25   n
.5741..3..1....6..6.378215............6.45.....5.67...56.824................71...   27   n
.5.41..3..1...3.....378..5..3.2..7....634.....25.67..3...82.3.7.............71...   27   n
.5.....3..........6.37.2154.3.2..76...6.452.1..5.67.4356....3.7..................   27   n
.574...3..........6.37..154.3.2...6.7.63452.1..5.67.4.56......................52.   28   n
.57.1.....1...3.....37......3.2..7....6345....25.67..35...243.72..5.........71...   28   n
.5.....3..........6.378..5..3.2..7....6.45....25.67..356.8243.7..........4..7.5..   28   n
.5741..3..1...36..6..7..1.4...2..7..7..3.52.1..5..7.4356....3.7.............71...   29   n
.5741..3..1....6..6.378.15.13.2.......634.....25.6....56.82....2.15..............   29   n
.5.41..3..1...3...6.378..5..3.2..7....634.....2..67..356.82.3.7.............71...   29   n
.5.....3.41.......6.3...15413.2..7..7.634.2.1.....7.435....43.7..........4..7.5..   29   n
..7.1.....1...3.....3782...13.2..7..7..3.52....5..7..35..82.3.72.15.........71...   29   n
..7.1.....1...3.....3782...13....7..7....5.....5..7..35..82.3.72.1....8...8.7152.   29   n
...4...3.4....36..6..7821.41.....7..7.6345..1..5.67.43...8243.7..................   29   n
...4...3.4....36..6..7821.4...2..7....63452.1..5.67.43...8243.7..................   29   n
.574...3..........6.37..154.3.2.....7.63452.1.25..7.4.5...24...2..5...........52.   30   n
.57.1..3..1...36..6.37.2154...2..7......4.2.1.....7.4356..243.7.............71...   30   n
.57.1..3..1...36..6.37..154...2..7..7..3.52.1..5..7.4356....3.7.............71...   30   n
.5.41..3..1...36..6.....1541.....7..7.6345..1..5.67.4356....3.7.............71...   30   n
.5.4...3.4....36..6.....1541.....7..7.6345..1..5.67.435....43.7..........4..7.5..   30   n
..741.....1...3.....3782...13.2..7..7.63452....5.67...5..82....2.15.........71...   30   n
.........41..........78.15413.2..7......4.2.1.2...7.435..8243.72..5......4..7.52.   30   n
.57.1....41....6..6..78.1...3.2..7..7.6.45....25.67..35..8243.7..........4..7.5..   31   n
.57.1.....1....6..6..78.1...3.2..7..7.6.45....25.67..356.8243.7..........4..7.5..   31   n
...4...3.41...3...6.37821.413.2..76...634.2.1....67.43...8243.7..................   31   n
.5741..3.41...36..6..7..1.4...2..7..7..3.52.1..5..7.435....43.7..........4..715..   32   n
.57.1..3.41...36..6.37821541.....7..7.......1.......435..8243.7..........4..715..   32   n
.57.1..3..1...36..6.37821541.....7..7.......1.......4356.8243.7..........4..715..   32   n
.57.1..3..1...36..6.37.2154...2..7....6.452.1..5.67.4356....3.7.............71...   32   n
.57.1..3..1...36..6.37..1541.....7..7.6345..1..5.67.4356....3.7.............71...   32   n
.57.1..3..1...36..6.37..154...2..7....63452.1..5.67.4356....3.7.............71...   32   n
.57.1.....1...3...6.37.2154.3.2...6.7.63452.1..5.67.4.56....................7152.   32   n
.5.41..3..1...36..6..78..5..3.2..76...6345....25.67..356.82.3.7.............71...   32   n
.5.4...3.4....36..6..78..5..3.2..76...6345....25.67..35..8243.7..........4..7.5..   32   n
..741.....1...3.....37.2...13.2..7..7..3452....5..7..35...2.3.72.1....8...8.7152.   32   n
..7.1.....1...3.....37.2...13.2..7..7..3452....5..7..35...243.72.1....8...8.7152.   32   n
.57.1..3.41...36..6.37.2154...2..7..7....52.1..5..7.435....43.7..........4..715..   33   n
.57.1..3.41...36..6.37..154...2..7..7..3.52.1..5..7.435....43.7..........4..715..   33   n
.57.1..3.41....6..6.378.15..3.2..7....6.45....25.67..35..8243.7..........4..7.5..   33   n
.5.....3..........6.378.15413.2..7..7.634...1.2..67.4356.8243.7..........4..7.5..   33   n
...4...3.4....36..6..78.154...2..76...63452.1..5.67.43...8243.7.............7.52.   33   n
...4...3.4....36..6.....1.41.....7..7.6345..1..5.67.435...243.72.1....8...8.7.52.   33   n
...4...3.41...3...6.378.15413.2..76...634.2.1....67.43...8243.7.............7.52.   34   n
.57.1..3.41...36..6.37.2154...2..7....6.452.1..5.67.435....43.7..........4..715..   35   n
.57.1..3.41...36..6.37..1541.....7..7.6345..1..5.67.435....43.7..........4..715..   35   n
.57.1..3.41...36..6.37..154...2..7....63452.1..5.67.435....43.7..........4..715..   35   n
.57.1..3..1...36..6.37821541..2..7..7.......1.25..7.4356.82.3.72..5.........71...   35   n
.57.1.....1...3...6.37.2154.3.2..76.7.6.452.1..5.67.4356....3.7.............7152.   35   n
.57.1.....1...3...6.37..154.3.2..76.7.63452.1..5.67.4356....3.7.............7152.   35   n
..7.1....41....6..6..78.1..13.2..7..7.6.45....25.67..35..8243.72.1....8..48.7.52.   36   n
..7.1.....1....6..6..78.1..13.2..7..7.6.45....25.67..356.8243.72.1....8..48.7.52.   36   n
.........41....6..6..78.15.13.2..76.7.63452...25.67..35..8243.72..5......4..7.52.   36   n
..........1....6..6..78.15.13.2..76.7.63452...25.67..356.8243.72..5......4..7.52.   36   n
.5741..3..1...36..6..7821.41..2..7..7..3.5..1.25..7.4356.8243.72..5.........71...   37   n
.5741..3..1...36..6..7..1.41..2..7..7.6345..1.25.67.4356..243.72..5.........71...   37   n
..7.1.....1...3...6.378215413.2...6.7.63452.1..5.67.4.5..82....2.15.........7152.   37   n
.57.1..3..1...36..6.37821541..2..7....6.4...1.25.67.4356.82.3.72.15.........71...   38   n
.57.1..3..1...36..6.37..1541..2..7....6345..1.25.67.4356..243.72.15.........71...   38   n
.5.....3..........6.378.15413.2..76...6.4...1.25.67.4356.8243.72.1....8..48.7.52.   38   n
..7.1.....1...3...6.378215413.2.....7.63452.1.25.67.4.56.82....2.15.........7152.   38   n
.5.41..3..1...36..6..78.1541..2..7....6345..1.25.67.4356.8243.72.15.........71...   39   n
.5.4...3.41...36..6.378.15.13.2..7....634.....25.67..35..8243.72.1....8..48.7.52.   39   y
.57.1..3.41...36..6.37.21541..2..7....6.4...1.25.67.435....43.72.1....8..48.7152.   40   n
.57.1..3..1...36..6.37.21541..2..7....6.4...1.25.67.4356..243.72.1....8...8.7152.   40   n
.57.1..3..1...36..6.37.21541..2..7....6.4...1.25.67.4356...43.72.1....8..48.7152.   40   n
..7.1.....1...3...6.378215413.2..76.7.6.452.1..5.67.435..82.3.72.15.........7152.   40   n


[daj95376]

Thanks dobrichev, your breakdown was exactly what I needed.

Regards, Danny

[daj95376]

"Free Press" puzzle presented by Keith in DailySudoku.com .

Code: Select all

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

 after basics
 +-----------------------------------------------------+
 |  12   58   6    |  7    3    9    | #125  4   *158  |
 |  12   59   7    |  8    4    25   |  3    6   #159  |
 |  89   4    3    |  1    6    25   |  2-5  7    89   |
 |-----------------+-----------------+-----------------|
 |  5    89   2    |  4    7    1    |  68   39   36   |
 |  4    7    89   |  6    5    3    |  18   19   2    |
 |  3    6    1    |  9    2    8    |  4    5    7    |
 |-----------------+-----------------+-----------------|
 |  78   1    58   |  25   9    4    | #567  23   36   |
 |  6    3    4    |  25   8    7    |  9    12   15   |
 |  79   2    59   |  3    1    6    |  57   8    4    |
 +-----------------------------------------------------+
 # 35 eliminations remain


I was originally convinced this was a BUG+4 scenario with <5> in the (#) cells and <1> in the (*) cell. However, if the 5s are excluded, then (5=12)r1c71 - (1)r1c9 exists and the puzzle is reduced to a BUG.

Should this still be considered a BUG+4 scenario? TIA!!!

[ronk]

I was originally convinced this was a BUG+4 scenario with <5> in the (#) cells and <1> in the (*) cell. However, if the 5s are excluded, then (5=12)r1c71 - (1)r1c9 exists and the puzzle is reduced to a BUG.

Should this still be considered a BUG+4 scenario? TIA!!!

Yes, it should IMO. Let's assume, as here, that a BUG+N has N extra candidates in N cells. There is no requirement that the Nth candidate be immune to a simple move when the other N-1 candidates are assumed false.