The New Sudoku Players' Forum

by **Kit_ISIS_Kat** » Fri Jun 09, 2006 3:01 am

In the post from a few weeks ago, it seems that there was a clue or two missing from the puzzle itself. I wonder if this is another example of the same. Any help would be greatly appreciated. More detailed comments are at the bottom of this email. Thanks!

Original Puzzle

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

Partial solution
5..|..8|3..
...|51.|..7
..2|36.|54.
---+---+---
.7.|..6|1..
9..|.7.|..5
6.8|4..|72.

---+---+---
.6.|..5|8..
3..|68.|...
.84|23.|956

{5} {149} {1679} {79} {249} {8} {3} {169} {129}
{48} {349} {369} {5} {1} {249} {26} {689} {7}
{178} {19} {2} {3} {6} {79} {5} {4} {189}

{24} {7} {35} {89} {259} {6} {1} {389} {3489}
{9} {1234} {13} {18} {7} {123} {46} {368} {5}
{6} {135} {8} {4} {59} {139} {7} {2} {39}

{127} {6} {179} {179} {49} {5} {8} {137} {1234}
{3} {1259} {1579} {6} {8} {1479} {24} {17} {124}
{17} {8} {4} {2} {3} {17} {9} {5} {6}

Question relates to 2nd mini-grid
{79} {249} {8}
{5} {1} {249}
{3} {6} {79}

The hint I was given was "Reduce based on Naked pairs". This would leave me with:
{79} {24}** {8}
{5} {1} {24}*
{3} {6} {79}

The program allowed me to place a 2 under the 8* but not a 4. What I want to know is what clue is there to tell me to eliminate the 4 from that cell or to tell me it is the 2 that belongs there?

Or from a different perspective, what clue is there to tell me that the 4 and not the two belongs in the cell** above where the 1 is located?

by **tarek** » Fri Jun 09, 2006 6:20 am

Hi there, what you are looking at is a HIDDEN pair rather than a naked pair.......The logic behind keeping only 24 in both cells is that if u look in that box......these 2 cells are the only cells which can hold 2 & 4 so one of them must be 2 the other must be 4.you can eliminate the rest....

now you cant go any further with hidden pairs regarding these 2 cells....

the puzzle is solved with advanced methods like colouring, this step is how i see it

Code: Select all: *--------------------------------------------------------* | 5 149 1679 | 79 24 8 | 3 169 129 | |*48 3489 369 | 5 1 *24 | 26 689 7 | | 178 189 2 | 3 6 79 | 5 4 189 | |------------------+------------------+------------------| |#24 7 35 | 89 259 6 | 1 389 3489 | |*9 -24 13 | 18 7 123 |*46 368 5 | | 6 135 8 | 4 59 139 | 7 2 39 | |------------------+------------------+------------------| | 12 6 179 | 179 49 5 | 8 137 1234 | | 3 1259 1579 | 6 8 *1479 |*24 157 14 | | 178 158 4 | 2 3 17 | 9 157 6 | *--------------------------------------------------------* *--------------------------------------------------------* | 5 *149 1679 | 79 *24 8 | 3 169 129 | | 48 3489 369 | 5 1 24 | 26 689 7 | | 178 189 2 | 3 6 79 | 5 4 189 | |------------------+------------------+------------------| |#24 *7 35 | 89 259 6 | 1 389 *3489 | | 9 -24 13 | 18 7 123 | 46 368 5 | | 6 135 8 | 4 59 139 | 7 2 39 | |------------------+------------------+------------------| | 12 6 179 | 179 *49 5 | 8 137 *1234 | | 3 1259 1579 | 6 8 1479 | 24 157 14 | | 178 158 4 | 2 3 17 | 9 157 6 | *--------------------------------------------------------* Eliminating 4 From r5c2 (Eyeless Finned Swordfish in Columns 167 with 1 fin in Box 4, or by constructing the Finned Swordfish in rows 147 with 1 fin in Box 4)

& the puzzle is solved

tarek

by **Carcul** » Sun Jun 11, 2006 10:21 am

Code: Select all: *-----------------------------------------------------------* | 5 149 1679 | 79 24 8 | 3 169 129 | | 48 3489 369 | 5 1 24 | 26 689 7 | | 178 189 2 | 3 6 79 | 5 4 189 | |-------------------+-------------------+-------------------| | 24 7 35 | 89 259 6 | 1 389 3489 | | 9 1234 13 | 18 7 123 | 46 368 5 | | 6 135 8 | 4 59 139 | 7 2 39 | |-------------------+-------------------+-------------------| | 127 6 179 | 179 49 5 | 8 137 1234 | | 3 1259 1579 | 6 8 1479 | 24 157 124 | | 178 158 4 | 2 3 17 | 9 157 6 | *-----------------------------------------------------------*

[r2c3]=3=[r2c2]={ATILA(4): r2c1|r4c1|r5c2|r5c7|r8c7|(r8c9)|r8c6|r2c6}
=4=[r8c9]-4-[r8c7]-2-[r2c7]-6-[r2c3],

which implies r2c3<>6 and the puzzle is solved.
For an explanation about the notation, check here.
"ATILA" stands for Almost Two Incompatible Loops Argument: check
this post.

Carcul

by **daj95376** » Sun Jun 11, 2006 4:53 pm

Technically speaking -- of which I'm not very good it seems -- the partial solution originally presented does have a Naked Pair <79> in block 2.

These steps will get your original puzzle to the following state.

Code: Select all: r6c7 = 7 Hidden Single r6c1 = 6 Hidden Single r8c4 = 6 Hidden Single b2 - 79 Naked Pair r2c4 = 5 Naked Single r3c5 = 6 Naked Single r3c7 = 5 Hidden Single r9c7 = 9 Naked Single r9c5 = 3 Naked Single b4 - 135 Naked Triple r147 - 2 Swordfish *-----------------------------------------------------------* | 5 149 1679 | 79 24 8 | 3 169 129 | | 48 3489 369 | 5 1 24 | 26 689 7 | | 178 189 2 | 3 6 79 | 5 4 189 | |-------------------+-------------------+-------------------| | 24 7 35 | 89 259 6 | 1 389 3489 | | 9 24 13 | 18 7 123 | 46 368 5 | | 6 135 8 | 4 59 139 | 7 2 39 | |-------------------+-------------------+-------------------| | 127 6 179 | 179 49 5 | 8 137 1234 | | 3 1259 1579 | 6 8 1479 | 24 157 14 | | 178 158 4 | 2 3 17 | 9 157 6 | *-----------------------------------------------------------*

As to your question about why r2c6 can not be 4, the answer is that it forces the elimination of all 4's in block 1 and results in an invalid puzzle.

Code: Select all: r2c6=4 => r5c6=2 => r5c2=4 => r1c2<>4 r2c6=4 => r2c1<>4 & r2c2<>4

by **ronk** » Sun Jun 11, 2006 8:47 pm

Carcul wrote:
Code: Select all
*-----------------------------------------------------------* | 5 149 1679 | 79 24 8 | 3 169 129 | | 48 3489 369 | 5 1 24 | 26 689 7 | | 178 189 2 | 3 6 79 | 5 4 189 | |-------------------+-------------------+-------------------| | 24 7 35 | 89 259 6 | 1 389 3489 | | 9 1234 13 | 18 7 123 | 46 368 5 | | 6 135 8 | 4 59 139 | 7 2 39 | |-------------------+-------------------+-------------------| | 127 6 179 | 179 49 5 | 8 137 1234 | | 3 1259 1579 | 6 8 1479 | 24 157 124 | | 178 158 4 | 2 3 17 | 9 157 6 | *-----------------------------------------------------------*

[r2c3]=3=[r2c2]={ATILA(4): r2c1|r4c1|r5c2|r5c7|r8c7|(r8c9)|r8c6|r2c6}
=4=[r8c9]-4-[r8c7]-2-[r2c7]-6-[r2c3],

which implies r2c3<>6 and the puzzle is solved.

Just coloring the two conjugate chains in digit 4 is easier to understand.

Code: Select all: . B . | . b . | . . . A 4 . | . . B | . . . . . . | . . . | . . . -------+-------+------- a . . | . . . | . . A . A . | . . . | a . . . . . | . . . | . . . -------+-------+------- . . . | . B . | . . b . . . | . . b | A . 4 . . . | . . . | . . .

The two chains are colored 'Aa' and 'Bb'. In row 2 and box 1 color 'B' (representing digit 4 as) true excludes 'A' true. In row 8, 'b' true also excludes 'A' from being true. Since either 'B' or 'b' must be true, digit 4 may be eliminated from all cells colored 'A'.

One possible nice loop expression: r2c1-4-r4c1=4=r5c2-4-r5c7=4=r8c7-4-r8c6=4=r2c6-4-r2c1,

which implies r2c1<>4 and the puzzle is solved with cascading singles.

by **Carcul** » Mon Jun 12, 2006 8:24 am

Ronk wrote:Just coloring the two conjugate chains in digit 4 is easier to understand.

Yes, I know. I also spoted that simple solution. But sometimes I think it's interesting (and, who knows, educational) to present/try to find a solution using an alternative way of thought (even if a simpler solution is available, as in this case), instead of keep solving puzzles using always the same way. If Kit_ISIS_Kat don't like my solution, then he/she will simply ignore it, with no problem. But I believe that it's always good to have several options available.

Carcul

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