## Triple Forcing Chains

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eleven wrote:Here uniqueness pattern 57:
r2c7=5 or r3c8=5 or r1c8=7.

r1c8=7 -> r1c5=5: r1c7!=5
r3c8=5 -> r6c8=2 -> r1c8=7 -> r1c5=5: r2c5!=5
r2c7=5 -> r8c7=7: r1c7!=7

Using candidates internal to your uniqueness pattern(UP):

r1c7 -7- r1c8 -2- UP:(r2c9 =2|9= r1c7), implies r1c7<>7

r2c9 =2|9= r1c7 means at least one of r2c9=2 and r1c7=9 must be true.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

Great, thanks.
eleven

Posts: 1846
Joined: 10 February 2008

Nice puzzle.

Code: Select all
` *-------------------------------------------------------------* | 1      2459   258 | 3      57     89  | 579    2457   6     | | 289    6      258 | 4      57     189 | 1579   3      2579  | | 349    359    7   | 6      2      19  | 8      15     459   | |-------------------+-------------------+---------------------| | 6      127    9   | 5      8      3   | 4      127    27    | | 378    1357   358 | 2      4      6   | 13579  1578   35789 | | 238    235    4   | 9      1      7   | 6      258    2358  | |-------------------+-------------------+---------------------| | 479    79     1   | 78     3      5   | 2      6      48    | | 237    8      23  | 1      6      4   | 357    9      357   | | 5      347    6   | 78     9      2   | 37     48     1     | *-------------------------------------------------------------*`

1. [r3c2]-9-[r3c689]-4-[r7c9]-8-[r7c4]-7-[r7c2]-9-[r3c2], => r3c2<>9.

2. [r9c2]-3-[r8c3]-2-[r12c3]=2|3=[r3c2]-3-[r9c2], => r9c2<>3.

3. -3-[r5c2]={[r3c2]=3=[r6c2]-3-[r6c9]=3=[r5c9]=9=[r5c7]=1=[r2c7]-1-
-[r3c8]-5-[r3c2]}=3=[r3c2]=5=[r3c89]-5-[r1c78|r2c79]={[r3c8]=5=
=[r3c9]-5-[r248c9]-9-[r12c7]-1-[r3c8]}=5=[r3c8](=1=[r2c7]-1-[r2c6]
=1=[r3c6])-5-[r456c8|r4c9]-7,8-[r5c7|r56c9]=8=[r7c9]=4=[r7c1]-4-
-[r3c1]=4=[r1c2]=2=[r456c2]-2-[r6c1]-{TILA: [r8c1]=2=[r8c3]=3=
[r5c3]-3-[r5c9]=3|2=[r1c3|r2c39]-2-[r2c1]=2=[r8c1]; [r8c1]-2-[r2c16]-9-
-[r24c9]-7-[r8c9]-5-[r6c9]-3-[r6c1]=3=[r5c3]-3-[r8c3]-2-[r8c1]}

and so r5c2 must be 3, which solves the puzzle.
Carcul

Posts: 724
Joined: 04 November 2005

Phew, this is the original puzzle (without the eliminations in Jasper's grid, which i could not explain).

I understand the first 2 steps (we already had the second), but not the third - too heavy, sorry, i dont have the time now to study it.
eleven

Posts: 1846
Joined: 10 February 2008

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