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Alphabet Xoup: O

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Alphabet Xoup: O

Postby m_b_metcalf » Sun Mar 05, 2023 9:53 am

Code: Select all
 . . . 1 2 3 . . .
 . . 2 . . . 4 . .
 . 5 . . . . . 2 .
 6 . . . . . . . 5
 3 . . . . . . . 7
 7 . . . . . . . 8
 . 7 . . . . . 9 .
 . . 1 . . . 3 . .
 . . . 6 9 4 . . .   easy

 . . . 4 5 8 . . .
 . . 5 . . . 6 . .
 . 3 . . . . . 5 .
 2 . . . . . . . 9
 3 . . . . . . . 7
 7 . . . . . . . 1
 . 7 . . . . . 9 .
 . . 4 . . . 8 . .
 . . . 2 9 1 . . .   hard
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Re: Alphabet Xoup: O

Postby Hajime » Sun Mar 05, 2023 12:53 pm

The easy one needs only one XY-wing (next to basics, which a did not spot with pencil & paper)
The hard one can be solved without forcing chains but with 7 bivalue XY-chains:
Hidden Text: Show
Code: Select all
[1,0] Pointing, Claiming  | (6)r1,b1 => (-6)r3c1 (-6)r3c3 | (3)r1,b3 => (-3)r2c8 (-3)r2c9 | (4)b8,r7 => (-4)r7c7 (-4)r7c9 | (8)b8,r7 => (-8)r7c1 (-8)r7c3 | (7)b8,r8 => (-7)r8c8 | (4)c1,b1 => (-4)r2c2 | (5)c1,b7 => (-5)r8c2 (-5)r9c2 | (5)b6,c7 => (-5)r7c7 (-5)r9c7 | (6)b6,c8 => (-6)r8c8 (-6)r9c8 | (8)b6,c8 => (-8)r2c8 | (2)b7,/ => (-2)r1c9 (-2)r2c8 (-2)r3c7 (-2)r5c5 | (1)b9,\ => (-1)r1c1 (-1)r2c2 (-1)r3c3 (-1)r4c4 (-1)r5c5
[2,1] r1c9=3 Naked Single
[3,2] r9c3=3 Hidden Single in col 3
[4,2] Naked/Hidden Pairs,Triplets,Quads  | NPair (47)r9c78 => (-4)r9c9 | NTriple (256)c9r789 => (-2)r2c9 (-2)r3c9 | NQuin (24567)b9e36789 => (-2)r7c7 (-2)r8c8 | NPair (13)\78 => (-3)r4c4 (-3)r6c6
[5,2] Naked/Hidden Pairs,Triplets,Quads  | NPair (48)b3e69 => (-4)r2c8 (-4)r3c7
[6,2] Pointing, Claiming  | (2)b3,r1 => (-2)r1c2 (-2)r1c3 | (3)b5,c5 => (-3)r2c5 (-3)r7c5 (-3)r8c5 | (2)b1,\ => (-2)r6c6 | (4)\,b5 => (-4)r4c5 (-4)r4c6 (-4)r5c6 (-4)r6c5 | (4)/,b5 => (-4)r6c6
[7,3] r7c6=4 Hidden Single in col 6
[7,4] r5c5=4 Hidden Single in box 5
[8,4] Naked/Hidden Pairs,Triplets,Quads  | NQuin (13569)\16789 => (-9)r2c2 (-9)r3c3 (-56)r4c4
[9,4] Generalized Intersection  | (7)\,r3,c4 => (-7)r3c4
[10,4] 2-String Kite (9)r1c7=r3c7-r8c2=r8c1 => (-9)r1c1
[11,5] r1c1=6 Naked Single
[11,6] r9c9=5 Naked Single
[12,7] r6c6=9 Naked Single
[12,8] r9c1=8 Naked Single
[12,9] r9c2=6 Naked Single
[13,9] Naked/Hidden Pairs,Triplets,Quads  | NQuad (1479)b1e2347 => (-7)r3c3 | NQuin (12489)b1e24579 => (-19)r1c3 | NQuin (12678)c3r13467 => (-168)r5c3 | 1 (9)b4e6 => (-9)r5c2 | NPair (28)\23 => (-8)r4c4 | NQuad (1279)/2378 => (-7)r4c6
[14,10] r1c3=7 Naked Single
[14,11] r4c4=7 Naked Single
[14,12] r5c3=9 Naked Single
[15,12] Naked/Hidden Pairs,Triplets,Quads  | NTriple (256)b5e367 => (-6)r4c5 (-56)r5c4 (-26)r6c5 | NPair (56)b5e37 => (-56)r5c6 | 1 (2)c6r5 => (-2)r2c6 (-2)r3c6
[16,13] r5c6=2 Naked Single
[16,14] r5c7=5 Naked Single
[17,15] r5c8=6 Hidden Single in row 5
[18,15] Naked/Hidden Pairs,Triplets,Quads  | NQuad (1289)c2r1258 => (-18)r4c2 (-8)r6c2
[19,15] XY-wing  [3]  (3)(3=7)r2c6-(7=1)r2c8-(1=3)r8c8 => (-3)r8c6
[20,16] r2c6=3 Hidden Single in col 6
[21,16] XY-chain [4]  (9)(9=1)r1c2-(1=8)r5c2-(8=1)r5c4-(1=9)r2c4 => (-9)r2c1
[22,17] r2c4=9 Hidden Single in row 2
[23,17] XY-chain [5]  (3)(3=8)r6c5-(8=6)r7c5-(6=2)r7c9-(2=1)r7c3-(1=3)r7c7 => (-3)r6c7
[24,17] XY-chain [5]  (5)(5=6)r6c4-(6=8)r6c3-(8=2)r3c3-(2=1)r7c3-(1=5)r7c1 => (-5)r7c4
[25,18] r7c1=5 Hidden Single in row 7
[26,18] Generalized Intersection  | (1)r7,c7,/ => (-1)r3c7
[27,18] XY-chain [6]  (9)(9=1)r1c2-(1=8)r5c2-(8=1)r5c4-(1=6)r3c4-(6=7)r3c6-(7=9)r3c7 => (-9)r1c7 (-9)r8c2 (-9)r3c1
[28,19] r1c2=9 Hidden Single in row 1
[28,20] r3c7=9 Hidden Single in row 3
[28,21] r8c1=9 Hidden Single in row 8
[28,22] r9c7=7 Hidden Single in col 7
[28,23] r2c8=7 Hidden Single in col 8
[28,24] r9c8=4 Hidden Single in box 9
[29,24] XY-chain [5]  (6)(6=1)r3c4-(1=8)r5c4-(8=1)r5c2-(1=2)r8c2-(2=6)r8c9 => (-6)r8c4
[30,24] XY-chain [5]  (1)(1=8)r5c2-(8=6)r6c3-(6=5)r6c4-(5=3)r8c4-(3=1)r8c8 => (-1)r8c2
[31,25] r8c2=2 Naked Single
[31,26] r8c9=6 Naked Single
[32,27] r2c2=8 Naked Single
[32,28] r2c9=4 Naked Single
[32,29] r3c3=2 Naked Single
[32,30] r3c9=8 Naked Single
[32,31] r5c2=1 Naked Single
[32,32] r5c4=8 Naked Single
[32,33] r6c5=3 Naked Single
[32,34] r7c3=1 Naked Single
[32,35] r7c7=3 Naked Single
[32,36] r7c9=2 Naked Single
[32,37] r8c5=7 Naked Single
[32,38] r8c6=5 Naked Single
[32,39] r8c8=1 Naked Single
[33,40] r1c8=2 Naked Single
[33,41] r2c1=1 Naked Single
[33,42] r2c5=2 Naked Single
[33,43] r3c1=4 Naked Single
[33,44] r4c5=1 Naked Single
[33,45] r4c6=6 Naked Single
[33,46] r4c7=4 Naked Single
[33,47] r6c4=5 Naked Single
[33,48] r6c7=2 Naked Single
[33,49] r6c8=8 Naked Single
[33,50] r7c4=6 Naked Single
[33,51] r7c5=8 Naked Single
[33,52] r8c4=3 Naked Single
[34,53] r1c7=1 Naked Single
[34,54] r3c4=1 Naked Single
[34,55] r3c5=6 Naked Single
[34,56] r3c6=7 Naked Single
[34,57] r4c2=5 Naked Single
[34,58] r4c3=8 Naked Single
[34,59] r4c8=3 Naked Single
[34,60] r6c2=4 Naked Single
[34,61] r6c3=6 Naked Single
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Re: Alphabet Xoup: O

Postby Hajime » Mon Mar 06, 2023 10:16 am

2 Diamonds (ED=1.5 without a sparkle)
Code: Select all
...198.....8...9...3.....5.4.......93.......77.......1.4.....9...7...2.....289...   ED=1.5/1.5/1.5
...435.....5...6...3.....5.2.......93.......75.......1.7.....9...4...8.....291...   ED=2.6/2.6/2.6
and some pearls
Hidden Text: Show
Code: Select all
...358.....8...9...4.....5.4.......97.......66.......1.7.....1...4...7.....287...   ED=2.9/2.9/2.6
...569.....5...6...3.....5.2.......83.......77.......1.7.....9...4...8.....291...   ED=3.0/3.0/2.6
...958.....5...6...3.....5.2.......63.......77.......1.7.....9...4...8.....291...   ED=3.4/3.4/2.6
...356.....5...6...3.....5.2.......93.......75.......1.7.....9...4...8.....291...   ED=3.6/3.6/2.6
...158.....5...9...4.....6.4.......93.......66.......1.7.....2...2...7.....287...   ED=4.0/4.0/2.6
...453.....5...6...3.....5.8.......93.......77.......1.7.....2...4...8.....291...   ED=4.2/4.2/2.6
...452.....5...6...2.....5.2.......33.......47.......1.3.....9...1...8.....697...   ED=4.5/4.5/2.6
...458.....5...3...2.....7.2.......33.......77.......1.6.....9...2...8.....291...   ED=4.6/4.6/2.6
...548.....5...7...3.....5.2.......93.......77.......1.6.....9...4...8.....291...   ED=5.0/5.0/2.6
...158.....4...9...6.....5.4.......93.......66.......3.7.....2...3...7.....287...   ED=6.5/6.5/2.6
...524.....5...6...3.....5.6.......93.......77.......1.7.....9...4...8.....291...   ED=6.6/6.6/2.6
...458.....5...6...3.....5.2.......63.......77.......1.7.....9...4...8.....281...   ED=7.1/7.1/2.6
...358.....5...6...1.....5.2.......93.......77.......6.7.....9...4...8.....291...   ED=7.2/7.2/2.6
...459.....5...6...3.....5.2.......63.......77.......1.7.....9...4...8.....291...   ED=7.3/7.3/2.6
...536.....5...6...3.....5.2.......93.......75.......1.7.....9...4...8.....291...   ED=7.5/7.5/2.6
...358.....5...6...3.....5.2.......63.......77.......1.2.....9...4...8.....291...   ED=7.6/7.6/2.6
...564.....5...6...3.....5.5.......93.......77.......1.7.....9...4...8.....291...   ED=7.7/7.7/2.6
...865.....5...6...3.....5.2.......93.......77.......5.7.....9...4...8.....291...   ED=7.8/7.8/2.6
...528.....2...6...3.....5.2.......93.......77.......1.7.....9...4...8.....691...   ED=7.9/7.9/2.6
...568.....5...6...3.....5.5.......93.......77.......1.7.....9...4...2.....291...   ED=8.0/8.0/2.6
...358.....6...9...2.....5.4.......93.......77.......5.7.....9...4...1.....289...   ED=8.1/8.1/2.6
...528.....5...6...3.....5.2.......93.......77.......5.7.....9...4...8.....691...   ED=8.2/8.2/2.6
...453.....5...6...3.....5.6.......83.......77.......1.7.....9...4...8.....291...   ED=8.3/8.3/2.6
...158.....5...6...3.....5.2.......93.......77.......4.7.....9...4...8.....691...   ED=8.4/8.4/2.6
...854.....5...6...3.....5.1.......93.......77.......1.7.....9...4...8.....296...   ED=8.5/8.5/2.6
...358.....1...9...3.....5.7.......93.......64.......1.2.....9...4...2.....289...   ED=8.6/8.6/2.6
...458.....5...6...3.....5.1.......93.......77.......1.7.....9...4...8.....296...   ED=8.8/8.8/2.6
...548.....5...6...3.....5.2.......93.......77.......5.7.....9...1...8.....291...   ED=8.9/8.9/2.6
...458.....5...6...2.....5.2.......33.......77.......1.7.....9...2...8.....291...   ED=9.0/9.0/2.6
...358.....5...9...3.....5.4.......93.......77.......6.2.....9...4...8.....261...   ED=9.1/9.1/2.6
...452.....5...6...2.....5.2.......33.......77.......1.3.....9...2...8.....691...   ED=9.2/9.2/2.6
...358.....5...9...4.....5.4.......93.......66.......1.7.....1...4...2.....217...   ED=9.3/9.3/2.6
...358.....5...9...3.....5.4.......93.......77.......1.4.....9...7...2.....289...   ED=9.4/9.4/2.6
...358.....5...9...3.....5.4.......93.......77.......1.7.....9...4...1.....289...   ED=9.5/9.5/2.6
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Re: Alphabet Xoup: O

Postby m_b_metcalf » Mon Mar 06, 2023 8:48 pm

Hajime wrote:2 Diamonds (ED=1.5 without a sparkle)
Code: Select all
...198.....8...9...3.....5.4.......93.......77.......1.4.....9...7...2.....289...   ED=1.5/1.5/1.5
...435.....5...6...3.....5.2.......93.......75.......1.7.....9...4...8.....291...   ED=2.6/2.6/2.6


A diamond (or pearl) has ED > 2.3. But, well done, I can add your 2.6 diamond to my very short list of x-diamonds:
Code: Select all
.............1...2..32.4.....4......3.15.64.7......3....58.217.8...6.............   ED=2.9/2.9/2.9  X
.............1...2.34..56....2......4..7.12.8......7....78.239.3...7.............   ED=4.3/4.3/4.3  X
.............1...2..34..5....4......6.78.53.4......8....89.276.3...5.............   ED=7.7/7.7/7.7  X
..1...2....34....55........6.5....7..8......6.............72.......6.....7...8.9.   ED=7.8/7.8/7.8  X
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re: x-diamonds

Postby Pat » Tue Mar 07, 2023 1:43 pm

Code: Select all

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

2.9
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Re: re: x-diamonds

Postby m_b_metcalf » Tue Mar 07, 2023 4:26 pm

Pat wrote:2.9
Or, to be more precise, ED=2.9/2.3/2.3, so not a diamond.

M
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Re: re: x-diamonds

Postby Hajime » Tue Mar 07, 2023 5:08 pm

m_b_metcalf wrote: so not a diamond.
And not an "O"
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Re: re: x-diamonds

Postby Pat » Tue Mar 07, 2023 6:01 pm

right, i often miss "naked singles";

and if we add r2c2,
still //2.6

sorry
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