... by: Serban

# 644 Basics to 23

1. Number 5 n=3 e=6 N=19 Nc=19 Ns=14 => H1=C4=5 basics to 37
1a.XYZ-wing 237 [EJ5,E6] => D4<>2 => D4=1 solve
Note ; G8=5 A1<>5

2. Number 6 n=2 e=7 N=29 Nc=44 Ns=30 => H8==J5=6 solve

3. Number 7 n=2 e=7 N=28 Nc=40 Ns=38 => J1=F3=7 solve

... by: Dieter

#644 - basics: %
populated cells: 23 = 28%
strategy: try to get hidden pairs or triplets. No solver used.
combinations of B8 = (3,4,9) and E8 = (2,3,5,9) as numbers 3,4,5 occur 3 times each
2 matrices left after basic checks: B8/E8 = (4/3) and (9/3) >> E8=3
B8/E8 =(9/3) solves with J7=2

... by: Dieter

#644 - basics: %
populated cells: 23 = 28%
strategy: try to get hidden pairs or triplets. No solver used.
combinations of E2 = (2,7,8) and E3 = (7,9)
2 matrices left after basic checks: E2/E3 = (7/9) and (8/9) >> E3=9
E2/E3 =(8/9) solves with G2=6 and D9=6
Could not find a better approach.

... by: Frans Goosens

#644

Combination 2-digits cells

D2=2 Wrong, Undo calculation
D2=4 No solution, Fixed
E3=7 Wrong, Undo calculation
E3=9 No solution, Fixed
E6=2 Wrong, Undo calculation
E6=7 ( F3=7 ) Solved,

Total solving time is : 62 sec.
Number of logical steps is : 7613

... by: MyDoku

HoDoKu solves this puzzle with 21 Forcing algorithm, my solver uses just 6. Here is my solver's solution path, which took 2 minutes and 15 seconds to solve.

Forcing Chain Contradiction at r6c9 when r7c5=1, therefore, r7c5<>1
Forcing Chain Contradiction at r9c5 when r4c1=1, therefore, r4c1<>1
Locked Candidates (Pointing): 1 at r6, b4 => r6c56<>1
XY Wing (29,79,27) at r4c1,r5c3,r5c6: r4c45<>2, r5c2<>2
AIC: 4 r9c3 =4= r6c3 -4- r4c2 -2- r4c1 -9- r5c3 7 => r9c3<>7
Forcing Chain Contradiction at r5c6 when r5c4=3, therefore, r5c4<>3
Hidden Single in row: r5c8 = 3
Hidden Single in block: r3c7 = 3
Hidden Single in block: r6c5 = 3
Locked Candidates (Claiming): 2 at r5, b5 => r6c6<>2
Locked Candidates (Pointing): 5 at c9, b6 => r8c9<>5
AIC: 4 r4c2 =4= r4c9 =5= r5c9 =9= r5c3 -9- r4c1 2 => r4c2<>2
Naked Single: r4c2=4
Hidden Single in column: r9c3 = 4
Locked Candidates (Claiming): 2 at c2, b1 => r2c1<>2
Forcing Chain Contradiction at r4c7 when r1c1=5, therefore, r1c1<>5
Locked Candidates (Pointing): 5 at c3, b1 => r8c3<>5
XY Wing (17,67,16) at r6c3,r6c6,r8c3: r8c6<>6
AIC: 4 r6c9 =4= r2c9 -4- r2c6 =4= r7c6 =6= r6c6 6 => r6c9<>6
Grouped AIC: 1 r9c9 =1= r8c9 -1- r8c3 -6- r78c2 =6= r3c2 =2= r2c2 =3= r2c1 -3- r9c1 =3= r9c4 3 => r9c4<>1
Forcing Chain Contradiction at r7c7 when r2c1=9, therefore, r2c1<>9
Grouped AIC: 3 r8c2 =3= r2c2 -3- r2c1 -7- r13c3 =7= r56c3 -7- r5c2 8 => r8c2<>8
Grouped AIC: 1 r7c46 =1= r7c1 =5= r8c1 =8= r8c4 8 => r8c4<>1
AIC: 3 r9c4 =3= r8c4 =8= r8c1 =5= r8c8 =2= r9c7 2 => r9c4<>2
Naked Single: r9c4=3
XY Chain: 3 r2c1 -7- r9c1 -1- r8c3 -6- r8c2 3 => r2c2<>3, r8c1<>3
Hidden Single in column: r2c1 = 3
Hidden Single in column: r8c2 = 3
Grouped AIC: 2 r2c2 =2= r3c2 =6= r7c2 -6- r8c3 =6= r8c89 -6- r9c79 =6= r9c5 =2= r23c5 2 => r2c6<>2
Grouped AIC: 4 r1c8 =4= r1c4 -4- r2c6 =4= r7c6 =6= r6c6 =7= r6c13 -7- r5c3 -9- r4c1 =9= r1c1 9 => r1c8<>9
Grouped AIC: 9 r1c1 =9= r4c1 -9- r5c3 -7- r6c13 =7= r6c6 =6= r7c6 =4= r2c6 -4- r2c8 9 => r1c7<>9
Forcing Chain Contradiction at r4c9 when r8c9=1, therefore, r8c9<>1
Hidden Single in column: r9c9 = 1
Naked Single: r9c1=7
Naked Single: r1c1=9
Naked Single: r4c1=2
Hidden Single in row: r7c7 = 7
Hidden Single in column: r5c3 = 9
Hidden Single in column: r4c7 = 9
Skyscraper (6) at r4c59, r9c57, connected in c5 => r8c9<>6, r6c7<>6
Naked Single: r8c9=9
Hidden Single in block: r2c8 = 9
Skyscraper (7) at r1c34, r6c36, connected in c3 => r23c6<>7, r5c4<>7
2 String Kite (6) at r1c7, r8c3 connected by r8c8, r9c7 in b9 => r1c3<>6
Locked Candidates (Pointing): 6 at r3, b1 => r3c9<>6
Hidden Single in column: r4c9 = 6
Hidden Single in block: r5c9 = 5
Naked Single: r5c4=2
Naked Single: r5c6=7
Full House: r5c2=8
Naked Single: r6c1=1
Full House: r6c3=7
Naked Single: r1c3=5
Naked Single: r1c5=8
Naked Single: r1c7=6
Naked Single: r1c8=4
Full House: r1c4=7
Naked Single: r2c9=7
Naked Single: r2c2=2
Naked Single: r2c5=1
Full House: r2c6=4
Naked Single: r3c3=6
Full House: r3c2=7
Naked Single: r3c4=5
Full House: r3c9=8
Naked Single: r4c4=1
Full House: r4c5=5
Full House: r6c6=6
Naked Single: r6c8=2
Naked Single: r6c7=8
Full House: r6c9=4
Full House: r7c2=6
Naked Single: r7c5=9
Naked Single: r3c5=2
Full House: r3c6=9
Naked Single: r7c6=1
Naked Single: r7c8=5
Naked Single: r7c1=8
Full House: r7c4=4
Full House: r8c1=5
Full House: r8c3=1
Full House: r8c4=8
Full House: r8c6=2
Full House: r8c8=6
Full House: r9c5=6
Last Digit: r9c7=2

Hope that helps.

... by: BGH

Using Frans Goosens pairs technique
24 @ D2 & 27 @ E5
2 @ D2 & 2 @ E5 Converges
2 @ D2 & 7 @ E5 Also Converges (Requires a 2nd step for BUG)
So without further ado, 2 solutions.