... by: Dieter

@BGH: Thank you for your comments
After basics A4=2; G5=5 we have 25 cells populated.
A7 then has 3 possible numbers: 1, 3, 5, A3 has 4, 5, 6, 8
I try to get most of the 7 numbers "covered" by two cells, e. g. 5 is covered by both.
It's not an exact mathematical approach and it takes some time to find two cells.
This week I found them very quickly.
Hope this helps a little.

... by: BGH

Dieter, could you explain how 1 & 7 are in your "occurs most frequently" two cell combinations
And how the 1 @ A7 is in your "occurs most frequently" two cell combinations.
I really want to try your method but can't understand 1 & 7 ??

D: Strategy: Numbers 5,3,4,8,9 occur most frequently, combine two cells.
combinations of A3 = (4,5,7,8) and A7 = (1,3,5)
A3=8 & A7=1 solve"

And BTW, I confirmed my solution (5 @ A8) and 2 @ F7 did not solve the grid after 3 @ A6 and
8 @ F8. You can do 2 @ F7 then 5 @ A8 to solve but that makes *4* steps. Anyway, not important. Answer to 1 paragraph would be interesting.

... by: Serban

# 670 A4=2 G5=5 Basics to 25
1.Number 1 n=2 e=7 N=23 Nc=10 Ns=5 => C5=1 solve
2. Number 6 n=2 e=7 N=20 Nc=57 Ns=34 => C6=E7=6 solve
3. Number 2 n=4 e=5 N=17 Nc=9 Ns=3 => F7=2 basics to 47

3a. F7=2 & any[ E4,C5]=1 solve
3b. F7=2 & any[D2,E7]=3 solve
3c. F7=2 & any[E2,D5]=4 solve
3d. F7=2 & any[F1,C2,H3,A8,J7]=5 solve
3e. F7=2 & any[E7,H8,F5,J4]=6 solve
3f. F7=2 & any[J1,E5]=7 solve
3g. F7=2 & any[D8,J9]=9 solve

... by: Envy E

Begin where Solver runs out of known solutions

+1 B4 +1 C2 +2 G2

+1 E4 +1 D9 +4 F9 +2 H9 +2 G2

+1 G4 +2 G2

With G2 set to 2 puzzle is solvable

... by: Dieter

@BGH:
3 @ A6 OK
8 @ F8 OK
5 @ F7 nOK; F7=2

... by: BGH

3 Step Solution to #670
Basics 30.7
3 @ A6 43.2 Cell Pair, Unit Pairs 8’s, Solves for all 8’s except URec
8 @ F8 45.7 Unique Rectangle
5 @ F7 Solution, Solves for all 5’s

Dieter's solution works & matches my solution

... by: Dieter

#670 - initially populated cells: 23 = 28,4%
No solver used.
basics: A4=2; G5=5
populated cells: 25= 30,9%
Strategy: Numbers 5,3,4,8,9 occur most frequently, combine two cells.
combinations of A3 = (4,5,7,8) and A7 = (1,3,5)
A3=8 & A7=1 solve.

... by: Serban

# 670 A4=2 G5=5 Basics to 25

1. Box 4 ABC456 n=4 e=5 Nc=12 Ns=2 => B4=7 & [C5=1 OR C6=6] solve

2. Box 6 GHJ456 n=4 e=5 Nc=10 Ns=5 => G6=1 & H6=7 solve

3. Number 4 n=3 e=6 N=20 Nc=17 Ns=3 => D5=G3=4 solve
Note: A1=G3=J6=4