... by: Frans Goosens

#688

Combination 2-digits cells

B1=1 ( C5=4 ) Solved,

Total solving time is : 15 sec.
Number of logical steps is : 1578

... by: osiguy

This looks resolvable with this sequence!

hiddenSingle R2C3 = 6✓
Notes before: 4 5 6 → placed 6
6 has only one spot in R2 (cell had candidates {4,5,6})
Round 2
pointingPair 2 eliminations
R1C7: 9 R1C8: 9
9 in Box 2 points along R1 — eliminates 2 | Removed: R1C7(9), R1C8(9)
pointingPair 1 elimination
R7C7: 6
6 in Box 8 points along R7 — eliminates 1 | Removed: R7C7(6)
claiming 4 eliminations
R1C7: 5 R1C8: 5 R3C7: 5 R3C9: 5
5 in R2 confined to Box 3 — eliminates 4 | Removed: R1C7(5), R1C8(5), R3C7(5), R3C9(5)
Round 3
nakedPair 5 eliminations
R3C1: 1,4 R3C3: 4 R3C6: 4 R3C7: 1
Naked Pair {1,4} in R3 at R3C5,R3C9 — eliminates 5 candidates | Removed: R3C1(1), R3C1(4), R3C3(4), R3C6(4), R3C7(1)
nakedSingle R3C6 = 5✓
Notes before: 5 → placed 5
Elimination left only {5} → place 5
Round 4
lastRemaining R1C3 = 5✓
Notes before: 2 4 5 8 → placed 5
5 can only go here in Box 1 — peers block all other spots
Round 5
pointingPair 1 elimination
R7C1: 4
4 in Box 1 points along C1 — eliminates 1 | Removed: R7C1(4)
Round 6
nakedQuad 1 elimination
R1C7: 1
Naked Quad {1,5,9,4} in R2C7,R2C8,R2C9,R3C9 | Removed: R1C7(1)
Round 7
forcingChain 1 elimination
R1C2: 1
Forcing Chain from R1C2: eliminate contradicted | Removed: R1C2(1)
Round 8
pointingPair 1 elimination
R8C1: 1
1 in Box 1 points along C1 — eliminates 1 | Removed: R8C1(1)
Round 9
nakedTriple 2 eliminations
R1C1: 2,8
Naked Triple {2,7,8} in R1 | Removed: R1C1(2), R1C1(8)
Round 10
forcingChain 1 elimination
R8C2: 8
Forcing Chain from R8C2: eliminate contradicted | Removed: R8C2(8)
nakedSingle R8C2 = 1✓
Notes before: 1 → placed 1
Elimination left only {1} → place 1
Round 11
forcingChain R1C2 = 8✓
Notes before: 2 8 → placed 8
Forcing Chain from R1C2: must be 8

... by: Dieter

#688 - initially populated cells: 24 = 29,6 %
No solver used, solver = brain.
basics: B3=6
populated cells: 25 = 30,9 %

Strategy: numbers 8,9 occur the least, combine two cells to achieve good population of complete Sudoku.
combinations of A2 = (1,2,8) and A7 = (1,2,5,7,8,9)
after basic checks 3 matrices left: A2/A7 = 2/7, 2/8 and 8/2
A2/A7 = 8/2 solves with D9=5

Optimization:
A7=2 & D9=5 OR A2=8 & D9=5solves.