Here is a sudoku puzzle coming from this magazine
I found that B5 and B6 can only contain 6 and 7. 8 cannot be in B5 because D1 would be a 8 and neither B3 not C1 could be a 8.
I thought it would help me to find out the next number, but I'm still stuck at this step.
What is the next step?
This is a formidable puzzle. Fortunately OP's request is to prove the next digit. The grid with all candidates is needed for this. I use chess notation: rows 1 to 9 (bottom to top) and columns a to i (left to right).
.---------------------------------------------------------------------.
| 567 2 356 | 4579 1 4567 | 37 379 8 | 9
| 9 1367 368 | 278 678 267 | 1237 5 4 | 8
| 1578 157 4 | 25789 578 3 | 6 1279 19 | 7
|----------------------+----------------------+-----------------------|
| 5678 567 2 | 1 567 9 | 4 3678 356 | 5
| 3 5679 568 | 457 4567 4567 | 1578 16789 2 | 5
| 4567 45679 1 | 3 2 8 | 57 679 569 | 4
|----------------------+----------------------+-----------------------|
| 145 1345 7 | 6 3458 145+2 | 9 12(3)8 1(3)5 | 3
| 1456 8 9 | 245 345 1245 | 12(3)5 12(3)6 7 | 2
| 2 1356 356 | 578 9 157 | 1(3)58 4 1(3)56 | 1
'---------------------------------------------------------------------'
a b c d e f g h i
Claim: Every possible position for the digit 3 at box ghi123 implies that h3 ≠ 2.
Proof:
. h3=3 => h3 ≠ 2
. g2=3 or h2=3 => e2 ≠ 3 => e3=3 => e3 ≠ 8 => h3=8
. g1=3 => g1 ≠ 8 => h3=8
. i1=3 or i3=3 => i6 ≠ 3 => h6=3 =>
h6 ≠ 8 => a6=8 => c5 ≠ 8 => c8=8
=> def8 has no 8 => (672) locked at def8
=> d7 ≠ 2 => h7=2
Having proved the claim, it follows that f3=2.
