My logic fails me. I’m working on 3 separate “difficult” Sudokus and after staring at them for hours (literally), I’m at an impasse. I’m hoping shaper minds can assist me, not in solving the puzzles (I can look up the answer in the back of the book), but in finding the next number:
#1 (E=blank)
E1E EE2 E4E
78E EEE E1E
E95 E1E E8E
E2E EEE E3E
95E E8E E27
E4E EEE E6E
E7E E9E 85E
E3E EEE EE1
E6E 4EE EEE
#2
E9E EE3 1EE
EEE 1E8 E92
5E1 EEE EE6
EEE EEE EE4
849 237 651
7EE EEE EE9
1EE 3EE 9E8
2EE 596 41E
9E4 8EE E6E
#3
EE5 EEE E3E
E91 68E E54
EEE 52E E1E
EE8 EEE 9E3
74E E3E 125
EE2 EEE 6E8
81E 37E 562
EEE E65 381
563 E1E 497
Thanks and happy solving!!
Got one:
#1 (E=blank)
E1E 8E2 E4E
78E EEE E1E
E95 E1E E8E
E2E EEE E3E
95E E8E E27
E4E EEE E6E
E7E E9E 85E
E3E EEE EE1
E6E 4EE EEE
yes, I see that. thanks. Of course, now I’m stuck again.
I stink at these puzzles. 
#3
ee5 eee e3e
e91 68e e54
eee 52e e1e
e58 eee 9e3
74e e3e 125
ee2 eee 6e8
81e 37e 562
eee e65 381
563 e1e 497
I see where you put the 5, but I don’t know how you narrowed it down. I had that it could fit in Row 4 Column 2 OR Row 6 Column 2.
It can’t be 2,4,7,8 (block), 1,6 (column) or 3,9 (row), so only 5 left.
Oh, yes. Maybe I just need to take a break.
Thanks for your help!
Lisa
#2 falls just short of one of those which I normally resort to brute force to solve. I narrow it down as much as possible, then make a guess - and see if the guess plays out. I hate having to do it, but I don’t know another way to do it. Advanced Sudoku techniques, maybe.
In the upper left box, there are only two squares that can contain 2, and two that can contain 8. The same two squares for each number. (The upper-right and bottom-middle - one of them will be 2, and the other will be 8.)
Because of this, you can be sure that wherever 3 and 7 appear in that box, they will be in the middle row. (The upper-left corner can’t have them, because of already placed numbers.)
This allows you to place a number in the upper-right box, in the middle-left square. Because of numbers already placed, it can only be three, five, or seven… and we can now eliminate three and seven.
So:
e9e ee3 1ee
eee 1e8 592
5e1 eee ee6
… and so on.
So does the OP still need our help, or has she moved on (or at least made some progress)?