2005/10/22 tough puzzle from sudoku.com.au

Short hints for a proof. 1) First eliminations to 23 filled cells. 2) Look at only possibles c1=6,c2=6 in their col. Look at only possibles g9=2,g8=2 in their col. Remove some possibles. Now easy eliminations take place again, leading to 46 filled cells. 3) Look at 59 in c2h2. Remove some possibles. Then simple eliminations take place again, up to 51 filled cells 4) Looking at only possibles d8=9,d1=9 in their col, remove possibles {d9=5,f9=5, f8=5}. Look then at only possibles e8=5,d8=5 in their block. Remove some possibles. From here, simple eliminations lead to unique solution.

Hints for a proof.

1) First eliminations : [c7=1%block, i5=1%block, g3=1%block] lead to 23 filled cells.
2) Look at only possibles c1=6,c2=6 in their col. They forbid {a1=6, a3=6, b1=6, b3=6}.
Look at only possibles g9=2,g8=2 in their col. They forbid {i9=2, h7=2, h9=2, i7=2}.
Now simple eliminations take place again, leading to 46 filled cells. (if needed : d3=6%row, e9=6%block, a7=6%block, f7=2%row, e1=2%block, i3=2%block, e6=1%col, d6=4%row, h6=7%row, h5=2%block, b5=6%row, i7=4%row, g4=4%block, h4=6%block, i4=8%block, g2=6%block, c1=6%block, h7=3%block, h9=8%block, i9=9%block, d7=8%row, i2=3%row, i1=7%block)
3) Look at only possibles c2=9,c2=5 in their cell. Whether c2=9 (in which case h2=5%cell) or c2=5, in both cases, we have no more {e2=5, d2=5, f2=5}.
Look at only possibles c2=5,c2=9 in their cell. Whether c2=5 (in which case h2=9%cell) or c2=9, in both cases, we have no more {e2=9, f2=9, d2=9}.
Then simple eliminations take place again, up to 51 filled cells. (if needed : d2=7%cell, f5=7%block, e5=8%block, f2=8%block, e2=4%row)
4) Look at only possibles d8=9,d1=9 in their col. Whether d8=9 (in which case e8=5%cell) or d1=9 (in which case f3=5%cell), in both cases, we have no more {f9=5, f8=5}.
Look at only possibles d8=9,d1=9 in their col. Whether d8=9 (in which case e8=5%cell) or d1=9 (in which case d9=1%col), in both cases, we have no more {d9=5}.
Look at only possibles e8=5,d8=5 in their block. They forbid {b8=5, c8=5, a8=5}.
From here, simple eliminations lead to unique solution. (if needed : c2=5%col, h1=5%block, h2=9%block, f3=5%block, a3=9%row, c6=9%block, b3=7%block, b6=2%block, a6=8%block, b8=8%block, c8=2%block, g9=2%block, g8=7%block, a9=7%block, b9=5%row, a5=5%block, e4=5%block, f4=9%block, d1=9%block, e8=9%block, d8=5%block, a8=4%block, f9=4%block, b1=4%block, f8=3%block, d5=3%block, b4=3%block, a1=3%block, d9=1%block, f1=1%block)