05/11/11 tough puzzle from sudoku.com.au

A complete proof

1) First eliminations : [b2=3%col, b3=8%col, i3=4%row, c2=4%row, c1=6%col, d8=4%row, e1=3%row, b9=4%row, i2=1%block, c5=5%col, a6=1%block, a4=6%block, g9=5%col, h5=7%cell, h4=4%cell, h6=6%cell, e6=4%row, e7=8%col, a8=8%block, a7=3%block, a9=7%block, e4=7%col, b6=7%block, b4=9%block, b5=2%block, e3=5%col, a1=5%row, a3=9%block, a2=2%block, g3=6%cell, d2=6%col, e9=1%cell] lead to 51 filled cells.

2) Look at only possibles h8=9,h8=1 in their cell. Whether h8=1 (in which case c8=9%cell) or h8=9, in both cases, we have no more {f8=9, g8=9}. Now easy fillings up to 53 filled cells. (If needed, g1=9%col, h1=2%cell)

3) Look at only possibles d1=8,i1=8 in their row. Whether i1=8 (in which case g5=8%col) or d1=8, in both cases, we have no more {d5=8}.
Now easy fillings up to 81 filled cells. (If needed, d5=1%cell, f3=1%row, d3=2%row, f4=2%row, i4=3%row, g8=3%row, g2=7%col, i1=8%block, i6=5%cell, g5=8%block, f2=8%block, f6=9%cell, d6=8%block, d1=7%block, d7=9%block, f7=5%block, f8=7%block, i7=7%block, f9=6%block, i8=6%block, h8=9%block, c9=9%block, c7=2%row, h7=1%row, c8=1%row, f5=3%row, i9=2%row, d4=5%row)

Short hints for a proof

4-FC needed here:

1) easy to 51 filled
2) looking at 19 in c8h8, eliminate some, then easy to 53 filled
3) looking at 8 in R1, eliminate d5=8. Then easy to unique solution.

Forbidding-chain-like proof

4-FC needed here :

around 51 filled : (h8=9)==(h8=1)--(c8=1)==(c8=9) forbids {g8=9, f8=9}
around 53 filled : (d1=8)==(i1=8)--(g2=8)==(g5=8) forbids {d5=8}

Equivalence with 2005/09/30

Now applying the same "dictionary" (renaming numbers, replacing cells) to proof of 05/09/30 you will mechanically get a proof of today's. E.g. first filled cell in 05/09/30 was b3=6%row; in today's it becomes b2=3%col. Try it ! Or see the method explained step by step on 10/08 example.
In case that you be lazy enough not to find it by yourself, see hints for today's proof (automatically derived from 05/09/30's proof).