05/11/06 tough puzzle from sudoku.com.au

A complete proof

1) First eliminations : [c8=8%row, a5=8%block, b8=5%row, c9=9%block, i8=9%block, g6=9%block, b3=9%block, c3=7%block, a9=4%row, e9=1%row, d7=7%block, f7=4%block, i1=1%row, c7=6%cell, e2=3%cell, e8=6%cell, f2=9%cell, d5=9%block, h5=5%row, g7=5%block, h7=8%block, i7=3%block, f5=3%row, d8=3%block, f8=2%block, b5=1%row, a7=1%block, b7=2%block, i5=7%row, d2=4%cell, b1=4%cell, c6=4%row] lead to 51 filled cells.

2) Look at only possibles g2=2,g2=7 in their cell. Whether g2=7 (in which case g9=2%cell) or g2=2, in both cases, we have no more {g4=2, g1=2}. Now easy fillings up to 53 filled cells. (If needed, a1=2%row, a2=6%cell)

3) Look at only possibles a6=5,a3=5 in their col. Whether a3=5 (in which case e1=5%row) or a6=5, in both cases, we have no more {e6=5}.
Now easy fillings up to 81 filled cells. (If needed, e6=7%cell, b4=7%block, b6=6%block, f4=6%block, e4=8%block, f3=8%block, g1=8%block, d3=1%block, e1=5%block, a3=5%block, c4=5%block, d6=5%block, a6=3%block, c1=3%block, d4=2%block, h6=2%block, g2=2%block, h2=7%block, g9=7%block, i9=2%block, h9=6%block, i3=6%block, g3=4%block, i4=4%block, h3=3%block, g4=3%block, h4=1%block, f6=1%block)

Short hints for a proof

4-FC needed here:

1) easy to 51 filled
2) looking at 27 in g2g9, eliminate some, then easy to 53 filled
3) looking at 5 in Ca, eliminate e6=5. Then easy to unique solution.

Forbidding-chain-like proof

4-FC needed here :

around 51 filled : (g2=2)==(g2=7)--(g9=7)==(g9=2) forbids {g1=2, g4=2}
around 53 filled : (a6=5)==(a3=5)--(c1=5)==(e1=5) forbids {e6=5}

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 c8=8%row. 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).