06/02/09 tough puzzle from sudoku.com.au

A very easy puzzle that you'll solve using only 2sets deep eliminations : pairs, colors. Recommended for beginners on tough level.
Thanks to Steve from Ohio and DJ from AZ, who helped me finding the best first step.

A complete proof

1) First eliminations : f5=9%block, g1=1%row lead to 25 filled cells.

2) Now :
Look at only possibles e1=7,e1=3 in their cell. Whether e1=7 (in which case a1=3%cell) or e1=3, in both cases, we have no more {f1=3, c1=3}.
Look at only possibles a1=3,a1=7 in their cell. Whether a1=3 (in which case e1=7%cell) or a1=7, in both cases, we have no more {c1=7, f1=7}.
Now easy fillings up to 43 filled cells. (If needed, f1=8%cell, f8=4%cell, d8=8%col, e7=1%block, b6=1%col, d4=1%col, c8=1%row, f2=3%cell, g3=3%col, a1=3%block, e1=7%row, e9=3%cell, d5=3%col, b5=5%cell, d9=7%cell, c4=3%row, c6=8%block, b7=3%block)
Note : you can also reach 43 filled cells with a single elimination, but it needs 3 sets : look at only possibles 378 in f1 ; whether f1=8 (giving f2=3%cell), f1=7 (giving a1=3%cell) or f1=3, e1 is never 3. Then easy fillings to 43 filled cells.

3) Look at only possibles c9=9,b9=9 in their block. They forbid{g9=9}.
Now easy fillings up to 44 filled cells. (If needed, g8=9%col)

Last effort.
4) Look at only possibles c9=6,c5=6 in their col. Whether c9=6 (in which case h8=6%row) or c5=6, in both cases, we have no more {h5=6}.
Now easy fillings up to 81 filled cells. (If needed, h5=2%cell, a8=2%row, h8=6%cell, c9=6%row, g7=2%row, i7=7%row, h7=8%row, c7=4%row, g4=8%block, g5=6%row, g6=7%block, b2=4%block, b3=8%block, b9=9%col, c5=7%row, f4=7%row, a4=6%cell, f6=5%block, e4=4%cell, i6=4%row, i9=5%cell, h1=4%col, c1=9%row, h3=9%block, g2=5%block, c3=5%col, e3=2%row, d6=2%block, a7=5%col, i3=6%row, e6=6%row, c2=2%cell, d2=6%col, g9=4%block, h4=5%row, a3=7%row, i2=8%col)

Short hints for a proof

Color step on 6s

1) easy to 25 filled.
2) Looking at a1 and e1 (2 sets, pair), eliminate some possibles, then easy to 43 filled.
3) Looking at 9s in Bb8 (1 set), eliminate some possibles, then easy to 44 filled.
4) eliminate h5=6 (gives pbm with 6s in Bb8, 2 sets). Then easy to unique solution.

Total sets used : 5, max depth : 2

Forbidding-chain-like proof

Color step on 6s

around 25 filled
(a1=3)==(a1=7)--(e1=7)==(e1=3) forbids {c1=3, f1=3}
(e1=7)==(e1=3)--(a1=3)==(a1=7) forbids {c1=7, f1=7}
around 43 filled
(c9=9)==(b9=9) forbids {g9=9}
around 44 filled
(h8=6)==(a8=6)--(c9=6)==(c5=6) forbids {h5=6}