06/02/10 tough puzzle from sudoku.com.au

Today's puzzle needs a single 3sets-deep elimination. Beginners can profitably study this one.

A complete proof

1) First eliminations : h1=5%block, e5=2%block, b9=2%row, g7=1%block, g3=7%block lead to 27 filled cells.

2)
Look at only possibles a3=8,a8=8 in their col. Whether a3=8 (in which case b2=1%block) or a8=8 (in which case a1=6%col), in both cases, we have no more {b2=6}.
Now easy fillings up to 81 filled cells. (If needed, f2=6%row, d3=8%block, c2=8%block, c7=5%cell, a8=8%block, b8=6%block, a1=6%block, c1=2%row, i7=6%row, f7=8%row, i2=3%col, g8=3%col, d9=6%row, i9=9%col, h8=4%cell, h9=8%block, g9=5%block, e8=5%col, h2=9%block, g2=2%block, g4=4%cell, g5=6%block, a4=2%row, i5=8%block, e7=3%block, c3=3%row, a3=9%block, c5=9%col, h5=1%cell, a6=1%col, b4=7%cell, d4=1%col, i6=7%block, b2=1%col, a5=5%col, f4=9%block, f6=5%block, b1=4%block, e2=4%block, c8=7%col, b5=3%cell, c6=4%block, e3=1%block, i4=5%cell, f9=4%row, d5=4%row, e9=7%row, d1=7%col, e1=9%row, d8=9%col, d6=3%col, f5=7%row, f1=3%block, h6=2%col)

Short hints for a proof

can you see the heptagon ?

1) easy to 27 filled.
2) with 8s in col a, eliminate b2=6. Then easy to the end.

Total sets used :3, max depth :3.

Forbidding-chain-like proof

can you see the heptagon ?

around 27 filled
(b2=1)==(a3=1)--(a3=8)==(a8=8)--(a8=6)==(a1=6) forbids {b2=6}

That's all for today, folks...