06/02/01 tough puzzle from sudoku.com.au
Want to see the whole thing? A complete proof
1) First eliminations : b8=9%block, i6=7%col, g4=4%block, g2=5%col, b6=6%cell lead to 28 filled cells.
2) Now :
Look at only possibles i8=1,i9=1 in their col. They forbid{h8=1, h7=1}.
Look at only possibles c6=3,c5=3 in their block. They forbid{c1=3, c2=3}.
3)
Look at only possibles g8=2,g8=3 in their cell. Whether g8=3 (in which case h8=2%cell) or g8=2, in both cases, we have no more {f8=2, e8=2, g9=2, c8=2, h7=2}.
Look at only possibles h8=3,h8=2 in their cell. Whether h8=2 (in which case g8=3%cell) or h8=3, in both cases, we have no more {f8=3, i8=3, h7=3, e8=3}.
Now easy fillings up to 29 filled cells. (If needed, c9=2%block)
4) Look at only possibles h7=6,h2=6 in their col. Whether h7=6 (in which case a7=1%cell) or h2=6 (in which case c2=1%cell), in both cases, we have no more {a2=1, a1=1, c8=1}.
Now easy fillings up to 47 filled cells. (If needed, c8=5%cell, c6=3%cell, a4=5%col, h4=1%cell, b4=7%cell, h6=5%block, f4=6%cell, e3=6%row, c5=8%block, a1=8%block, a2=3%col, d9=8%col, e4=8%col, f9=5%row, d3=5%block, i8=8%row, i9=1%block, b5=1%row)
5) Look at only possibles e9=7,e9=9 in their cell. Whether e9=7 (in which case f8=4%cell) or e9=9 (in which case e6=4%cell), in both cases, we have no more {e8=4}.
Now easy fillings up to 51 filled cells. (If needed, f8=4%block, f5=7%col, d5=2%row, d2=7%col)
6) Look at only possibles d1=1,d7=1 in their col. Whether d1=1 (in which case c1=6%cell) or d7=1 (in which case a7=6%cell,g9=6%row), in both cases, we have no more {g1=6}.
Now easy fillings up to 81 filled cells. (If needed, c1=6%row, c2=1%block, h2=6%block, h7=9%cell, e9=9%block, d6=9%row, d1=4%col, f1=9%block, d7=1%cell, g5=9%block, h5=3%row, g8=3%row, h8=2%row, i2=9%block, a7=6%row, g9=6%block, e2=2%cell, e7=3%cell, i1=3%row, f3=3%row, f7=2%row, b2=4%cell, i3=4%row, e6=4%col, a9=7%row, a8=1%cell, e8=7%row, g1=2%block, e1=1%col, b3=2%col)
| Depth 4 needed here |
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| The 8-FC is needed here : |
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