05/10/30 tough puzzle from sudoku.com.au
Want to see the whole thing? A complete proof
1) First eliminations lead to 23 filled cells. (if needed : h3=3%col, i5=3%col, b7=3%col)
2) Look at only possibles h9=4,h8=4 in their col. They forbid{`i9=4`, `g9=4`, `i7=4`, `g7=4`}.
Look at only possibles b1=9,b2=9 in their col. They forbid{`a3=9`, `c3=9`, `c1=9`, `a1=9`}.
Now simple eliminations take place again, leading to 46 filled cells. (if needed : d3=9%row, a7=9%row, e9=9%row, f7=4%row, i3=4%row, e1=4%row, e6=3%col, d6=6%row, g6=8%row, i7=6%row, h4=6%row, h2=9%col, b1=9%row, g5=4%col, c5=9%row, g4=9%row, i4=1%block, g7=5%block, g9=1%block, i2=5%row, d7=1%row, i1=8%block, i9=7%col)
3) Look at only possibles b2=2,b2=7 in their cell. Whether b2=2 (in which case g2=7%cell) or b2=7, in both cases, we have no more {`d2=7`, `f2=7`, `e2=7`}.
Look at only possibles b2=7,b2=2 in their cell. Whether b2=7 (in which case g2=2%cell) or b2=2, in both cases, we have no more {`f2=2`, `e2=2`, `d2=2`}.
Then simple eliminations take place again, up to 51 filled cells. (if needed : d2=8%cell, f5=8%row, e5=1%block, f2=1%block, e2=6%row)
4) Look at only possibles d8=7,d1=7 in their col. Whether d8=7 (in which case e8=2%cell) or d1=7 (in which case f3=2%cell), in both cases, we have no more {`f9=2`, `f8=2`}.
Look at only possibles d8=7,d1=7 in their col. Whether d8=7 (in which case e8=2%cell) or d1=7 (in which case d9=3%col), in both cases, we have no more {`d9=2`}. Now easy to 54 filled cells. (if needed : d9=3%cell, f1=3%row, f9=6%cell)
5) Look at only possibles e8=2,d8=2 in their block. They forbid{`c8=2`, `a8=2`, `b8=2`}.
From here, simple eliminations lead to unique solution. (if needed : b2=2%col, g1=2%block, f3=2%block, a3=7%row, c3=8%row, b6=7%row, g2=7%row, d1=7%row, c6=4%row, a6=1%block, c8=1%block, a8=6%row, h8=8%row, a9=8%row, c9=2%block, a5=2%block, e4=2%block, d8=2%block, f4=7%row, e8=7%row, c1=6%row, f8=5%row, d5=5%row, c4=5%row, a1=5%row, h9=4%row, b8=4%row)
| The hard step is at 51 filled : |
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| The hard step is at 51 filled : |
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Now applying the same "dictionary" (changing rows, columns, values) to proof of 05/09/24 you will mechanically get a proof of today's. E.g. first filled cell in 05/09/24 was g5=1%block; in today's it becomes i5=3%block. 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 above hints for today's proof (automatically derived from 05/09/24's proof).
Go : back to sandbox