05/10/29 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 : b7=4%block, i5=4%block, h3=4%block)
2) Look at only possibles b2=9,b1=9 in their col. They forbid{`c3=9`, `a2=9`, `c2=9`, `a3=9`}.
Look at only possibles h8=3,h9=3 in their col. They forbid{`g7=3`, `g8=3`, `i8=3`, `i7=3`}.
Now simple eliminations take place again, leading to 46 filled cells. (if needed : f3=9%row, a7=9%row, e8=9%col, d7=3%row, e2=3%col, e4=4%col, f4=1%row, g4=6%row, i7=1%row, h6=1%block, h1=9%col, b2=9%row, i3=3%row, g5=3%block, c5=9%row, g6=9%col, i6=8%cell, g7=5%block, i1=5%row, g8=8%col, f7=8%cell, i8=2%block, i2=6%col)
3) Look at only possibles b1=2,b1=7 in their cell. Whether b1=2 (in which case g1=7%cell) or b1=7, in both cases, we have no more {`d1=7`, `e1=7`, `f1=7`}.
Look at only possibles b1=7,b1=2 in their cell. Whether b1=7 (in which case g1=2%cell) or b1=2, in both cases, we have no more {`f1=2`, `d1=2`, `e1=2`}.
Then simple eliminations take place again, up to 51 filled cells. (if needed : f1=6%cell, d5=6%col, d1=8%col, e1=1%cell, e5=8%col)
4) Look at only possibles f9=2,f2=2 in their col. Whether f9=2 (in which case e9=7%cell) or f2=2 (in which case d3=7%cell), in both cases, we have no more {`d8=7`, `d9=7`}.
Look at only possibles f9=2,f2=2 in their col. Whether f9=2 (in which case e9=7%cell) or f2=2 (in which case f8=4%col), in both cases, we have no more {`f8=7`}. Now easy to 54 filled cells. (if needed : f8=4%cell, d8=1%cell, d2=4%row)
5) Look at only possibles e9=7,f9=7 in their block. They forbid{`a9=7`, `c9=7`, `b9=7`}.
From here, simple eliminations lead to unique solution. (if needed : b1=7%col, d3=7%row, f2=2%block, g1=2%block, a3=2%block, b4=2%block, g2=7%row, c3=6%cell, c4=3%row, c9=8%col, a9=1%block, h9=6%row, a8=6%row, c8=7%row, e6=7%row, d6=2%block, e9=2%block, f9=7%row, b9=3%row, c2=1%row, a2=5%row, f5=5%row, a4=8%col, a5=7%col, d9=5%col, c6=5%col, h8=3%cell)
| 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=4%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