d:/donn 11-18.htm

05/11/18 tough puzzle from sudoku.com.au

Want to see the whole thing? A complete proof
Just stuck somewhere and willing to have still work to do ? Short hints for a proof
Studied enough forbidding chains to appreciate this Forbidding-chain-like proof ?
Understood the equivalent puzzles stuff? Equivalence with 09/24

A complete proof

Filled cells are left blank on diagrams for easier reading.
First eliminations : [e7=9%block, c8=9%block, g2=9%block] lead to 23 filled cells.

Look at only possibles i8=2,h8=2 in their row. They forbid{i7=2, i9=2, g7=2, g9=2}.
Look at only possibles a2=4,b2=4 in their row. They forbid{c1=4, c3=4, a1=4, a3=4}.
Now easy fillings up to 46 filled cells. (If needed, c6=4%col, g3=4%col, i5=4%col, g4=2%col, c7=2%col, a5=2%col, f5=9%row, f6=1%col, f9=5%col, g7=1%col, d8=1%col, b8=4%row, a2=4%col, e9=2%row, e1=4%col, d9=4%col, d7=7%block, g9=3%block, g6=7%col, b7=3%col, i9=7%block, i7=6%block, a7=5%row)

Look at only possibles b9=6,b9=8 in their cell. Whether b9=8 (in which case b2=6%cell) or b9=6, in both cases, we have no more {b6=6, b5=6, b4=6}.
Look at only possibles b9=8,b9=6 in their cell. Whether b9=6 (in which case b2=8%cell) or b9=8, in both cases, we have no more {b5=8, b6=8, b4=8}.
Now easy fillings up to 51 filled cells. (If needed, b6=5%cell, e4=5%col, b4=7%row, b5=1%col, e5=7%block)

Look at only possibles h6=6,a6=6 in their row. Whether h6=6 (in which case h5=8%cell) or a6=6 (in which case c4=8%cell), in both cases, we have no more {h4=8, i4=8}.
Look at only possibles h6=6,a6=6 in their row. Whether h6=6 (in which case h5=8%cell) or a6=6 (in which case i6=9%row), in both cases, we have no more {i6=8}.
Now easy fillings up to 54 filled cells. (If needed, i6=9%cell, a4=9%col, i4=1%cell)

Now, Look at only possibles h5=8,h6=8 in their block. They forbid{h3=8, h2=8, h1=8}.
Now easy fillings up to 81 filled cells. (If needed, b2=8%row, c4=8%col, a9=8%col, c3=6%col, f2=6%col, b9=6%col, a6=6%col, c1=5%col, f1=2%col, f3=7%col, h1=7%col, i8=2%col, i3=5%col, i1=8%col, d5=8%col, h6=8%col, e3=8%col, d4=6%col, h5=6%col, h8=5%col, h4=3%col, e6=3%col, d1=3%col, a3=3%col, h2=2%col, h3=1%col, a1=1%col)

Short hints for a proof

One of the two heptagons is highlighted.


1) First eliminations to 23 filled cells.
2) Look at only possibles 2 in R8. Look at only possibles 4 in R2. Remove some possibles. Now easy eliminations take place again, leading to 46 filled cells.
3) Look at only possibles 68 in b2b9. Remove some possibles. Then simple eliminations take place again, up to 51 filled cells.
4) Looking at only possibles 6 in R6, remove h4=8,i4=8,i6=8 (beware, heptagons).
5) Look then at only possibles 8 in Bh5. Remove some possibles. From here, simple eliminations lead to unique solution.

Forbidding-chain-like proof

One of the two heptagons is highlighted.


around 23 filled
(i8=2)==(h8=2) forbids {g9=2, i9=2, i7=2, g7=2}
(a2=4)==(b2=4) forbids {a1=4, a3=4, c1=4, c3=4}
around 46 filled
(b9=6)==(b9=8)--(b2=8)==(b2=6) forbids {b4=6, b6=6, b5=6}
around 51 filled
(h5=8)==(h5=6)--(h6=6)==(a6=6)--(c4=6)==(c4=8) forbids {i4=8, h4=8}
(h5=8)==(h5=6)--(h6=6)==(a6=6)--(a6=9)==(i6=9) forbids {i6=8}
around 44 filled
(h5=8)==(h6=8) forbids {h2=8, h1=8, h3=8}

Equivalence with 09/24

Now applying the same "dictionary" (renaming numbers, replacing cells) 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 i7=1%col; in today's it becomes c8=9%row. 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 hints for today's proof (automatically derived from 05/09/24's proof).