I'm going to start this thread modestly, with a solution to the puzzle that at the moment is last on ravels list, my own contribution, the toughest 21-clue puzzle in the Pt-grid:
- Code: Select all
+-------+-------+-------+
| 1 . . | . . . | . . 9 |
| . . 7 | . 8 . | . . 6 |
| . . . | 3 . . | . 5 . |
+-------+-------+-------+
| . . . | . 4 . | 8 . . |
| 7 . . | . . 1 | . . . |
| . 9 6 | . . . | . . . |
+-------+-------+-------+
| . . 8 | 2 . . | . . . |
| 5 . . | . . . | . 6 3 |
| . 6 . | . 7 . | 4 . . |
+-------+-------+-------+
I did eliminations where I saw that I could. When I did some elimination, I tried to follow with other eliminations that would either benefit from the last, or continue the path of the last elimination. I tried to solve bivalue cells and values with only two possibilities in an unit whenever I could.
After the basics:
- Code: Select all
*-----------------------------------------------------------------------------*
| 1 23458 2345 | 4567 256 24567 | 237 23478 9 |
| 2349 2345 7 | 159 8 2459 | 123 1234 6 |
| 6 248 249 | 3 129 2479 | 127 5 12478 |
|-------------------------+-------------------------+-------------------------|
| 23 1235 1235 | 5679 4 235679 | 8 2379 257 |
| 7 2345 2345 | 8 2359 1 | 6 239 25 |
| 8 9 6 | 57 235 2357 | 12357 12347 12457 |
|-------------------------+-------------------------+-------------------------|
| 349 1347 8 | 2 13569 34569 | 1579 17 157 |
| 5 1247 1249 | 149 19 8 | 1279 6 3 |
| 239 6 1239 | 159 7 359 | 4 128 1258 |
*-----------------------------------------------------------------------------*
1. r7c5<>9:
[r7c5](-9-[r89c4])-9-[r8c5]-1-[r89c4]-45-[r1c4]
-5-[r6c4]-7-[r1c4]-6-[r1c5]=6=[r7c5]
2. r7c6<>9:
[r7c6]-9-[r7c7]=9=[r8c7]-9-[r8c3]
-9-[r8c45]-14-[r8c3]-2-[r9c1]
=6=[r7c5]=3=[r9c6]-3-[r9c1]
-9-[r8c5]-1-[r89c4]=1=[r2c4]=9=[r2c1]-9-[r9c1]
3. r7c1<>9:
[r7c1]-9-[r2c1]=9=[r3c3]-9-[r3c5]
-9-[r7c7]=9=[r8c7]-9-[r8c5]=9=[r5c5]-9-[r5c8]
-1-[r89c4]=1=[r2c4]-1-[r2c89]
-1-[r3c5]-2-[r3c2]
=4=[r2c1]-4-[r2c8]
-4-[r3c2]-8-[r3c9]=8=[r9c9]=2=[r9c8]-2-[r2c8]
-2-[r5c8]-3-[r2c8]
Solves a single and progresses the puzzle here:
- Code: Select all
*--------------------------------------------------------------------*
| 1 23458 2345 | 456 256 24567 | 237 2478 9 |
| 2349 2345 7 | 159 8 2459 | 123 124 6 |
| 6 248 249 | 3 129 2479 | 127 5 148 |
|----------------------+----------------------+----------------------|
| 23 1235 1235 | 569 4 569 | 8 39 7 |
| 7 345 345 | 8 59 1 | 6 39 2 |
| 8 9 6 | 7 23 23 | 5 14 14 |
|----------------------+----------------------+----------------------|
| 34 1347 8 | 2 1356 3456 | 9 17 15 |
| 5 1247 1249 | 149 19 8 | 127 6 3 |
| 239 6 1239 | 159 7 359 | 4 128 158 |
*--------------------------------------------------------------------*
4. r7c8<>1:
[r7c8](-1-[r29c8])-1-[r7c9]-5-[r9c9]-8-[r9c8]-2-[r2c8]-4-[r6c8]-1-[r7c8]
5. r6c5<>2:
[r6c5]=3=[r7c5]=6=[r7c6]-6-[r4c6]=6=[r4c4]-6-[r1c4]
=4=[r8c4]-4-[r1c4]-5-[r1c23]=5=[r2c2]-5-[r45c2]
=5=[r7c9]=1=[r7c2]-1-[r4c2]=1=[r4c3]=5=[r5c3]-5-
[r5c5](-9-[r3c5])-9-[r8c5]-1-[r3c5]-2-[r6c5]
Some more singles solved, current state:
- Code: Select all
*--------------------------------------------------------------------*
| 1 23458 2345 | 456 256 4567 | 237 248 9 |
| 2349 2345 7 | 159 8 459 | 123 124 6 |
| 6 248 249 | 3 129 479 | 127 5 148 |
|----------------------+----------------------+----------------------|
| 23 1235 1235 | 569 4 569 | 8 39 7 |
| 7 345 345 | 8 59 1 | 6 39 2 |
| 8 9 6 | 7 3 2 | 5 14 14 |
|----------------------+----------------------+----------------------|
| 34 134 8 | 2 156 3456 | 9 7 15 |
| 5 7 1249 | 149 19 8 | 12 6 3 |
| 239 6 1239 | 159 7 359 | 4 128 158 |
*--------------------------------------------------------------------*
6. r4c1<>3:
[r4c1]-3-[r7c1]-4-[r8c3]
-3-[r4c8]=3=[r5c8]=9=[r5c5]-9-[r3c5]
-9-[r8c5]-1-[r8c7]=1=[r23c7]-1-[r3c9]
-2-[r8c3]
-1-[r3c5]-2-[r3c23]
-1-[r8c3]-9-[r3c3]-4-[r3c9]
-4-[r3c2]-8-[r3c9]
7. r7c5<>5:
=5=[r7c5]{BUG-lite:[r147c456]-5-[r1c456]}
=6=[r1c5]-6-[r1c6]
-6-[1c4]-4-[r8c4]
-4-[r1c6]-7-[r3c6]
-4-[r3c6]-9-[r3c3]-4-[r8c3]
8. r7c5<>1:
[r7c5]-1-(-1-[r89c4])[r8c5]-9-[r89c4]-45-[r1c4]-6-[r1c5]=6=[r7c5]
Still no solution, current state of the puzzle:
- Code: Select all
*--------------------------------------------------------------------*
| 1 23458 345 | 456 25 4567 | 237 248 9 |
| 349 2345 7 | 159 8 459 | 123 124 6 |
| 6 248 49 | 3 129 479 | 127 5 148 |
|----------------------+----------------------+----------------------|
| 2 135 135 | 569 4 569 | 8 39 7 |
| 7 345 345 | 8 59 1 | 6 39 2 |
| 8 9 6 | 7 3 2 | 5 14 14 |
|----------------------+----------------------+----------------------|
| 34 134 8 | 2 6 345 | 9 7 15 |
| 5 7 1249 | 149 19 8 | 12 6 3 |
| 39 6 1239 | 159 7 359 | 4 128 158 |
*--------------------------------------------------------------------*
Finned X-wing: r3c9<>1
Finned X-wing: r5c2<>5
9. r1c7<>2:
[r1c7]-2-[r1c5]-5-[r5c5]-9-[r8c5]-1-[r8c7]-2-[r1c7]
10. r9c3<>1:
[r9c3]-1-[r7c2]=1=[r7c9]-1-[r8c7]-2-[r8c3]=2=[r9c3]
11. r8c3<>2:
=2=[r8c3]=1=[r7c2]=4=[r7c1]-4-[r2c1]
-2-[r8c7]-1-[r9c9]=1=[r6c9]=4=[r3c9]-4-[r3c3]-9-[r2c1]
-9-[r3c6]
-4-[r3c6]-7-[r3c7]-2-[r2c7]-3-[r2c1]
12. r8c3<>1:
[r8c3]-1-[r4c3]=1=[r4c2]
=9=[r3c3]-9-[r3c6]
-1-[r8c5]=1=[r3c5]-1-[r3c7]-7-[r3c6]
-7-[r1c7]-3-[r1c3]
-9-[r5c5]-5-[r5c23]=5=[r4c3]-5-[r1c3]-4-[r1c8]
-5-[r1c5]-2-[r1c8]-8-[r3c9]-4-[r3c6]
Now lots of SSTS techniques bring us here:
- Code: Select all
*--------------------------------------------------*
| 1 28 35 | 46 25 67 | 37 48 9 |
| 49 35 7 | 159 8 459 | 13 2 6 |
| 6 28 49 | 3 129 79 | 17 5 48 |
|----------------+----------------+----------------|
| 2 35 1 | 569 4 569 | 8 39 7 |
| 7 4 35 | 8 59 1 | 6 39 2 |
| 8 9 6 | 7 3 2 | 5 14 14 |
|----------------+----------------+----------------|
| 34 1 8 | 2 6 34 | 9 7 5 |
| 5 7 49 | 149 19 8 | 2 6 3 |
| 39 6 2 | 59 7 359 | 4 18 18 |
*--------------------------------------------------*
13. r1c7=7:
[r1c7]=7=[r1c6]=6=[r1c4]=4=[r8c4]=1=[r2c4]-1-[r2c7]-3-[r1c7]
Singles remain. It's funny how the fact that it's last on the list can give a false impression that it would be easy...
This is probably not the best solution, but it's one way of doing it. Afterwards when I look at it, I can see that step 8 is actually exactly the same as step 1, feel completely stupid for not noticing that when I did the first step... It could perhaps have shortened the solution a bit.
I apologize in advance for all possible typos and mistakes in the notation.
RW