Ronk wrote:If r4c7=1, then r1c8<>9
... are both valid. (I haven't actually seen a proof for the later though.)
3 1 9 | 6 7 48 | 248 25 458
6 7 2 | 38 5 348| 48 1 9
5 8 4 | 2 9 1 | 7 6 3
-----------+-----------+------------
278 4 137| 9 238 5 | 6 27 18
28 6 35 | 7 1 38 | 2348 9 458
9 23 157| 4 238 6 | 238 57 15
-----------+-----------+------------
4 9 8 | 5 6 2 | 1 3 7
27 23 37 | 1 4 9 | 5 8 6
1 5 6 | 38 38 7 | 9 4 2
Carcul wrote:Ronk wrote:If r4c7=1, then r1c8<>9
... are both valid. (I haven't actually seen a proof for the later though.)
I don't think this last one is valid. The only thing that we can say with certain is, if there is only one solution, we cannot have r1c8<>9 and r4c7<>1. So, if r4c7<>1 => r1c8=9, if r1c8<>9 => r4c7=1.
Carcul wrote:We have a type 2 AUR in cells r1c6, r1c7, r2c6, and r2c7, and in the solution of this grid it turns out that r2c6=3 and r1c7=2.
3 1 9 | 6 7 48 | 48+2 25 458
6 7 2 | 38 5 48+3| 48 1 9
5 8 4 | 2 9 1 | 7 6 3
--------------+--------------+---------------
278 4 137 | 9 238 5 | 6 27 18
28 6 5 | 7 1 38 | 2348 9 458
9 23 157 | 4 28 6 | 238 57 15
--------------+--------------+---------------
4 9 8 | 5 6 2 | 1 3 7
27 23 37 | 1 4 9 | 5 8 6
1 5 6 | 38 38 7 | 9 4 2
ronk wrote:My starting implication chains are based on the fact that for this type 2 AUR example ... either r1c8=9 or r4c7=1 and therefore ...
r4c7=1 => r4c9<>1 => r4c9=4 => r4c8<>4 => r4c8=8
r4c7<>1 => r1c8=9 => r1c8<>8 => r4c8=8 => r4c8<>4
Where is the error in logic? Is is possible such a simple deduction is not expressible with a nice loop simpler than the one you posted? Tell me it isn't so!
Jeff wrote:[r4c8]-4-[r4c9]-1-(AUR:[r4c7][r1c7][r4c8]-4|8-[r1c8])=8=[r4c8] => r4c8<>4 => r4c8=8
Jeff wrote:Carcul, I don't disagree with your notation, but just to suggest an alternative for brainstorming.
Carcul wrote:Jeff wrote:[r4c8]-4-[r4c9]-1-(AUR:[r4c7][r1c7][r4c8]-4|8-[r1c8])=8=[r4c8] => r4c8<>4 => r4c8=8
I don't want to be boring or arrogant, but I still don't agree with this loop. If r4c8=4 then there is no contradiction in the cells that you have used in the loop.
Carcul wrote:Yes, I now my notation might be confusing sometimes (or manytimes), but I prefer to write a "condensed" notation and then explain separately the origin of a link if necessary (this is just a personal preference).
Carcul wrote:what is the exact meaning of the word "brainstorming"?
Carcul wrote:And how about the exercise of AURs that I posted above, refering to a grid in the thread "Nice loops for elementary level players - the x-cycle", what do you think?
+----------------+----------------+----------------+
| 4 1258 12 | 15 9 7 | 6 158 3 |
| 38 158 9 | 6 134 34 | 7 158 2 |
| 367 156 1367 | 135 8 2 | 9 15 4 |
+----------------+----------------+----------------+
| 9 3 1267 |^17 1246 46 | 8 ^67 5 |
| 2678 268 4 | 9 *236 5 |*23 67 1 |
| 267 126 5 | 137 *1236 8 |*23 4 9 |
+----------------+----------------+----------------+
| 2356 7 236 | 4 356 36 | 1 9 8 |
| 1 4 8 | 2 7 9 | 5 3 6 |
| 356 9 36 | 8 356 1 | 4 2 7 |
+----------------+----------------+----------------+
we get r4c6<>6
Carcul wrote:In chain notation we have:
[r4c6]-6-[r5c5|r6c5]-1-[r4c4]-7-[r4c8]-6-[r4c6] => r4c6<>6.
Ronk wrote:r5c5 and r6c5 "behave" like a single bivalued cell.
1 45+2 9 | 6 3 45 | 7 25 8
235 8 35 | 7 1 9 | 25 4 6
6 45 7 | 2 8 45 | 3 1 9
-------------------+-------------------+-----------------
345 25 45+23 | 45 9 7 | 6 8 1
45 7 1 | 3 6 8 | 245 9 25
9 6 8 | 1 45 2 | 45 3 7
-------------------+-------------------+-----------------
245 3 6 | 9 45 1 | 8 7 245
8 1 45+2 | 45 7 6 | 9 25 3
7 9 45 | 8 2 3 | 1 6 45
Ronk wrote:In your AUR type numbering, which type number is for the simplest of AURs ... the AUR+1?
This example has an AUR (45) + 1 at cells r1c26 and r3c26: