Hodoku says that after basics this puzzle can be reduced to Singles with a Sue De Coq elimination
but how do you spot such an animal, and how does it work? You can cut to the chase with
148327..9267594381.3.861742396452178714638925852..9....8.2.6..7.7..852...21..38..77
- Code: Select all
+----------------+----------------+----------------+
| 1 4 8 | 3 2 7 | 56 56 9 |
| 2 6 7 | 5 9 4 | 3 8 1 |
| 59 3 59 | 8 6 1 | 7 4 2 |
+----------------+----------------+----------------+
| 3 9 6 | 4 5 2 | 1 7 8 |
| 7 1 4 | 6 3 8 | 9 2 5 |
| 8 5 2 | 17 7 9 | 46 36 346 |
+----------------+----------------+----------------+
| 459 8 359 | 2 1 6 | 45 359 7 |
| 469 7 39 | 9 8 5 | 2 1369 346 |
| 4569 2 1 | 79 47 3 | 8 569 46 |
+----------------+----------------+----------------+
Previously I always ended up solving these puzzles with alternative techniques. This time I think I found the SDC and understood the eliminations, but I’m interested in your comments on the technique for this puzzle. I haven’t seen any recent threads on the basic idea of SDC, only comments about variations, extensions, programming and algorithms, which are a bit off-planet for me. I note that there are some examples in Sue De Coq’s original thread on Disjointed Subsets, which I will work through in time.
Anyway, what I see here is that cells r7c137 and r8c3 form a bent Quad, which allows the elimination of 4 from r7c5, solving it to 1, reducing the puzzle to stte. The logic is fairly simple: If r7c7 is 4, then r7c5 can’t be 4. If r7c7 is 5, then 4 occurs in the intersection and again r7c5 can’t be 4 (this is true for either option in r8c3.)
The same sort of thing happens in the box. If r8c3 is 3, then 9 occurs in the intersection. If r8c3 is 9 then 3 occurs in the intersection, allowing the elimination of 3 and 9 from anywhere else in the box. This true for either option in r7c7.
I see this technique as having characteristics much in common with the XYZ Wing, in that it depends on a cell outside a box and a cell inside a box, which can’t see each other, but both interacting with cells inside the box which they can see, in this case a group of cells called an intersection, rather than a single cell called a pivot. This could help you spot them if you are scanning for both at the same time.
