Cn is column number, reading left to right.
Rn is row number, reading top to bottom.
I wanted to record my 1000th completion, and here it is. This one was tricky, but good fun. It started:
There isn’t much to go on here. I had a vague idea that I could do something with the 5s, but Seven is a Magic Number wouldn’t help me with those, nor with any of the other pairings. I thought about trying to leave a 1 – 3 – 1 in the top row (the X – Y – X strategy), but I couldn’t see a way to do so without leaving other numbers of the 1 – 9 set.
Given all my uncertainty, I opted to use the Check, Survey, Undo strategy. (Spoiler: I didn’t Undo.)
I was first struck by the vertical, though blocked, 5s in C1. I could eliminate the 7 – 3 horizontal match at C1R4 – C2R4, then eliminate the newly exposed 4 – 6 vertical match at C2R3 – C2R5, then eliminate the newly exposed 1 – 1 horizontal match at C1R5 – C3R5.
The vertical 5 – 5 would be an elimination of a 5 from the first part of the list and a 5 from the Checked part of the list. This means I would be left with two 5 – 5 matches rather close together. I realised that I could then eliminate the matching pair set of 5s. I proceeded.
Let’s pause here. One way or another I’m going to eliminate the 5 – 5 set, but can I plan ahead for the next set? What will the next set be? Look at the 8s. Look at the sequence between the 8 at C7R2 and the 8 at C5R5.
Given the position of the 3s, I realise I’ll have to eliminate at least one of the 1- 9 matches from outside the sequence in question (between the two 8s). Also, there is an even number of 1 – 9 digits in the sequence, so I’ll actually need to eliminate two of those from outside the sequence. That’s not a problem. (This will make more sense as you study the screenshots below).
The two 3s are separated by a 6. That 6 will have to go before the 3s. That means it is essential to eliminate the C7R5 – C7R6 vertical match. If I do that, the remaining 6s in the sequence are stranded, as is at least one of the 1 – 9 matches. The sixes will have to be eliminated from outside the sequence, which is possible.
Keep in mind we’re inspecting what to do with those remaining 5s. All of these considerations suggest that I should not eliminate the 6s between the 5s horizontally. Vertical elimination it is.
Believing I had accounted for everything correctly, I proceeded.
Refocus your attention on the 8s. At this point I notice that I will have to Check at least one more time, so I’ll just set that up as nicely as I can.
Note: be careful with the 1 – 9 matches. You have to eliminate them in just the right order so not to leave any stranded. Notice the moves from second to the third, and the third to the fourth screenshot here, where I eliminate 9 – 9 matches with one member outside the targeted 8 – 8 sequence. Since I’ve done this twice, I preserve the even number of digits in the 1 – 9 set in the sequence — and I preserve their eliminability.
The only familiar pattern I notice is X – Y – X. Particularly, I see that it’s possible to create two 4 – 3 – 6 sequences. I will surely have to Check yet again, but no stress. Hardly any numbers will remain. Proceed by eliminating the relevant 1s.
At this point, I did a ‘Check, Survey, Undo‘. I saw that if I eliminated the first 7 – 3 sequence, then upon Checking I could eliminate the 4 – 3 – 6 sequences. I proceeded.
The remainder is trivial:
All of this ended in a proud moment 🙂