X-Cycles
A single digit's strong and weak links are traced into a closed loop — a continuous loop yields eliminations at its weak links, a discontinuous one pins or clears its meeting cell outright.
How it works
- 1Digit 7 runs a closed loop through A1, F1, F5 and A5. Two of the links are strong: column A has only A1 and A5 left for 7, and column F has only F1 and F5.
- 2The other two are weak. Rows 1 and 5 both hold more 7s than the loop's own pair — C5 is one of them — so all those links say is that at most one end of each can be the 7.
- 3Strong, weak, strong, weak: the loop alternates and closes evenly, which makes it continuous, and the four cells split into two colours that take turns being true.
- 4A continuous loop pays out at its weak links. One of A5 and F5 is already the 7 for row 5, so no other cell in that row can be — C5 loses its 7. (A loop that doesn't close evenly instead places or clears the single cell where the two odd links meet.)
- First colour in the chain
- Second colour in the chain
- Where the conclusion lands
- Candidate ruled out
- Strong link — At least one endpoint must be true.
- Weak link — At most one endpoint can be true.