Advanced family · 04
Chains & Loops
Alternating candidate relationships that turn local links into forced deductions.
The chain family
ALTERNATING LINKS CARRY A CANDIDATE CONSEQUENCE FROM ONE CELL TO THE NEXT
Chains connect candidate relationships using strong and weak links. A strong link says that if one candidate is false, the linked candidate must be true. A weak link says that if one candidate is true, the linked candidates must be false. Remeber, a strong link is literally a special case of weak links.
In a chain, those relationships alternate. The useful deduction comes from following what must happen from one end of the chain to the other.
The question: What candidate relationship can be followed without breaking the alternating logic?
A second look
STRONG AND WEAK LINKS ARE THE LANGUAGE OF A CHAIN.
You already met Strong & Weak Links in the Advanced introduction. Here, the same ideas are used as building blocks for chains: links alternate, the chain can be followed in either direction, and the endpoints tell you what the chain proves.
Remeber, a strong link is literally a special case of weak links.
Explore the family
CHAIN TECHNIQUES
01 · Chains & Loops
Remote Pair
A chain of matching bivalue cells creates a shared elimination zone.
Remote Pair →02 · Chains & Loops
X-Chain
A single candidate travels through alternating strong and weak links.
X-Chain →03 · Advanced
X-Cycle
A single candidate closes into a loop that either proves eliminations or forces the break.
X-Cycle →04 · Chains & Loops
XY-Chain
Bivalue cells pass a two-candidate relationship from one end to the other.
Y-Cycle →05 · Chains & Loops
AIC
Alternating inference chains generalize strong and weak links across candidates.
Nice Loop / AIC →OTHER CHAINS
They are chains too...
Skyscraper, Two-String Kite, Turbot Fish, and Three-String Kite all belong to chain family, specifically, they are specialized variations of X-Chain, just a bit shorter with three or four links;
Simple Coloring is also a chain technique and a specialized variantion of X-Chain.