Strong and weak links, without jargon

Turn two simple promises into a chain you can follow.

A node is a specific possibility

In a chain, “A” usually means a particular candidate in a particular cell, such as “r2c4 is 6.” It does not mean the whole cell or every candidate there. True means that specific digit is placed; false means that specific candidate is ruled out.

For exampleThe 2 in r2c4 and the 6 in r2c4 are two different candidate nodes even though they share a cell.

Strong: at least one must be true

If a row needs a 6 and only two candidate locations remain, at least one of them must be 6. They form a strong link. If the first is false, the second is forced true. A cell with exactly two candidates also supplies a strong link between its two candidates.

For exampleRow 2 has 6 only at A and B. If A is not 6, B must be 6. Check the entire row before calling this a two-location link.

Weak: they cannot both be true

Two candidate 6s that see each other cannot both be true. They form a weak link, even if the house has more places for 6. If the first is true, the second is false. But if the first is false, a weak link alone tells us nothing about the second.

For exampleA row allows 6 in A, B, and C. A and B are weakly linked: A being false leaves either B or C available.

Alternate the promises

A strong–weak–strong chain A–B–C–D has a useful consequence. Assume A is false: the first strong link makes B true, the weak link makes C false, and the last strong link makes D true. If A was true instead, A already supplies the digit. Either way, at least one endpoint is true.

For exampleIf A and D are both candidate 6s, any outside candidate 6 whose cell sees both endpoints can be erased.

A link can satisfy both promises

Two remaining locations for a digit in one house are both strongly and weakly linked: at least one is true, and not both are true. A chain uses whichever direction of reasoning that step needs. In this trainer a solid line shows a strong step and a dashed line shows a weak step.

For exampleDo not read a dashed line as “one end must be true.” Its promise is only “not both.”

Quick check

A and B share a weak link. You discover that A is false. What can this link alone tell you about B?

B must be true.
Nothing definite about B yet.
B must also be false.

Show the answer

Nothing definite about B yet. Exactly. Both might be false. You need another constraint before forcing B.

Try it with the interactive lessons Play an easy puzzle

Next, when you are ready: 2-String Kite.