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Module 6 · Links & ChainsLesson 24 of 28

Strong and Weak Links

Distinguish Strong and Weak Links and propagate their basic true/false implications.

Outcome

You can distinguish Strong and Weak inference relationships, recognize when one candidate pair is both, and propagate true/false states without reversing the logic incorrectly.

Intro copy

Advanced Chains need only two basic moves:

Strong:
false → true

Weak:
true → false

The difficulty is not memorizing those arrows.

It is knowing which relationship you actually have.

Step 1 — Strong Link

Show one row with exactly two candidate 7s.

Prompt:

If the left 7 is false, what happens?

Learner chooses right 7 = true.

Then reverse.

Label:

Strong: cannot both be false

Step 2 — Weak Link

Show a row with four candidate 7s.

Select two.

Prompt:

If the first is true, what happens to the second?

False.

Then:

If the first is false, is the second forced true?

No.

Label:

Weak: cannot both be true

Step 3 — Same pair, both roles

Show a conjugate pair.

Ask:

  • Can both be false? No.
  • Can both be true? No.

Therefore:

Strong + Weak

This is a key chain concept.

Step 4 — Inside a cell

Bivalue {3,8}

Ask:

  • 3 false → 8?
  • 3 true → 8?

Results:

  • false → true;
  • true → false.

So the candidates are Strong + Weak.

Trivalue {3,8,9}

Select 3/8.

  • 3 true → 8 false;
  • 3 false → 8 not forced.

Weak only.

Step 5 — Classification cards

Eight states:

  1. two same-digit candidates, only positions in row;
  2. two selected among three same-digit row candidates;
  3. conjugate pair in box;
  4. bivalue cell;
  5. two candidates inside trivalue cell;
  6. same-digit peers in column with four positions total;
  7. remote candidates that do not see each other;
  8. one deliberately ambiguous-looking diagram.

Learner labels:

  • Strong + Weak;
  • Weak only;
  • no direct link.

Step 6 — Propagation drill

Abstract chain:

A = B - C = D

Start A false.

Learner chooses:

  • B true;
  • C false;
  • D true.

Then start A true.

Prompt:

Can the Strong Link tell us B's state directly?

For normal candidate conjugate pairs, yes, because the endpoints are also Weak and cannot both be true.

The UI should explain that this dual use depends on the candidate relationship, not on abstract Strong Link terminology alone.

Practice

Mix:

  • unit links;
  • within-cell links;
  • false positives;
  • short propagation paths.

Hint ladder

  1. “Ask whether both can be true.”
  2. “Ask whether both can be false.”
  3. “Cannot both be true → Weak.”
  4. “Cannot both be false → Strong.”
  5. “Both answers can be true for the same pair.”

Completion

  • 10 link classifications;
  • 4 propagation paths;
  • zero reversed-Weak-Link errors in the final set.

Next

How Chains Work

Now combine the link roles into useful endpoint deductions.

Reference

Read Strong Links and Weak Links for the complete definitions and examples.