Triple-bit recovery
Recover repeated bits while stating exactly how many errors the model tolerates.
Adult planning suggestion: about 9–12 · Logic & rule checking
- Players
- 1–4 cooperatively
- Time
- 15–25 minutes
- Materials
- 0/1 cards and three-cell groups
Prepare
Encode each source bit independently:0 becomes 000 and 1 becomes 111. Keep triple boundaries visible. For source 101, the transmitted groups are 111 |000 |111. Copying is a paper model, not encrypted communication.
Play
A sender flips at most one bit in each triple, and records which bit changed on a private audit line. No insertion, deletion or movement between groups is permitted. A receiver sees only the altered three-cell groups.
Worked example
Decode each triple by majority. For 101 |010 |110, the majorities are 1,0,1, recovering 101. The first group has one flipped middle bit, the second one flipped middle bit, and the last one flipped last bit.
Finish and check
Now deliberately break the assumption: change 111 into 001 by flipping two bits. Majority reads 0 and is wrong about the original 1. The activity cannot guarantee recovery after two errors in the same group, even if other groups have none.
Adaptation and limits
Compare decoded bits with the original and reveal the audit. Stop after one valid case and one failing case have been explained. Three cells per source bit add redundancy; this is not how every real error-correcting system works and must not be described as a QR-code implementation.
Purpose, observation and provenance
Within this activity: Recover repeated bits while stating exactly how many errors the model tolerates.
Ask the receiver to state each triple’s majority and then explain the two-flips-in-one-group counterexample.
Our rules, examples and printable diagrams are separately prepared. The earliest inventor of the broader mechanism is not established here.
CS Field Guide: Error control — Reference distinguishes error detection and correction. Our repetition-code example is original and does not reproduce QR coding.
Secondary practice: Cooperation and explaining a check.
For a class of 30, use ten groups of three. Prepare one player-material set per group and keep the host key with the adult. Rotate operator, recorder and checker after each worked example; a reader or scribe may help without choosing answers. Avoid public ranking or diagnostic labels.
Age bands are planning suggestions. Background references may address older learners and do not validate suitability for this age band. Goals describe observable actions, not measured long-term gains or institutional endorsement.
Free alternative: Copy the supplied grids, labels and cards onto reused paper. No specialist product is needed. Adults may prepare pieces or act as a scribe.
Printable materials
Preview at 100% scale, with browser headers and footers off. Cut with suitable help. Keep host keys separate. This is a manual tabletop kit, not an online opponent, automatic judge or solver.
Rules to keep beside the materials
- Encode each source bit independently:0 becomes 000 and 1 becomes 111. Keep triple boundaries visible. For source 101, the transmitted groups are 111 |000 |111. Copying is a paper model, not encrypted communication.
- A sender flips at most one bit in each triple, and records which bit changed on a private audit line. No insertion, deletion or movement between groups is permitted. A receiver sees only the altered three-cell groups.
- Decode each triple by majority. For 101 |010 |110, the majorities are 1,0,1, recovering 101. The first group has one flipped middle bit, the second one flipped middle bit, and the last one flipped last bit.
- Now deliberately break the assumption: change 111 into 001 by flipping two bits. Majority reads 0 and is wrong about the original 1. The activity cannot guarantee recovery after two errors in the same group, even if other groups have none.
- Compare decoded bits with the original and reveal the audit. Stop after one valid case and one failing case have been explained. Three cells per source bit add redundancy; this is not how every real error-correcting system works and must not be described as a QR-code implementation.
Triple-bit recovery — play materials
| Group | Original triple | Received triple | Majority |
|---|---|---|---|
| 1 | 111 | ||
| 2 | 000 | ||
| 3 | 111 |
| Failing case | Original | Received | Majority |
|---|---|---|---|
| 2 errors | 111 | 001 |
Host check — keep private until finished
101|010|110 decodes 101;111→001 fails majority recovery.
These are model answers or legal examples, not records of an experiment or learner outcomes.
Related activities
Activity library · Parity row repair: rules and printable materials