Rewrite tape head
Follow a state table that can rewrite one tape cell and move a head.
Adult planning suggestion: about 9–12 · Logic & rule checking
- Players
- 3 per group
- Time
- 20–30 minutes
- Materials
- Printed record sheet, pencil and paper markers
Prepare
Use cells−1 through 6. Put 1 in cells 0,1,2 and blank□ elsewhere. Head begins at 0 in state q. One pupil holds the head marker, another writes tape changes and a third reads the transition row.
Follow the rule
Table: in q on 1, write 0, move right one cell, stay q. In q on□, write 1, do not move, enter HALT. There are no other symbols or active states in this kit.
Check each step
One transition is atomic: read the old symbol, find the matching table row, write, move and update state. A newly written 0 does not get read again because the same transition has already moved the head.
Worked example
From 111□, the first three steps write 000 and advance to cell 3. Step 4 writes 1 in the blank and halts. On a fresh copy, try input 11; keep the initial tape separate from the result.
Finish and adapt
Stop at HALT or after ten transitions, marking an unfinished run if the safety limit is reached. This finite paper exercise illustrates a tape-machine mechanism; it does not prove a general program correct or label children as fast or slow.
Purpose, observation and provenance
Within this activity: Follow a state table that can rewrite one tape cell and move a head.
Observe whether reading, writing and moving are recorded as one ordered transition.
Our rules, examples and printable diagrams are separately prepared. The earliest inventor of the broader mechanism is not established here.
Cornell: Turing machines — Technical background, not an evaluated primary-school lesson. This paper exercise and examples are our adaptation; age and support are adult planning suggestions.
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.
Rewrite tape head · Player sheet
Before you begin
- Use cells−1 through 6. Put 1 in cells 0,1,2 and blank□ elsewhere. Head begins at 0 in state q. One pupil holds the head marker, another writes tape changes and a third reads the transition row.
- Table: in q on 1, write 0, move right one cell, stay q. In q on□, write 1, do not move, enter HALT. There are no other symbols or active states in this kit.
- One transition is atomic: read the old symbol, find the matching table row, write, move and update state. A newly written 0 does not get read again because the same transition has already moved the head.
| State | Read | Write | Move | Next |
|---|---|---|---|---|
| q | 1 | 0 | R | q |
| q | □ | 1 | 0 | HALT |
| Cell | −1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|---|
| Initial | □ | 1 | 1 | 1 | □ | □ | □ | □ |
| Step | Read / write | Head / state |
|---|---|---|
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
Rewrite tape head · Host key — keep separate
111 becomes 0001 in four transitions, head 3;11 becomes 001 in three, head 2.
What to observe
Observe whether reading, writing and moving are recorded as one ordered transition.
Use the three-person roles described in the rules; offer reading or writing support without selecting answers.
Read the rules as well as this example. Other valid solutions may exist for the puzzle boards. This key is not a claim of uniqueness or measured learning gains.
| Constraint / action | Evidence / correction |
|---|---|
| ________ | ________ |
| ________ | ________ |
| ________ | ________ |
| ________ | ________ |