Two mechanisms on paper

Print one copy per pair or table. The nine-card activity is a provisional adaptation for rehearsal, not a settled workshop decision. All times are estimates.

Nine shuffled cards

Use any nine distinct cards. One person deals; another remembers a card. Shuffle openly. Before beginning, predict that the remembered card will finish fifth from the top after two rounds.

  1. Deal face up from the top of the packet, one at a time, left to right into three columns. Make three rows, top to bottom.
  2. The spectator remembers one card and names its column.
  3. Read each column top row to bottom row. Arrange the three column lists end to end: an unselected column, the selected column, the other unselected column.
  4. Make those nine cards into a face-down packet whose TOP-to-BOTTOM order matches that list. To avoid reversing it, start with the LAST card and put each preceding card on top until the FIRST card is on top.
  5. Deal again exactly as in step 1. The spectator names the remembered card’s column again. Collect exactly as in steps 3–4.
  6. Count from the top of the packet. The fifth card is the remembered card.

An example trace

Suppose the shuffled packet happens to read A through I from top to bottom, and the spectator remembers B. The letters stand for any nine distinct cards.

First deal:       A  B  C
                  D  E  F
                  G  H  I

Chosen column:    B, E, H
New TOP-to-BOTTOM: A, D, G, B, E, H, C, F, I

Second deal:      A  D  G
                  B  E  H
                  C  F  I

Chosen column:    A, B, C
New TOP-to-BOTTOM: D, E, F, A, B, C, G, H, I
                              ↑ fifth is B

Why it works

The first collection puts the chosen card in position 4, 5 or 6. The next deal places those positions in the middle row. Putting the indicated column between the other two places its middle card fifth. The starting shuffle can change. The reason still holds.

Discuss: what inputs did the dealer receive? Which ordering rules mattered? Can you predict what happens if the selected column goes first instead? This is one algorithm, not a proof of Turing completeness.

Adapted from NRICH, Spot the Card. Nine-card instructions and trace written for this workshop. Allow roughly 13 minutes including setup, execution and explanation; rehearse the physical collection.

The next-word hat

Four to six people per table. Gather a cup or hat, identical slips, pencils and a shared response sheet. Choose a reader. Read this prompt:

Tell a short story about a surprising discovery at school.

  1. Start with an empty response. Everyone writes ONE proposed next word, or STOP, on a slip. Words may include punctuation.
  2. Mix all slips and draw one without looking. Keep duplicates as separate chances.
  3. If the slip says STOP, finish. Otherwise append that word to the shared response.
  4. Clear the hat. Read the prompt and the whole response again. Everyone proposes a fresh next word or STOP for the new context.
  5. Repeat. Stop if STOP is drawn, or at the agreed cap of eight selected words. The cap is a time limit, not a learned decision.
  6. Save the response. Reset to the SAME prompt and empty response. Repeat the SAME process a second time.

Do not prewrite a sentence and cut it up. Do not keep old suggestions when the context changes. Do not choose a different first word deliberately. Random draws may lead to different paths, but identical results are possible.

Discussion

Which words appeared on several slips? Did a selected word change what you would propose next? Why did the response stop? Where did your suggestions come from?

This models sampling during generation. It does not model neural-network training. People supply proposals; a model calculates token probabilities from learned parameters and context. Model tokens can be smaller than words, and generation need not use random decoding.

Allow approximately 12 minutes for instructions, two short runs and discussion. If time is tight, shorten the second run rather than changing the mechanism.

After either activity

What mechanism could learners explain before running it again? What could they change? What dependencies would remain if this became a real classroom tool?

No phone or account is required. A partner can dictate or read slips. The future phone-assisted version and microphone-triggered reveal are outside this draft.