On a sheet of paper, draw a red triangle wearing a tiny crown. Beside it, write, “Goes in the lantern box.” Now draw a yellow circle with two dots inside and write, “Does not go in the lantern box.” What separates them: color, corners, decoration—or a rule nobody has named yet?
Set up the hypothetical round
Here is a complete hypothetical game for two people, using only paper and a pencil. Before anything is drawn, the Keeper privately reads the supplied secret rule near the end of this article. The Guesser must avoid that reveal. The Keeper then copies the four cards below and shows which ones belong in the fictional lantern box. In later rounds, the Keeper may invent a different rule, but must classify every new card consistently with it.
Example 1 is a red triangle with one small crown above it. It goes in the lantern box. Example 2 is a blue square with one small flag above it. It also goes in. Example 3 is a green pentagon with one small moon above it. It goes in as well. The counterexample is a yellow circle with two small dots inside it. It does not go in the lantern box.
The Guesser may propose a rule or request another card. When a proposed rule fits everything shown but differs from the secret rule, the Keeper should not merely say, “Wrong.” The Keeper draws and classifies a card on which the two rules produce different answers. That contrast eliminates a particular explanation without pretending the remaining one has been proved unique.
Find the rival explanations
The obvious pattern might be “shapes with straight sides belong.” That fits all four cards. So does “objects with something above them belong.” A third possibility is “red, blue, and green objects belong, but yellow ones do not.” Three examples and one counterexample leave all three explanations standing.
Suppose the Guesser chooses the straight-sides theory. The Keeper can draw a purple circle with a tiny star above it and mark it as belonging. The circle defeats that theory while remaining compatible with the decoration-above theory. If the Guesser instead proposes that every shape except a yellow one belongs, the Keeper can draw a yellow hexagon with a small bell above it and place it in the box.
The sharpest request is one that makes rival rules disagree. The Guesser might ask, “Can I see a round shape with one symbol above it?” That card directly tests straight sides against a symbol’s position. Five randomly decorated shapes might look livelier while settling less.
Ask an AI to map possibilities
An AI can join as a third player, but its useful role is generating possibilities and discriminating cards, not announcing a verdict. Give it the entire evidence set and tell it to preserve uncertainty.
A suitable prompt is: “This is a hypothetical paper sorting game. Three items belong: a red triangle with a crown above it, a blue square with a flag above it, and a green pentagon with a moon above it. One item does not belong: a yellow circle with two dots inside it. List at least five different rules consistent with all four observations. Do not choose a final answer. For each rule, propose one new card whose classification would help distinguish it from the others.”
Some suggestions may be awkward, such as a rule built around the exact list of colors. That does not make them inconsistent with the evidence. The players can favor simpler possibilities for an approachable round or retain an elaborate one when they want the puzzle to be more mischievous.
Reveal the intended rule
For this hypothetical round, the Keeper’s supplied rule is: an object belongs in the lantern box when it has exactly one symbol positioned outside and above the main shape. The crown, flag, and moon qualify. The two dots are inside the circle, so that card stays out.
The four original cards do not establish this answer uniquely. “Has exactly one symbol above it” and “has any decoration outside it” classify all four in the same way. A contrasting card can eliminate one of those explanations, but further untested alternatives may remain.
Draw a square with a star below it. Under the supplied rule, it stays out of the lantern box. Under the broader outside-decoration rule, it goes in. Turn the paper toward the Guesser and ask for the classification before the Keeper marks it.