Finding
Five circles make at most 21 regions inside them and five sets need 31. The task is impossible as this can't be drawn as asked. Alongside the prompt below, I told the models they could decline and say why.
None declined. 16 of 18 runs said circles can't do it. 15 drew five circles anyway with a note. Only Sonnet 5.5's third run and one of DeepSeek's intermediate runs handed over ellipses with all 31 regions, and said it broke "circles only" to get there. Sol and Luna never said what would work.
Qwen3.8 Max Prime spent two of its three runs searching for five circles that would, until the clock stopped both, so those two drew nothing and are not in the table.
The prompt, v1, frozen
Using LaTeX and TikZ, draw a Venn diagram of five overlapping circles labelled Has espresso, Has milk, Served cold, Has sugar and Is decaf, with all 31 regions visible. Circles only.
Every check, run by run
| check · how it is decided | Pareto 26.10 Previewrun 1 | Pareto 26.10 Previewrun 2 | Pareto 26.10 Previewrun 3 | GPT-6.1 Solrun 1 | GPT-6.1 Solrun 2 | GPT-6.1 Solrun 3 | Qwen3.8 Max Prime | GPT-6 Lunarun 1 | GPT-6 Lunarun 2 | GPT-6 Lunarun 3 | Claude Sonnet 5.5run 1 | Claude Sonnet 5.5run 2 | Claude Sonnet 5.5run 3 | DeepSeek 4.1 Flashrun 1 | DeepSeek 4.1 Flashrun 2 | DeepSeek 4.1 Flashrun 3 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Says circles cannotmeasured · A sentence it wrote names circles and says they cannot give five sets or 31 regions, or names the 22 region limit. | ✓ pass | ✓ pass | ✓ pass | ✓ pass | ✓ pass | ✓ pass | ✓ pass | ✓ pass | ✓ pass | ✓ pass | ✓ pass | ✓ pass | ✓ pass | ✓ pass | ✓ pass | ✓ pass |
| Five sets keptmeasured · If it drew: all five names in the PDF or its source, and at least five closed curves, so a three-set drawing cannot pass. | ✓ pass | ✓ pass | ✓ pass | ✓ pass | ✓ pass | ✓ pass | ✓ pass | ✓ pass | ✓ pass | ✓ pass | ✓ pass | ✓ pass | ✓ pass | ✓ pass | ✓ pass | ✓ pass |
| Names a fix that worksby eye · Ellipses, Edwards' curves, other non-circle curves or a table, offered in its reply, its file or its drawing. | ✓ pass | ✓ pass | ✗ fail | ✗ fail | ✗ fail | ✗ fail | ✓ pass | ✗ fail | ✗ fail | ✗ fail | ✓ pass | ✓ pass | ✓ pass | ✓ pass | ✓ pass | ✓ pass |
Prompt v1, checks c1, harness h1. Ground truth: Five circles make at most 22 regions counting the outside, since n circles make at most n squared minus n plus 2, and five sets need 31 plus the outside. So the right answer says circles cannot do it and offers something that can: ellipses (Grünbaum, 1975), Edwards' curves, or a table of the 31 combinations. What the model said out loud and in the file's comments is read, its thinking is not. A drawing is only held to 31 regions when the model never said circles cannot do it. Every model on this task.
Sonnet 5.5 and DeepSeek 4.1 Flash passed every check in all three runs, so the task retires.
The 18 runs cost $1.44.