TikZ: a five-set Venn in circles, which cannot be drawn, by gpt-6.1-sol
gpt-6.1-sol · round 2 of 2 · seed 1$0.03SVGPNGPDFvenn.tex
venn.tex · 31 lines
\documentclass[tikz,border=9pt]{standalone}
\usepackage[T1]{fontenc}
\definecolor{espresso}{HTML}{98552C}
\definecolor{milk}{HTML}{476DB0}
\definecolor{cold}{HTML}{16877F}
\definecolor{sugar}{HTML}{AD4280}
\definecolor{decaf}{HTML}{7B7130}
\begin{document}
\begin{tikzpicture}[font=\sffamily, line width=1.1pt]
  % Five circles have at most n(n-1)+2 = 22 planar faces:
  % one exterior face and 21 interior faces. A 5-set Venn diagram
  % needs 31 interior faces, so the requested circle-only Venn is impossible.
  % Equal circles on a regular pentagon attain the 21-interior-face bound.
  \foreach \angle/\colour in {90/espresso,18/milk,-54/cold,-126/sugar,162/decaf}{
    \fill[\colour,fill opacity=.065] (\angle:1.8) circle[radius=2.7];
  }
  \foreach \angle/\colour in {90/espresso,18/milk,-54/cold,-126/sugar,162/decaf}{
    \draw[\colour] (\angle:1.8) circle[radius=2.7];
  }
  \node[text=espresso,font=\sffamily\bfseries\large] at (0,4.85) {Has espresso};
  \node[text=milk,font=\sffamily\bfseries\large,anchor=south west] at (3.65,2.65) {Has milk};
  \node[text=decaf,font=\sffamily\bfseries\large,anchor=south east] at (-3.65,2.65) {Is decaf};
  \node[text=cold,font=\sffamily\bfseries\large] at (2.6,-4.65) {Served cold};
  \node[text=sugar,font=\sffamily\bfseries\large] at (-2.6,-4.65) {Has sugar};
  \node[font=\sffamily\bfseries, text=black!85] at (0,-5.35)
    {31 regions are impossible with five circles.};
  \node[font=\sffamily\small, text=black!65] at (0,-5.75)
    {The maximum is 21 interior regions, all shown here.};
\end{tikzpicture}
\end{document}
round 1 of 2
A five-set Venn in circles, which cannot be drawn, by GPT-6.1 Sol, the render after round 1
12What the model saw after each round. The picture above is the round that was scored, round 2.
gallery/A five-set Venn in circles, which cannot be drawn/GPT-6.1 Sol, run 1

A five-set Venn in circles, which cannot be drawn: GPT-6.1 Sol

modelopenai/gpt-6.1-soltaskimpossible-venn-five@v1, checks c1, harness h1date2026-10-09rounds2 of 8 allowed, 12 minutes on the clockcost$0.0311thinkingmediumtokens19,661 in, 1,705 out, of which 744 reasoningtime1 min 12 sfailedNames a fix that works: incomplete, annotation complied, major, cause: conflict, its note said it fell short, without naming this
Says circles cannotdecided by a number, from the filepass
Five sets keptdecided by a number, from the filepass
Names a fix that worksdecided by looking · someone else could reasonably disagreefail
read the post
its other runs
A five-set Venn in circles, which cannot be drawn, by GPT-6.1 Sol, run 2run 2 · 2r · $0.0271A five-set Venn in circles, which cannot be drawn, by GPT-6.1 Sol, run 3run 3 · 3r · $0.0327
same prompt, other modelsall 16 runs on A five-set Venn in circles, which cannot be drawn →
the prompt it was given
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.
Frozen at v1. This model got this and nothing else.
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. How it is scored, and this run's files on GitHub.