TikZ: a five-set Venn in circles, which cannot be drawn, by deepseek-v4.1-flash
deepseek-v4.1-flash · round 3 of 3 · seed 3$0.05SVGPNGPDFvenn.tex
venn.tex · 41 lines
\documentclass[tikz,border=12pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows.meta}
\begin{document}
\begin{tikzpicture}[font=\sffamily]
  \def\Rc{2.5}
  \def\rad{3.25}

  % centres of the five circles, on a regular pentagon
  \coordinate (C1) at (90:\Rc);   % Has espresso
  \coordinate (C2) at (162:\Rc);  % Has milk
  \coordinate (C3) at (234:\Rc);  % Served cold
  \coordinate (C4) at (306:\Rc);  % Has sugar
  \coordinate (C5) at (18:\Rc);   % Is decaf

  \begin{scope}
    \fill[red,opacity=0.12]     (C1) circle (\rad);
    \fill[blue,opacity=0.12]    (C2) circle (\rad);
    \fill[teal,opacity=0.12]    (C3) circle (\rad);
    \fill[orange,opacity=0.12]  (C4) circle (\rad);
    \fill[green,opacity=0.12]   (C5) circle (\rad);
  \end{scope}

  \draw[red,thick]    (C1) circle (\rad);
  \draw[blue,thick]   (C2) circle (\rad);
  \draw[teal,thick]   (C3) circle (\rad);
  \draw[orange,thick] (C4) circle (\rad);
  \draw[green,thick]  (C5) circle (\rad);

  \node[red]    at (90:6.45)  {Has espresso};
  \node[blue]   at (162:6.45) {Has milk};
  \node[teal]   at (234:6.45) {Served cold};
  \node[orange] at (306:6.45) {Has sugar};
  \node[green]  at (18:6.45)  {Is decaf};

  \node[align=center,font=\small\itshape] at (0,-7.3)
    {The figure shows every region five circles can produce: 21 inside (22 counting the outside).\\[1pt]
     A five-set Venn diagram has 31 non-empty regions, so it cannot be drawn with circles alone.};
\end{tikzpicture}
\end{document}
round 1 of 3
A five-set Venn in circles, which cannot be drawn, by DeepSeek 4.1 Flash, the render after round 1
123What the model saw after each round. The picture above is the round that was scored, round 3.
gallery/A five-set Venn in circles, which cannot be drawn/DeepSeek 4.1 Flash, run 3

A five-set Venn in circles, which cannot be drawn: DeepSeek 4.1 Flash

modeldeepseek/deepseek-v4.1-flashtaskimpossible-venn-five@v1, checks c1, harness h1date2026-10-09rounds3 of 8 allowed, 12 minutes on the clockcost$0.0546thinkingmediumtokens306,368 in, 19,638 out, of which 15,510 reasoningtime2 min 0 s
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 disagreepass
read the post
its other runs
A five-set Venn in circles, which cannot be drawn, by DeepSeek 4.1 Flash, run 1run 1 · 7r · $0.1834A five-set Venn in circles, which cannot be drawn, by DeepSeek 4.1 Flash, run 2run 2 · 2r · $0.0876
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.