TikZ: a five-set Venn in circles, which cannot be drawn, by deepseek-v4.1-flash
deepseek-v4.1-flash · round 7 of 7 · seed 1$0.18SVGPNGPDFvenn.tex
venn.tex · 44 lines
\documentclass[tikz,border=10pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}[scale=1.0]
  % Five congruent circles centred on a regular pentagon.
  % All pairs overlap.  Five circles can form at most 22 regions;
  % a true five-set Venn diagram (31 regions) is impossible with circles.
  \def\R{2.0}
  \def\rad{2.5}
  \foreach \i in {0,...,4} {
    \pgfmathsetmacro{\ang}{90 + \i*72}
    \pgfmathsetmacro{\cx}{\R*cos(\ang)}
    \pgfmathsetmacro{\cy}{\R*sin(\ang)}
    % choose a colour and label
    \ifcase\i
      \def\col{blue!70!black}\def\fillcol{blue!25}\def\lab{Has espresso}
    \or
      \def\col{red!70!black}\def\fillcol{red!25}\def\lab{Has milk}
    \or
      \def\col{green!50!black}\def\fillcol{green!25}\def\lab{Served cold}
    \or
      \def\col{orange!80!black}\def\fillcol{orange!25}\def\lab{Has sugar}
    \or
      \def\col{violet!80!black}\def\fillcol{violet!25}\def\lab{Is decaf}
    \fi
    \draw[thick, draw=\col, fill=\fillcol, fill opacity=0.28]
      (\cx,\cy) circle (\rad);
    \pgfmathsetmacro{\lx}{(\R+\rad+0.7)*cos(\ang)}
    \pgfmathsetmacro{\ly}{(\R+\rad+0.7)*sin(\ang)}
    % anchor the label so it sits outside the circle
    \ifnum\i=0 \def\anc{south}\fi
    \ifnum\i=1 \def\anc{east}\fi
    \ifnum\i=2 \def\anc{north}\fi
    \ifnum\i=3 \def\anc{north}\fi
    \ifnum\i=4 \def\anc{west}\fi
    \node[font=\small, anchor=\anc, align=center] at (\lx,\ly) {\lab};
  }
  \node[font=\small, align=center] at (0,-5.6)
    {Five circles can show at most 22 regions.\\
     A true five-set Venn diagram (31 regions) requires ellipses or other curves.};
\end{tikzpicture}
\end{document}
round 1 of 7
A five-set Venn in circles, which cannot be drawn, by DeepSeek 4.1 Flash, the render after round 1
1234567What the model saw after each round. The picture above is the round that was scored, round 7.
gallery/A five-set Venn in circles, which cannot be drawn/DeepSeek 4.1 Flash, run 1

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 h1date2026-10-09rounds7 of 8 allowed, 12 minutes on the clockcost$0.1834thinkingmediumtokens2,224,246 in, 47,750 out, of which 40,553 reasoningtime4 min 35 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 2run 2 · 2r · $0.0876A five-set Venn in circles, which cannot be drawn, by DeepSeek 4.1 Flash, run 3run 3 · 3r · $0.0546
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.