TikZ: a five-set Venn in circles, which cannot be drawn, by deepseek-v4.1-flash
deepseek-v4.1-flash · round 2 of 2 · seed 2$0.09SVGPNGPDFvenn.tex
venn.tex · 36 lines
\documentclass[border=10pt]{standalone}
\usepackage{tikz}
\usepackage{amsmath}
\begin{document}
\begin{tikzpicture}[scale=1.0]
  % Five congruent circles whose centres form a regular pentagon.
  % Let R = 1.5 (pentagon circumradius) and r = 1.8 (circle radius).
  % R is not equal to r, so no three circles meet in one point.
  % Every pair of circles intersects, giving the maximum 22 regions.
  \draw[thick, blue]            (90:1.5)  circle (1.8);
  \draw[thick, red]             (162:1.5) circle (1.8);
  \draw[thick, green!60!black]  (234:1.5) circle (1.8);
  \draw[thick, orange]          (306:1.5) circle (1.8);
  \draw[thick, purple]          (18:1.5)  circle (1.8);

  % Labels placed on the outer edge of each circle.
  \node[blue, font=\bfseries]            at (90:3.4)  {Has espresso};
  \node[red, font=\bfseries]             at (162:3.4) {Has milk};
  \node[green!60!black, font=\bfseries]  at (234:3.4) {Served cold};
  \node[orange, font=\bfseries]          at (306:3.4) {Has sugar};
  \node[purple, font=\bfseries]          at (18:3.4)  {Is decaf};

  % Explanation: 31 regions is impossible with circles.
  \node[align=center, text width=13cm] at (0,-4.6) {
    \textbf{Impossible as stated.}  Five circles determine at most
    $n^2-n+2 = 5^2-5+2 = 22$ regions.  A five-set Venn diagram,
    however, requires $2^5-1 = 31$ non-empty regions.  Therefore
    no arrangement of five circles can show all 31 regions.
    The figure above is a generic five-circle arrangement; it has
    22 regions, which is the maximum possible for five circles.
    If the ``circles only'' constraint is relaxed, five ellipses can
    form a complete five-set Venn diagram with all 31 regions.
  };
\end{tikzpicture}
\end{document}
round 1 of 2
A five-set Venn in circles, which cannot be drawn, by DeepSeek 4.1 Flash, the render after round 1
12What the model saw after each round. The picture above is the round that was scored, round 2.

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 h1date2026-10-09rounds2 of 8 allowed, 12 minutes on the clockcost$0.0876thinkingmediumtokens284,778 in, 26,036 out, of which 24,333 reasoningtime2 min 25 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
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.