venn.tex · 41 lines
\documentclass[tikz,border=14pt]{standalone}
\usepackage[T1]{fontenc}
\definecolor{espresso}{HTML}{A65032}
\definecolor{milk}{HTML}{267C70}
\definecolor{cold}{HTML}{346CB0}
\definecolor{sugar}{HTML}{AC7620}
\definecolor{decaf}{HTML}{8254A0}
\begin{document}
% Five circles have at most n(n-1)+2 = 22 plane regions,
% including the exterior. Thus a 31-region Venn diagram is impossible.
% These circles are in general position and attain 21 interior regions.
\begin{tikzpicture}[font=\sffamily, line width=1pt]
\node[font=\sffamily\bfseries\Large, text=black!85] at (0,6.05)
{Five coffee attributes};
\node[font=\sffamily\small, text=black!65] at (0,5.50)
{Circle-only overlap diagram};
\coordinate (A) at (90:2);
\coordinate (B) at (162:2);
\coordinate (C) at (234:2);
\coordinate (D) at (306:2);
\coordinate (E) at (18:2);
% Fill first, then redraw every boundary so none is obscured.
\foreach \p/\c in {A/espresso,B/milk,C/cold,D/sugar,E/decaf}
\fill[\c,fill opacity=.10] (\p) circle[radius=2.6];
\foreach \p/\c in {A/espresso,B/milk,C/cold,D/sugar,E/decaf}
\draw[\c] (\p) circle[radius=2.6];
\node[text=espresso,font=\sffamily\bfseries] at (0,4.90) {Has espresso};
\node[text=milk,font=\sffamily\bfseries,anchor=east] at (-4.75,.62) {Has milk};
\node[text=cold,font=\sffamily\bfseries] at (-2.40,-4.48) {Served cold};
\node[text=sugar,font=\sffamily\bfseries] at (2.40,-4.48) {Has sugar};
\node[text=decaf,font=\sffamily\bfseries,anchor=west] at (4.75,.62) {Is decaf};
\node[align=center,text=black!75,font=\sffamily\small,text width=13cm] at (0,-5.55)
{\textbf{All 31 regions cannot be obtained with circles.}\\[4pt]
Five circles create at most 22 regions including the exterior,\\
or 21 inside their union. This drawing attains that maximum.};
\end{tikzpicture}
\end{document}round 1 of 3
A five-set Venn in circles, which cannot be drawn: Pareto 26.10 Preview
modelunbiased/pareto-26.10-previewtaskimpossible-venn-five@v1, checks c1, harness h1date2026-10-09rounds3 of 8 allowed, 12 minutes on the clockcost$0.0470thinkingmediumtokens50,990 in, 8,713 out, of which 0 reasoningtime1 min 14 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
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.
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.