From: Zack M. Davis Date: Fri, 17 Jul 2026 00:40:32 +0000 (-0700) Subject: self-host the Putnam diagram X-Git-Url: https://zackmdavis.net/blog/source?a=commitdiff_plain;h=8aecb1a317225c3a8b1ef5ffbf3dcd7740e31c1b;p=An_Algorithmic_Lucidity.git self-host the Putnam diagram --- diff --git a/content/2025/the-end-of-the-movie-sf-state-2024-putnam-competition-team-a-retrospective.md b/content/2025/the-end-of-the-movie-sf-state-2024-putnam-competition-team-a-retrospective.md index 951f851..ddff5b5 100644 --- a/content/2025/the-end-of-the-movie-sf-state-2024-putnam-competition-team-a-retrospective.md +++ b/content/2025/the-end-of-the-movie-sf-state-2024-putnam-competition-team-a-retrospective.md @@ -61,7 +61,7 @@ Luck seemed to deliver. On a skim, B1, B2, and B4 looked potentially tractable. > **B2.** Two convex quadrilaterals are called _partners_ if they have three vertices in common and they can be labeled ABCD and ABCE so that E is the reflection of D across the perpendicular bisector of the diagonal AC. Is there an infinite sequence of convex quadrilaterals such that each quadrilateral is a partner of its successor and no two elements of the sequence are congruent? -![](https://cdn.artofproblemsolving.com/attachments/6/e/cc9da12a49043410c50733cb6843e5ec1005d3.jpeg) +![]({static}/images/partner_quadrilaterals_putnam_2024_b2.jpeg) I imagined rotating the figure such that AC was the vertical axis and its bisector was the horizontal axis, and tried to imagine some way to perturb D and E to get a sequence of quadrilaterals that wouldn't be congruent (because the angles ∠CDA and ∠CEA were changing), but for which we could alternately take ABCD and ABCE so that successive shapes in the sequence would be partners. I couldn't see a way to make it work. Then I thought, what if perturb B instead? diff --git a/content/images/partner_quadrilaterals_putnam_2024_b2.jpeg b/content/images/partner_quadrilaterals_putnam_2024_b2.jpeg new file mode 100644 index 0000000..d69d836 Binary files /dev/null and b/content/images/partner_quadrilaterals_putnam_2024_b2.jpeg differ