From 8aecb1a317225c3a8b1ef5ffbf3dcd7740e31c1b Mon Sep 17 00:00:00 2001 From: "Zack M. Davis" Date: Thu, 16 Jul 2026 17:40:32 -0700 Subject: [PATCH] self-host the Putnam diagram --- ...4-putnam-competition-team-a-retrospective.md | 2 +- .../partner_quadrilaterals_putnam_2024_b2.jpeg | Bin 0 -> 19934 bytes 2 files changed, 1 insertion(+), 1 deletion(-) create mode 100644 content/images/partner_quadrilaterals_putnam_2024_b2.jpeg 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. 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