The Labelling Trick That Cracks IMO 2023 Problem 5

One red circle in every row of a triangle, and a ninja that can only step down-left or down-right. How many red circles can it always collect, however cleverly the reds are placed? We find the exact answer, build the colouring that shows it cannot be beaten, and prove the matching bound with one labelling idea that pushes the count up by one every time the row number doubles. Problem: IMO 2023 Problem 5 (Shortlist C3) Official solution: https://www.imo-official.org/assets/d... Answer cross-checked against: evanchen.cc, imo-official.org Chapters: 0:00 The Problem 0:51 A Greedy Attempt 1:47 Finding the Answer 2:56 The Construction 4:59 The Lower Bound 7:32 The Doubling Step 9:11 Why It Works 9:58 Takeaway The solution in this video is our own write-up and explanation; see the link above for the source. Animations made with Manim Community Edition. #IMO2023 #IMO2023Problem5 #ISL2023C3 ━━━━━━━━━━━━━━━ 🧮 Everyday Olympiad: one olympiad problem, solved step by step. 👉 Subscribe for more problems:    / @matholover   ✏️ Try it yourself first: pause after the problem statement and give it 10 minutes. 💬 Which problem should we solve next? Comment the competition and year!