Скачать или смотреть Schools Don't Teach the Pigeonhole Principle (But Math Olympiad Winners Use It)

Struggling with Math Olympiad proof questions? The Pigeonhole Principle is the secret pattern that guarantees marks on "prove that..." questions—and most Sec 1–3 students have never heard of it. In this video, you'll learn the 3-step method to solve ANY pigeonhole proof question in under 2 minutes (no guessing needed).

✅ What You'll Learn:
• What the Pigeonhole Principle actually is (explained with the 4 houses, 5 pigeons example)
• How to solve the marble problem: Guarantee 20 marbles of the same color
• The most difficult part: How to EXPLAIN and JUSTIFY your proof answer
• Real SEAMO-style challenge: Prove that among 51 numbers from 1–100, at least 2 are multiples of each other
• The Q × 2^N rewriting technique that unlocks the solution
• The "50 rooms" visualisation that makes the proof obvious
• Why this guarantees your answer (and how to write it for full marks)

⏱️ Timestamps:
0:00 – Why this proof looks harder than it really is
0:20 – Big idea: What the Pigeonhole Principle really says
1:10 – Step 1: Spotting your “pigeons” and “holes” in the exam question
2:10 – Step 2: Forcing a clash – setting up the key inequality using PHP
3:10 – Step 3: Wrapping up the proof and explaining what the result means
4:30 – Quick recap: 3-step template you can reuse in any PHP proof
​5:20 – What to practice next so you don’t forget this method
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🎯 Why Learn from Terry Chew Academy
Terry Chew has helped 10,000+ students master Math Olympiad techniques over 20+ years. Our students consistently score A*/A1 grades and win medals at SEAMO, SASMO, RIPMWC, and NMOS competitions.

We specialise in heuristic problem-solving shortcuts that save exam time and guarantee marks—strategies your school curriculum doesn't cover. The Pigeonhole Principle is one of the most powerful proof techniques for Sec 1–4 students, yet most schools only teach it superficially (or skip it entirely).

The hardest part isn't solving—it's EXPLAINING your answer. This video shows you exactly how to justify your proof so examiners give you full marks.

💬 Practice Question (Comment Your Answer!):
Challenge from the video: In the marble problem, we needed 78 marbles to guarantee 20 of the same color.

Now try this: You have 7 pairs of gloves (14 gloves total) in a dark drawer. How many gloves must you pull out to GUARANTEE you have at least one matching pair (left and right)?

Hint: Think about the worst-case scenario using Pigeonhole Principle!

Drop your answer below 👇

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