Past Papers/Junior Mathematical Olympiad/JMO Proof Push

Practice Collection

JMO Proof Push

Demanding Section B-style problems for students ready for longer, multi-step written proofs.

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10 problemsExtended written proofs
Start with an ordered session
This collection is designed to feel like a focused training run, not a catalogue. Begin at the first problem and work through in order, or dip into the list below if you want to target a specific past-paper question.
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Best for: harder problems · proof push · late questions

Problems in this collection

Each problem keeps the collection context, so next and previous navigation stays inside this training set.

Problem 14 · Junior Mathematical Olympiad 2005

First problem in this session

Start session

Problem 15 · Junior Mathematical Olympiad 2012

Position 2 in this session

Open problem

Problem 13 · Junior Mathematical Olympiad 2014

Position 3 in this session

Open problem

Problem 16 · Junior Mathematical Olympiad 2016

Position 4 in this session

Open problem

Problem 16 · Junior Mathematical Olympiad 2019

Position 5 in this session

Open problem

Problem 11 · Junior Mathematical Olympiad 2021

Position 6 in this session

Open problem

Problem 16 · Junior Mathematical Olympiad 2021

Position 7 in this session

Open problem

Problem 15 · Junior Mathematical Olympiad 2022

Position 8 in this session

Open problem

Problem 16 · Junior Mathematical Olympiad 2022

Position 9 in this session

Open problem

Problem 16 · Junior Mathematical Olympiad 2024

Position 10 in this session

Open problem