Past Papers/Junior Mathematical Olympiad/JMO Combinatorics & Logic

Practice Collection

JMO Combinatorics & Logic

Counting, grids, paths, puzzles, and invariants that need careful case analysis and clear proof writing.

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14 problemsCounting and logical structure
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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: combinatorics · counting · logic · grids

Problems in this collection

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

Problem 16 · Junior Mathematical Olympiad 2004

First problem in this session

Start session

Problem 15 · Junior Mathematical Olympiad 2006

Position 2 in this session

Open problem

Problem 16 · Junior Mathematical Olympiad 2009

Position 3 in this session

Open problem

Problem 14 · Junior Mathematical Olympiad 2010

Position 4 in this session

Open problem

Problem 13 · Junior Mathematical Olympiad 2015

Position 5 in this session

Open problem

Problem 15 · Junior Mathematical Olympiad 2016

Position 6 in this session

Open problem

Problem 14 · Junior Mathematical Olympiad 2017

Position 7 in this session

Open problem

Problem 15 · Junior Mathematical Olympiad 2018

Position 8 in this session

Open problem

Problem 16 · Junior Mathematical Olympiad 2018

Position 9 in this session

Open problem

Problem 15 · Junior Mathematical Olympiad 2019

Position 10 in this session

Open problem

Problem 14 · Junior Mathematical Olympiad 2022

Position 11 in this session

Open problem

Problem 16 · Junior Mathematical Olympiad 2023

Position 12 in this session

Open problem

Problem 13 · Junior Mathematical Olympiad 2024

Position 13 in this session

Open problem

Problem 5 · Junior Mathematical Olympiad 2025

Position 14 in this session

Open problem