Exact Science

Problem of the Day #185
From Intermediate Maths Olympiad Cayley 2020 Q1. In ΔABC, exterior angles a°, b°, c° satisfy a+b=3c — prove the triangle must be right‑angled.

Problem of the Day #184
Make 100 by inserting “+” between digits 1–7!
📚 Group lessons enrolling — see link in bio.

Problem of the Day #183
Fill each square with the same digit to make the equation correct. 🔢
A classic cryptarithm-style puzzle — simple rules, tricky reasoning!

📚 Explore more number puzzles in our Olympiad Maths groups — details via our website.

Problem of the Day #182
MOG 2013 – Q5b
Prove that ∛(√108 + 10) − ∛(√108 − 10) = 2.
(Hint: let a=∛(√108+10), b=∛(√108−10); use (a−b)^3 and ab.)

Registration for 2025/2026 lessons open — link in bio.

Problem of the Day #181
UK - Mathematical Olympiad for Girls - 2013 – Q3b
A spiral walk around O uses perpendicular steps of length 3, starting with OP₀ = 29. What’s the next n for which OPₙ is an integer?
Group lessons are enrolling -- see link in bio.

Problem of the Day #180
A rectangle tiled by 9 squares. Find the rectangle’s side lengths. Looks like geometry - but the trick is setting up hidden equations.
Courses enrolling - see link in bio.

Problem of the Day #179
Find all triples of prime numbers!
A number theory puzzle blending algebra with primes!

📚 Tackle more problems like this in our Olympiad Maths courses — visit our site to join.

Problem of the Day #178

A classic inequality problem — expand, rearrange, and reason algebraically.

📚 Build your skills in inequalities and proof with our Olympiad Maths groups — enrol via the site!

Problem of the Day #177

From Komal (Hungary), April 2025 🇭🇺

Uncle János reveals clues about his and his mother’s ages. Can you deduce how old she was when he was born?

Problem of the Day #176
Burgers on the Pan 🍔
Given the pan size and fry time per side, what’s the minimum time to cook all burgers perfectly?

📚 Learn how to solve logic-heavy coding problems like this in our Olympiad Programming courses — sign up now via our website!

🚀 Group Maths & Programming Classes – Now Enrolling!
Whether you're in London or anywhere in the world — join our engaging small group lessons, available on-site in Westminster or online worldwide.

🔍 Each group is kept small to ensure focused attention — it often feels like a 1:1 lesson!

✅ Trial lessons available
📅 Check time slots & details at exactscience.co

🚀 Group Maths & Programming Classes – Now Enrolling!

Whether you're in London or anywhere in the world — join our engaging small group lessons, available on-site in Westminster or online worldwide.

🔍 Each group is kept small to ensure focused attention — it often feels like a 1:1 lesson!

✅ Trial lessons available
📅 Check time slots & details at exactscience.co