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18/09/2026

Cut this into 2 identical pieces. You can rotate or flip.
Pause for the 5 seconds if you want to try it.
Then try it here: https://www.problems.cc/p/Vh5gpa

Problem of the Day #193JMO 2017 · Section B Q6The Junior Maths Olympiad is today - good luck to everyone taking part! ✨...
08/06/2026

Problem of the Day #193
JMO 2017 · Section B Q6

The Junior Maths Olympiad is today - good luck to everyone taking part! ✨

For the final JMO post, here is a challenging Section B number theory problem. It is a good reminder that in Section B, a clear written explanation matters just as much as finding the answer.

We have also uploaded blog posts on how to write clear written proofs for Olympiad-style problems - useful for anyone preparing for JMO Section B and future competitions.

Problem of the Day #192JMO 2005 · Section B Q3The Junior Maths Olympiad is tomorrow - good luck to everyone taking part...
08/06/2026

Problem of the Day #192
JMO 2005 · Section B Q3

The Junior Maths Olympiad is tomorrow - good luck to everyone taking part!

Today’s problem is a final angle-chasing practice question. It is a good reminder that in geometry, marking equal sides and equal angles carefully can often unlock the whole solution.

You can find more JMO-style Geometry problems on Problems.cc, including a dedicated Geometry practice collection.

Source: Junior Mathematical Olympiad 2005, Section B Q13 · UK Maths Trust

Problem of the Day #191JMO 2011 · Section B Q11JMO is in two days, so today’s problem is a short but very useful divisi...
07/06/2026

Problem of the Day #191
JMO 2011 · Section B Q11

JMO is in two days, so today’s problem is a short but very useful divisibility question.

Every digit of a positive integer is either a 3 or a 4, with each digit occurring at least once.

The integer is divisible by both 3 and 4.

What is the smallest such integer?

This is a good Section B problem because the answer is not about guessing - it is about using divisibility rules carefully.

Source: Junior Mathematical Olympiad 2011, Section B Q11 · UK Maths Trust

Problem of the Day #190JMO 2013 · Section B Q1JMO is next week, so today’s problem is a good Section B-style number the...
06/06/2026

Problem of the Day #190
JMO 2013 · Section B Q1

JMO is next week, so today’s problem is a good Section B-style number theory question.

How many numbers less than 2013 are both:

1. the sum of two consecutive positive integers, and
2. the sum of five consecutive positive integers?

This is a great problem for practising how to turn a worded condition into a clean mathematical statement.

Problem of the Day #189JMO 2022 · Section B Problem 3JMO is next week, so today’s problem is from Section B, where a fu...
05/06/2026

Problem of the Day #189
JMO 2022 · Section B Problem 3

JMO is next week, so today’s problem is from Section B, where a full written explanation matters.

Charlie chooses one cell from a blank n×n square grid and shades it.

The resulting grid has no lines of symmetry.

In terms of n, how many different cells could be shaded?

Think carefully about which cells would still leave a line of symmetry.

Source: Junior Mathematical Olympiad 2022, Section B Problem 3

Problem of the Day #188JMO 2010 · Section A Q7JMO is next week, so today’s problem is a short but careful angle problem...
04/06/2026

Problem of the Day #188
JMO 2010 · Section A Q7

JMO is next week, so today’s problem is a short but careful angle problem.

In an isosceles triangle, the difference between the largest and smallest angles is 6
∘
What is the largest possible angle?

The key word is possible — there may be more than one case to check.

Source: Junior Mathematical Olympiad 2010, Section A Q7

Problem of the Day #187JMO 2000 · Section A Q10JMO is next week, so today’s problem is a great test of careful proporti...
03/06/2026

Problem of the Day #187
JMO 2000 · Section A Q10

JMO is next week, so today’s problem is a great test of careful proportional reasoning.

It is not just about more gardeners and more flower beds — the diameter changes too.

Try it before checking the answer.

Source: Junior Mathematical Olympiad 2000, Section A Q10

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