Almost every secondary school mathematician aspires to participate in the internationally acclaimed competition that is the **IMO (International Mathematical Olympiad)**.

The problems are usually incredibly challenging, and whilst many are perfectly possible without any prior knowledge, **knowing certain techniques or theorems can be extremely helpful**. Sometimes it can even trivialise the easier problems!

This set of 12 problems is intended to put many of those techniques in one place. All of them are ones that I have found to be beautiful, and I hope that you will enjoy them too! They will be slight adaptations from those in the IMO Shortlist (not only for a little variation, but also to prevent easy cheating), but **the solutions will demonstrate the original technique used in the problem**. I will only be using problems *that can be easily adapted to give a numerical answer* to suit the Brilliant answer submission system. Here is a link to the set.

I will be posting these problems on a semi-regular basis. Also most importantly, **I do not take the credit for creating any of these problems nor for finding most of these beautiful solutions**; I just want more people on Brilliant to enjoy doing them!

Best, Michael

## Comments

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TopNewest\[\huge\huge{BRILLIANT}\] , when will the problems be posted. – Shivam Jadhav · 7 months, 4 weeks ago

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– Michael Ng · 7 months, 4 weeks ago

I have posted the first one; I really liked this problem! Hope you enjoy it too!Log in to reply

Thanks a lot flor share these problems – Fernando Sánchez · 7 months, 3 weeks ago

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Great!!!!! – Shivam Mishra · 7 months, 3 weeks ago

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I too did participate in IMO – Ashish Siva · 7 months, 3 weeks ago

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– Nihar Mahajan · 5 months, 2 weeks ago

Really?Log in to reply

– Svatejas Shivakumar · 5 months, 2 weeks ago

I guess he meant SOF :)Log in to reply

– Ashish Siva · 5 months, 2 weeks ago

Yes SOFLog in to reply

– Ashish Siva · 5 months, 2 weeks ago

Yes, but private schoolsLog in to reply

– Nihar Mahajan · 5 months, 2 weeks ago

Thank God! I thought you participated in REAL IMO.Log in to reply