# Second day at camp: Lectures, Problems and Juggling

I'm pretty sure most students could not sleep last night excited to get involved in lectures and problem sets! After breakfast at 8am, the students rushed to their lecture rooms to get inspired by the lecturers.

In the morning, May Meng (2014 IMO Manager) taught the Juniors some Algebra (Inequalities), and Chris Tuffley (2014 IMO Leader) extended the Senior's knowledge on how to count in combinatorics(Catalan Numbers).

May Meng inspiring the Juniors with an inspiring problem. Does anyone want to try? The problem is trying to prove the inequality on the second line.

Students inspired by the solution to the problem

Chris Tuffley (standing) challenged the Seniors with a "seemingly" simple combinatorics question. Do you think you can manage to solve this?

Apparently that's the solution to the previous problem... Do you see how we get there?

After morning tea, the second set of lectures consisted of Junior Number Theory, taught by Peter Huxford (2014 IMO Contestant) and Senior Number Theory, taught by Dr Arkadii Slinko.

Peter Huxford (standing) explaining a solution to an exercise problem.

Hao Jia being brave enough to stand in front of people to show his solution

Amay Aggarwall explaning why x^2-1 must be a multiple of 8 if x is odd

Tony Wang explaining an alternate solution

Woah what...???!!! Apparently the top list consists of primes less than 1000, and the next command outputs the smallest prime number greater than 765467898761...

Once the lectures have finished and everyone enjoyed their lunch, all the students (including Peter and I) headed to the dining hall to solve some challenging problems. Amazingly, one of the students, George Han, managed to claim to have solved all 8 problems!

Students tackling the problems in the problem set

Ari Markowitz explaining how to solve Question 1

Miles Lee explaining an alternative solution to Question 1

Gary Qian showing a clever way of solving Question 2

Keiran Lewellen preparing for the explanation of Question 4

Xuzhi Zhang explaining an alternative solution to Question 4

George Han explaining the solution to the last question

Once the problem session finished and re-energized ourselves with beef and pork, Peter Bier (an Engineering lecturer in University of Auckland) visited to attempt to master(?) everyone in juggling. Personally, I have attended the camp for 4 years, and I still can't juggle...

Students making juggling balls from balloons, rice and zipper bags

The final product

Kevin Shen

Yongwhan Shin (left) and Tony Wang (right)

Hao Jia (left) and Johnny Mottershead (right)

Wenrui Ma

Weber Wang

Kevin Lin

Chris Wan doing the awesome behind-the-back

Martin Luk (front) and George Li (back) performing a duo juggling

Gary Qian

Miles Lee

Winston Yao

Peter Bier showing how it's supposed to be done

Bon-Nyeong Goo

William Wang

Brian Qi

Claire Shi

Tony Wang

Liujia Chen

Weber Wang (left) and George Han (right) attempting to juggle with half the amount of effort needed for one man to juggle

Thanks to Peter Bier, most of us managed to master(?) the techniques of juggling.

After the evening activity, some boys gathered up in the lounge to play an intense game of Mafia, trying to accuse each other in order to save themselves.

Miles Lee (second on the left) and Ari Markowitz (third on the left) accusing each other. Meanwhile, Weber Wang (third on the right) is accusing the cameraman... hmm...

Tony Wang (second on the right) and Hao Jia (third on the right) accusing the same person.

A lot of things happened today, and I'm sure that students are looking forward to the schedule tomorrow, which includes my lectures (yes, the highlight of tomorrow) and paper-planes!

Keep in touch to hear more maths camp stories.

P.S. I apologise for the poor resolution of the photos.

-Photos and post by Ian Seong