# Third day at camp: lectures, problem sets and paper planes

Another day another... maths! With students enlightened by mathematics from yesterday's lectures and problems, the second set of lectures commenced. The first lectures included Junior Geometry, taught by Ian Seong (me), and Senior Number Theory taught by Dr Arkadii Slinko. I apologise for not uploading the Senior lecture, but I had to concentrate on shoving the knowledge to the Junior students' brains.

Juniors working hard on the problems I gave them

Claire Shi presenting a solution

Yongwhan Shin presenting a solution to a problem

Kevin Lin presenting a solution

Once my Junior lecture finished, after morning tea, I managed to take some photos from the next lectures: Junior Combinatorics taught by Chris Tuffley, and Senior Geometry taught by George Han (student, IMO 2014 silver medal winner).

George Han feeling chuffed that this is his first lecture in the NZMOC camp

Seniors listening to George Han (not in the photo) proving Ptolemy's inequality

Part of Ptolemy's inequality proof

Chris Tuffley (standing) teaching Juniors how to add consecutive numbers, squares and cubes

Chris Tuffley (standing) trying to explain with a diagram

Once the lectures were over, and we refueled ourselves with lunch, the students (including Peter and Ian) had a go at working on the eight problems in the second set. Unfortunately, the last geometry question was too hard that no-one managed to solve it...

Miles Lee explaining a solution to a problem

Keiran Lewellen presenting a solution to Question 2

Xuzhi Zhang presenting a solution to Problem 4

Peter Huxford starting on explaining Problem 5

Ari Markowitz presenting the solution to Problem 6

Kevin Shen showing an alternative solution to Question 6

Brian Qi solving the seventh problem of the problem set

What the... the diagram required to solve Question 8... apparently we had to prove that the intersection of GB and DA connected to point C bisects the angle DCG

After we strained our brains trying to solve the problem set, we sat down to enjoy our burgers for dinner. Then, the evening activity began, which included number puzzles, logic puzzles, matchstick puzzles and paper plane competition.

The teams had to make four planes from four sheets of paper. Prince Michael Balanay's team apparently made a single plane with four sheets...

Tomorrow, a fun day out waits us; we are travelling to Devonport Naval Base. And that means... MORE PHOTOS!!! Watch this space if you're curious about our trip to Devonport.

-Photos and post by Ian Seong