Singapore Invitational Mathematical Challenge

SIMC Diary #1

Introduction

This series of diaries, namely 7/5, 22-28/5 will be published.I am one of the representatives of HKUST(Hong Kong University of Science and Technology, ust for short) to participate in the Singapore invitational mathematical challenge (SIMC for short), SIMC is a modeling challenge held two years once, and this year is the 5th SIMC, and because I can take part in SIMC again, this diary can be a note for me.

Oh yes! This is actually the same intro in SIMC Diary #0! Wait! If you haven’t seen SIMC Diary #0, there are no worries.You won’t have any problems seeing this diary, except…

I am really bad at English(I may mention it in another page of introduction), I have also proven that my writing is actually “non-readable” to some English country. If you can read this post, you are an imaginative person(or an Asian). OK, let’s start an introduction on SIMC.

Singapore International Mathematical Challenge

SIMC is a modeling challenge held two years once. Actually What is “Modeling”? SIMC 2014 Part A question will give you that feeling:

“Part A: Tourist in a hurry

You are a tourist. You have a list of attractions that you are going to visit. You

have set aside a certain amount of money for local transportation. There are three modes of transport– on foot (free but slow), public transport (cheap), and taxi (fast but expensive).

Your goal is to figure out the optimal route: you always begin at your hotel and come back to it, but you can choose the order in which you visit the attractions and how you travel to the next attraction. You want to minimise the total time you spend travelling between attractions and stay within your transport budget. Suppose that you are given all the data: the budget, the list of attractions, and the tables of costs and times needed to travel   between locations.”
(Just leave as a note, Singapore’s questions have a bad english, “traveling”, “minimize”. Although my english is worse than them.)
Actually, in here you don’t have a best answer, instead of a better answer. We(we have four people as a team) receive a set of problems on a real life problem, and we will hand in a report after 30 hours. And prepare a 15 minutes presentation with a 2 minutes Q&A Session.
This year, 5th SIMC is hold by NUS High School & Education and the Minstry of Education, Singapore.30 countries, 62 school participated in this challenge. But that’s way far enough, let’s get into the next session.

HKUST SIMC Team

Let’s me explain myself. I am a secondary 3(In US, it is grade 9) student, in a secondary school (called Pui Ching Middle School), but instead of representing my own school, I am representing HKUST, so you may ask, how and why?

The way is simple: First UST is a university, and School of Science build a center to provide the talented students some activites(it’s actually common), it is called The Center for the Development of the Gifted and Talented (CDGT for short), CDGT hold a program, call Dual Program(DP for short), it divides into four aspects (Maths, Physics, Chemistry and Life Science), I am the student in DP Maths aspect. I will study four years(one year for a level), call Prestage(talk about Pre-calculus), Level 1 (Calculus), Level 2(Calculus) and Level 3(Multivariable Calculus) I am a level 2 student (unforunately, I can’t go to Level 3, in some sense, I failed). CDGT invite all DP Maths lv2,3 and Physics lv2,3 to partcipate in the SIMC training, and here is the photo of us.

Dr. Leung and Mr. Ching are two old leaders of SIMC 2014 and 2012. They also select our four team members. Four from seven, we have a hard competition. Finally, we have four team members: Me(Mark), Jeff, Jeffery and WT Tai. In this year, our leader is Dr. Avery Ching with our deputy leader Mr. Thomas Chan. And now this is why I am here.

Day 1

After I had eaten my breakfast with my dad, I sat on A21 airport bus, going to Airport.I met Thomas Chan(CDGT staff) and Dr.Ching there. We are really bored waiting except

1. We learned bridge(only bidding)
2. We solve some problems, listed below:

Problem 1. Given a  $n \times n$ chessboard, There are $k$ blocks in black, and $N^2-k$ in white, if a white block  has upper, downwards, right and left has at least two blocks are in black: Kram will paint it in black, Given Kram will paint it in all black. Prove that $k >N$.

Problem 2. Given there are 100 balls, namely 1…100 and Kram put some balls in bag 1 , bag 2 and bag 3. The weird stuff is, if you pick two balls in distinct bags, sum them up, then Kram can find which bags which two is. Find how it works and prove it is the unique arrangement.

3.  We find that Thomas Chan is fact cute!

4. I have been invited to have dinner with PCMS team and the principal.

And then, we get back NUS campus, and WE EAT WITHIN THE CAMPUS!!! Unlike PCMS team, we EAT WITHIN THE CAMPUS! We only have very little chance get out from campus, but WE EAT WITHIN THE CAMPUS! At nine, I backed to my room.

Hint of the problem

1. Consider the perimeter of the chessboard.
2. Define some function to solve problem.