THE OFFICIALSIMC NEWSLETTERISSUE 3 MAY 23, 2012

1

The A-Mazing Challenge

Students take up the ChallengeBy Victoria Tay, Lim Si Jia and other sources

The air was tense as the par-ticipants awaited the release of the Challenge Question. Mixed emotions of distress, anticipa-tion and enthusiasm played out on their faces as they gathered in the auditorium to receive the problem that would test their skill, perseverance and teamwork for the following two and a half days. The nerve-wracking silence was almost absolute, broken only by the sounds of tentative fidgeting and whispered discussion. This all changed, however, once the participants were given the clear to open the envelopes that held the Challenge Ques-tion within.The Challenge consisted of four questions, each of consider-able difficulty. When asked their opinion, the majority of them

remarked on the complexity of the subject at hand. Even so, they showed admirable gump-tion. “We have to think of suit-able distances on our own for one section,” said Mimi Yama-moto, a student of Kumamoto Kita Senior High School. “There are infinite possibilities.”The participants’ methods of tackling the questions contrast-ed greatly. Some were involved in heated discussions while oth-ers quietly pored over the ques-tions. Most of the classroom whiteboards were filled with mathematical workings and dia-grams, as the participants were absorbed in their calculations. The enthusiasm and focus of the participants were appreci-ably intense.

As the day progressed, the arduous task of calculation and optimisation began to take its toll on some groups. By late afternoon, some teams had re-tired early, preferring to rest and recharge before taking another shot at the formidable chal-lenge. Others remained at their seats, attacking the problem from multiple angles with heads bowed. In the end, the SLOs had to pry them away from their work!Many teams brainstormed solutions over meals and spent the night chewing over the questions. Some took stock of lessons they had learnt for the day. That situation is likely to continue today.

2

“I’m enjoying this very much. Singapore is very terrific!”

Ms Jane Garvey from The MacRob-ertson Girls High School

An enriching and educational day for the eductors

(CSIA) asked, “Are there pirates?” This reporter had no choice but to spring the painful truth on Mr Game. Nev-ertheless, the ride was undoubtedly en-joyable, with many educators snapping photos all throughout.

Afterwards, the educators were brought to the Buddha Tooth Relic Temple where they witnessed the monks chanting and visitors presenting votive offerings. Next, some educa-tors were taken to the Sri Mariamman, Singapore’s oldest Hindu temple, where they were given a brief insight into Hinduism. Others got the chance to shop in Chinatown, where they also attended a formal tea ceremony in “Tea Chapter”, one of many traditional tea houses dotting the area. Sitting on low wooden tables and chairs, surrounded by Chinese paintings and calligra-phy, the educators found themselves engrossed with an explanation of the traditional tea ceremony. The students in attendance had a rare chance to see their teachers taking on the role of a student so willingly. Many of them shared afterwards that it was a calming and rejuvenating experience, especially after the blistering heat of the day. To

top off the tour, our visitors stopped by Bugis Street for the challenge of choosing among a variety of shops with a wide array of designer wear, jew-ellery, textiles, and antiques. All in all, it was a fruitful day for the educators, having learnt more about instruments to facilitate the learning of their stu-dents; and learning about the diverse culture of Singapore.

On the second day of SIMC, educators were treated to some of the sights and sounds of our little red dot. Our report-ers were there to take it all in too. The Educators’ Programme began yesterday with an introduction to Texas Instruments and the teaching methods and astounding abilities of TI-Nspire. Ms Tay Su Yin, an Education Technology consultant, introduced the functions of TI-Nspire, which aids in the learning and understanding of the students in real life demonstrations. TI-Nspiresoftware , allows teachers to carry out an interactive lesson with stu-dents and enables them to create polls, generate discussions, set quizzes and worksheets and even do recordings! In a hands-on session, educators were treated to an appealing presenta-tion with Ms Kwee Tiow Choo, Senior Teacher of Hwa Chong Institution, encouraging the educators to pick up the software quickly.After this, NUS High School teachers took their fellow visiting educators on a tour of key popular attractions in this Lion city. First up was boat ride down the Singapore River. While waiting for the boat, Mr Lloyd Game of Camborne Science and International Academy

Educators Sample Tech-nology and a City TourBy Lim Pei Ying, Lim Si Jia & Mavis Teo

3

Behind the ScenesBy Lim Pei Ying and Goh Wee Thean

Lights, Camera, Action! Sometimes, the more spectacular the end product, the more we tend to overlook the person behind it. Despite her busy schedule, Mrs Chong Ai Lin, Head of the SIMC Student Programmes Committee, man-aged to give us a sneak peek behind the scenes of SIMC 2012. What do you hope the participants would take away from this competition?

I hope they would enjoy their time spent here meeting like-minded young people who share a passion for mathemat-ics. I also hope that they would find our staff and students hospitable and gracious hosts. It would also be great if they would realise that Singapore has both the resources to invest in talented people and the ability to provide them with what they need to further hone their talent.How do you feel about playing such a big role in such a major competition?

Naturally, there is a certain amount of stress involved, but it is still very enjoyable. My role is mainly to oversee the stu-dent programme. Working with the other teachers-in-charge and the SLOs has really been a good experience.Would you please share some of the details of the work behind organising the competition?

There were the considerations of planning the programme for our visitors. We needed it to be balanced in order for them to experience Singapore’s culture and meet their expectations of the mathematical challenge at the same time. We wanted to show them the research landscape in Singapore as well, so we will be taking them to A*STAR and the Singapore Science Centre. For their cultural immersion, we have planned other exciting trips. As for the SLOs, we have a good mix of student leaders and non-student leaders so as to extend the opportunity to be facilitators to as many students as possible. We have also tried to pair some of our school’s foreign students with teams from their countries. Would you like to say a word or two to cheer the partici-pants on? Just one thing: JIA YOU! (a common Chinese expression to cheer people on that has the meaning of “Keep going!”)

What motivated you to participate in this year’s SIMC?

We look forward to encountering some fantastic and inter-esting questions and to do our best to solve them. ~Ritsumei-kan High SchoolThere are many mathematics and computer science com-petitions in our country, but we feel that SIMC will be quite different and we are looking forward to the new experience ~Fazekas Mihály Secondary Grammar SchoolHow did you prepare for SIMC?

The members of our team were chosen through an indi-vidual competition organised by two members of our alumni. In addition, we wrote a computer programme and used a web application form to aid the school in its allocation of students to different lectures for a school event in March. ~Fazekas Mihály Secondary Grammar School We ferreted out the fundamentals of the topics for the chal-lenge. In addition, we planned some strategies such as brainstorming sessions. We also carried out some discus-sions before the challenge. ~Chung Ling Penang High SchoolWhat do you think you will learn from joining this event?

We are confident that we will benefit from it as preparation for our future careers. Besides, gaining exposure to such Mathematical skills is something we usually wouldn’t be able to learn in the classroom. It’s amazing! ~Chung Ling Penang High SchoolWhat do you feel about your chances of winning this year’s SIMC?

We are very honoured to be invited this year and would be so happy if we could do well in the challenge. ~Tokyo Tech High School of Science & Technology

Interview with SchoolsBy Ewin Teo

B W AAAA AAAB AABB AABC ABCD0 0 625 256 256 81 16

0 1 0 308 256 276 152

1 0 500 317 256 182 108

0 2 0 61 96 222 312

Perhaps Mastermind was your favourite puzzle game– and still is. A brilliant, mind-bending code-breaking game played amongst two, Mastermind challenges one player to guess the code set by the other player, within a certain number of tries. The codes comprise four different-coloured code pegs – repeated colours are allowed – chosen from a pile of code pegs of various colours, and the code-setter indicates how accurate each guess is using key pegs – white for a code peg of the right colour but placed in the wrong position, black for a code peg of the right colour and position. As every experienced Mastermind player will know, the secret lies in using the key pegs to judge which code pegs to replace in the next guess. You may be delighted to know then, that there is a simpler way to break the code, thanks to Hsiao I Ann’s and Lee Yue Xin’s project on the Strategy behind Mastermind, which won a Silver award in the Singapore Math-ematics Project Festival 2012. Their project sought to answer what every avid Mastermind player wants to know about winning the game: the best strategy to breaking the code, and the minimum number of guesses necessary.

So what is the best move for the first guess? The first guess can be essentially broken down into 5 dif-ferent types, namely AAAA, AAAB, AABB, AABC and ABCD, where each combination represents a differ-ent number of repeated colours. While one might think any choice is just as good as any other for the first move, it is not the case. For example, if our first guess is 4 blue pegs (type AAAA), then it can only be marked in five ways as it not possible to be marked with any white pegs. However, if our guess involves more colours, then it can be marked in more ways, which give more logi-cal information. Using computer analysis, it can be shown that the number of solutions left in each case is most evenly distributed in the case of the guess AABB.

How many possible solutions are there in ar-ranging the digits 1 to 9 into each closed area so that the sum if the digits inside every circle is the same? Each closed area should contain only one digit and no digits should be repeated. Draw all the possible solutions.

Masterminding SuccessStrategy behind MastermindBy Ian Foo, Lau Yu Han and Jonathan Tan

This issue of Epigraph is proudly brought to you by the SIMC 2012 Publications CommiteeIan FooEditor

Sharne SulaimanTa Ngoc Tu AnhLayout Artists

Victoria Tay, Lim Si JiaEwin Teo, Lim Pei YingMavis TeoJournalists

Photos courtesy of The Media Club

Epigraph | May 23, 2012

Your Daily Dose of MathematicsToday’s Puzzle

The numbers on the first cube are 0, 1, 2, 3, 4 and 5, and the numbers on the second cube are 0, 1, 2, 6, 7 and 8.“But what about nine?” you say. Well, try turn-ing the six upside down.

Yesterday’s Solution

If our first move is AABB (example, 2 red followed by 2 blue pegs) and it is marked as 2 black pegs and 0 white pegs, then there are 96 solutions left. It turns out the best first move is AABB, since the worst case is can be marked has at most 256 solutions. This method turns out to be a good strategy for playing the game and it would ensure a win within five guesses. Now you know how to ace your next game of Mas-termind.

4