Math Qn on White, Black and Red Marbles

This is posted by LL ☺

Qn on cbox: There are two containers A and B. Each of them contains 9 white marbles, 9 black marbles and 9 red marbles. If 10 marbles are removed from A and placed into B. how many marbles must be returned from B to A to make sure that there are at least 8 marbles of each colour in A?

Solution:
A: 9W, 9B, 9R
B: 9W, 9B, 9R

10 marbles are removed from A and placed into B. Assume 9W and 1B (any combination will do).
A: 0W, 8B, 9R
B: 18W, 10B, 9R

Now, return marbles from B to A to make sure that there are at least 8 marbles of each colour in A.
The most unlucky picks from B would be: 9R and 10B (A: 0W, 18B, 18R) followed by 8W (A: 8W, 18B, 18R)
Hence for worst case, number of marbles returned is 9+10+8 = 27 marbles.

High School Olympiads

This is posted by LJ's mum

At primary level, the more prestigious local Maths and Science competitions/olympiads include:
- NMOS (National Mathematical Olympiad of Singapore) and SPSO (Singapore Primary Science Olympiad) for P5, organised by NUS High
- SMOPS/APMOPS (Singapore - Asia Pacific Mathematical Olympiad for Primary School) for P6, organised by HCI
- RIPMWC (RI Primary Mathematics World Contest) for P6, organised by RI

At secondary/JC level, there are many more Maths and Science competitions/olympiads available. These include: Singapore Mathematical Olympiad (SMO Junior/Senior/Open), American Maths Contest (AMC 10/12), Australian Maths Competition (AMC Westpac), Singapore Junior Physics Olympiad (SJPhO), Singapore Physics Olympiad (SPhO), Singapore Junior Chemistry Olympiad (SJChO), Singapore Chemistry Olympiad (SChO), Singapore Biology Olympiad (SBO), National Olympiad in Informatics (NOI) etc. The ultimate of the olympiads would be to represent Singapore in the following prestigious international Maths and Science olympiads for high school students (Singapore's medal tally in 2010 are given):
- International Mathematical Olympiad (IMO) (4 Silver, 1 Bronze)
- International Physics Olympiad (IPhO) (1 Gold, 4 Silver)
- International Chemistry Olympiad (IChO) (2 Gold, 2 Silver)
- International Biology Olympiad (IBO) (1 Gold, 3 Silver)
- International Olympiad in Informatics (IOI) (1 Gold, 1 Silver, 2 Bronze)

The selection of Singapore representatives (only citizens and PRs are eligible) for the above competitions is through rigorous selection processes. Typically, high-potential students are selected from the local competitions (SMO, SChO, SPhO, SBO, NOI, etc.) and they will go through weekly training by NUS lecturers/professors/trainers and then sit for a series of selection tests, before the final national teams to represent Singapore are selected. The national teams then go through more intensive training sessions (could be daily, starting from June holidays up till international olympiads in early/mid July).

The International olympiads are usually held in July of each year (with the exception of IOI, which may be held in August). It is not impossible for a student to represent Singapore in more than 1 Olympiad. However, it is evident that with all the intensive trainings and the international olympiads being held closely together (in June/July), a student may have to make the difficult choice of giving up one olympiad for another. Or the student could try again, to gain a coveted place in the "dropped" olympiad's national team, in the following year.

I think if one is going to pursue the ultimate in Olympiads (i.e. represent Singapore in IMO/IPhO/IChO/IBO/IOI), one will need to put his/her heart and soul into it. One should probably be involved in not more than 2, or at most 3 types of national-level olympiads. If you get involved in too many, you could become "Jack of all trades, master of none". It is also not practical to be involved in too many, as the competitions, training sessions and selection tests are bound to clash with one another, not forgetting that in the midst you will have heavy school workload to juggle, so the balancing act is going to be extremely challenging.

For Lim Jeck, he is focussing more on IMO, but he is also involved in Physics Olympiad Training (school elective module) and NOI/IOI training. He is taking part in the Maths/Physics/Informatics olympiads. So far he has represented Singapore in IMO twice, in 2009 and 2010. Hopefully he has the chance to represent Singapore in IMO again in 2011 - 2013 (and clinches a Gold eventually), and also in IOI, in 2012 or 2013.

APMO 2011

This morning I took the Asian Pacific Maths Olympiad at NUS High. There were 5 questions, we were given 4 hrs. Question 3 is on Geometry. I took 1.5 hours to do the first 4 questions. For the next 2.5 hours I tried to solve question 5, but I think I only managed to solve it partially.

So I think I solve a total of 4.5 questions, which is better than how I did the previous 2 years :)

Afternote: I got about 31 or 32 marks for APMO 2011. Past year APMO test papers, solutions and results can be found in http://www.mmjp.or.jp/competitions/APMO/

无聊的造句

马上 — 我很开心地骑在马上。（老师评语：我很不开心。）

难过 — 前面这条水沟很难过。（老师评语：老师更难过。）

又。。又 — 我的妈妈又矮又高又胖又瘦。（老师评语：你妈妈是百变金刚吗？）

其中 — 我的其中一只左脚受伤了。（老师评语：你是蜈蚣吗？）

天真 — 今天真热。（老师评语：你好天真。）

Inspirational Conversation between Pencil and Eraser

Pencil: I'm sorry....

Eraser: For what? You didn't do anything wrong.

Pencil: I'm sorry 'cause you get hurt because of me. Whenever I made a mistake, you're always there to erase it. But as you make my mistakes vanish, you lose a part of yourself. You get smaller and smaller each time.

Eraser: That's true. But I don't really mind. You see, I was made to do this. I was made to help you whenever you do something wrong. Even though one day, I know I'll be gone and you'll replace me with a new one, I'm actually happy with my job. So please, stop worrying. I hate seeing you sad. :)

Parents are like the eraser whereas their children are the pencil. They're always there for their children, cleaning up their mistakes. Sometimes along the way... they get hurt, and become smaller (older, and eventually pass on). Though their children will eventually find someone new (spouse), but parents are still happy with what they do for their children, and will always hate seeing their precious ones worrying, or sad.

This is for all parents out there.....

~ Author Unknown ~

SIMO Hiking

Yesterday, after our regular SIMO training, we hiked from NUS to Vivo City. The group photos below are with courtesy of Ding Yue.

Competitions

This is posted by LL ☺☻♪ ♫ ☼

In the coming months, I am taking part in the following competitions:
- HCI's Singapore-Asia Pacific Mathematical Olympiad for Primary Schools (SMOPS)
- RI's Primary Maths World Contest (RIPMWC)
- St Andrew's Maths and Science Competition
- Clementi Town Sec's Mathematical Talent Quest
- Singapore and Asean Schools Maths Olympiad (SASMO)
- RGS' Maths Competition
- Little Red Dot Young Professor Challenge
- Singapore Mathematical Olympiad (SMO Junior)
- UNSW ICAS (Maths)
- UNSW ICAS (Science)
- Australian Maths Competition
- AMC8

I think there may be 1 or 2 more, which I cannot remember.

Happy Year of the Rabbit!

1, 2, 3, 4, 5 Math Qn

Someone needed help with the following question:
The digits 1, 2, 3, 4 and 5 can form 120 five-digit numbers, each without any repeating digit. What is the sum of these 120 numbers?

Solution by Lim Li:
Each of the digits 1, 2, 3, 4 and 5 appears 24 (i.e. 120/5) times in the Ones, Tens, Hundreds, Thousands and 10 Thousands place.
1+2+3+4+5 = 15
24 x 15 = 360
Hence,
+++++360
++++360
+++360
++360
+360
------------
=3999960 (sum of all 120 numbers)
------------

Mathlinks aka Art of Problem Solving

This is posted by LJ's mum.

Mathlinks is a website/forum that Lim Jeck frequents, on an almost daily basis. It is where he hones his Maths Olympiad problem solving skills. Since joining Mathlinks on 10 March 2010, he has contributed 760 posts (as at 25 January 2011) which works out to an average of 2.73 posts per day. Out of a total of 78,927 members, Lim Jeck aka oneplusone is currently ranked the 455th most active user. The most active user has to-date made 12,301 posts in the various forums!

He also participates in an unofficial Olympiad Marathon initiated by a fellow forum user. Currently, he is ranked 1st, after some 14 rounds of questions.

Cut the Rope HD (iPad game)

We are currently the top in national and local for the Cut the Rope game in Cardboard, Fabric and Foil box leaderboard categories, with scores of 140240, 137120 and 132890 respectively.

Cut the Rope is a strategic game that tests your puzzle solving skills. There is this cute fat round green monster, Om Nom, who has a penchant for candy. The objective of the game is to bring the candy to Om Nom's mouth which is almost as big as him. If the candy is attached to a rope, you can "Cut the Rope" with your finger. To complete a level, you need to decide which ropes and when to cut, to swing/drop/float/etc the candy into his mouth, collecting as many stars as possible in the process.

We have aready completed the game and have nothing much to do as I am too "sian" to achieve national tops for the gift and cosmic box.

Funny Photos from Newspapers

Professional Photography?!

From The Straits Times - Feng Tianwei, who rescued Singapore from quarter-final exit during the Asian Games 2010.

From My Paper - Monaco's Princess Stephanie was in Singapore to support her daughter, who participated in the inaugural YOG 2010.

2000th 7-digit Math Question

Someone posted the following question:
All the 7-digit numbers containing each of the digits 1, 2, 3, 4, 5, 6, 7 exactly once, and not divisible by 5, are arranged in the increasing order. Find the 2000th number in this list.

Solved by Lim Li ☺☻:
Since the 7-digit number cannot be divisible by 5, the last digit cannot be 5.
If the 1st digit is fixed, there are 1x2x3x4x5x5 = 600 numbers
[1]765432 => 600th number
[2]765431 => 1200th
[3]765421 => 1800th
If the 1st and 2nd digits are fixed, there are 1x2x3x4x4 = 96 numbers
[41]76532 => 1896th
[42]76531 => 1992nd
:
[4312]756 => 1996th
[4315]267 => 1997th
[4315]276 => 1998th
[4315]627 => 1999th
[4315]672 => 2000th
Hence the 2000th number is 4315672

A Busy Year for 2011 ...

This is posted by LJ's mum.

2011 is going to be a very busy year for the kids.

For Lim Min, she is going to RI. While she takes about 20 mins to travel by MRT & bus to RGS, she will now need to spend about 40 mins to travel to RI (Queenstown MRT to Marymount MRT). I heard from ex-RGS now-RI parents that students are much busier in RI and they have to take 2 CCAs, which means they work harder and play harder as compared to when they are in secondary school! Lim Min will be taking GP and 4 H2s - Maths, Physics, Chemistry and Economics. She has done very well for her Maths (scoring 98 & 100 for the Maths 1 & Maths 2) and 3 Sciences (scoring 90 or close) while in RGS so it's a pity that she has to drop Biology to take the contrasting subject, Economics. But I heard Economics is an interesting subject so I guess, you lose some and you gain some.

For Lim Jeck, he is going to have an incredibly busy schedule! He is taking two NUS modules - Linear Algebra from NUS Faculty of Science and Competitive Programming (this module is free and ungraded) from the School of Computing. On top of that, he has the usual National Team Training at NUS Math Dept on Saturday mornings. Including the NUS modules, I think his timetable will have 2 days that end at 6 pm, 2 days end at 7 pm (Linear Algebra, 4-7 pm) and 1 day ends at 9 pm (Competitive Programming, 6-9 pm). He did well for his previous NUS module - Calculus and got an A+, which means he is able to claim the bulk of the course fee from NUS High. I think NUS High really suits him to a T, as he can enjoy working on his passion while maximising his potential in his strong areas - maths, physics, chemistry and programming.

For Lim Li, next year is PSLE year. Needless to say, she will have to stay back in school most of the days and her school teachers are going to give her tonnes of homework in preparation for the PSLE. She should have no problem doing well for Maths and Science, but I think she has to put in more effort for English and Chinese, her weaker subjects. I am sure her Chinese teacher, Ms Chai, will do the necessary to prepare the class well, so Lim Li should do all right (hopefully, get a high A) as long as she does all the work assigned by Ms Chai, diligently. I am more worried for her English. Maybe I would work out a schedule to revise English with her.

Hope everyone can have a fruitful year ahead!

Hikaru No Go

"Hikaru No Go" is a Japanese comic manga series as well as anime. It is our family favourite, as even my parents also read the comic books and watched the DVDs which we borrowed from the libraries. It also piques our interest in the Go game, which we are playing now :)

Hikaru No Go is the story of a 6-grader, Shindo Hikaru (left on above picture: boy with yellow hair), who by chance meets a 1000-year old ghost, Fujiwarano Sai (right on above picture: man with almost lady-like features) , who was trapped in a Go Board before his release. Together, Hikaru Shindo and Sai make a great go-playing team and they follow the path that leads them to the divine move or "Hand of God"; along the way they meet many memorable characters, such as Waya, Isumi, Ochi and Hikaru's and Sai's respective destined rivals, Touya Akira and Touya Kouyo.

There are many touching scenes such as those depicting the close friendship ties fostered between Hikaru and Sai, as well as among the the group of friends as they graduate from Insei to become Pro, or professional Go players, the integrity conflict and how a depressed Hikaru goes searching for Sai when he leaves suddenly. This is definitely a manga which I would recommend to anyone, even if you don't play Go.

3N Royal Caribbean Cruise

My family went for a 4 Days 3 Nights Best of Malaysia on Royal Caribbean Cruise (Legend of The Seas) from 20 Dec to 23 Dec. We stayed in 2 rooms, Oceanview stateroom, Deck 2. It was a relaxing and enjoyable trip, with lots of fun games, rock climbing and delectable food. We also joined the shore excursion to Penang - visit to butterfly farm, SEA's longest bridge, kampongs.

Playing table soccer.

Playing wii.

Endless supply of twist ice cream.

Lobster and elephant made by our stateroom attendant.

Towel folding class where we learnt how to fold tortoise, dog, elephant and monkey.

We enjoyed rock climbing.

Fine Dining at Romeo and Juliet restaurant, with starter, main course and desserts (which we shared).

Our favourite hang-out place - the Optix (Deck 10), where we played table soccer, wii and card games.

My Cousin's Wedding

Extended family group photo taken after my cousin (Han Kee)'s wedding banquet at Ritz-Calton, on 12 Dec 2010.

Top in Singapore for Froggy Jump

Lim Li is now officially the top scorer in Singapore for Froggy Jump, with a score of 2,071,984. The 2nd highest score in Singapore is 1,152,708. The world's highest score is 67,116,504 (by someone in USA), and Lim Li is ranked 223rd in the world.

The above shows the locations of the top 6 scorers in Singapore.

And of course, the top scorer lives in Queens!

Comic Books

Comic books which we devour during the school holidays. Every week, we read 20-30 books. All were borrowed from the Central Public Library and Jurong Regional Library.

My Favourite Comic Books

This is posted by LL ☺☻ 1st - Case Closed

2nd - Fullmetal Alchemist

3rd - Skip Beat

4th - Shaman King

5th - Hunter x Hunter