SMO 2011 (Junior Section) Answers

SMO 2011 Junior Special Round Participants List
##Click here for errors in SMO 2011 Solution Book's Junior Rd 1 Q16, 19, 26 and 28. Document is prepared by wmdsg.
1. D
2. C
3. C
4. B
5. B
6. A
7. B
8. E
9. C
10. E
11. 2
12. 5
13. 3
14. 129
15. 0
16. 7981 (3 Sep: answer in solution book is 9241 - refer to ## above)
17. 224
18. 1001
19. 256 (3 Sep: answer in solution book is 16 - refer to ##)
20. 4022
21. 101
22. 19
23. 169
24. 288
25. 14
26. 3 (3 Sep: answer in solution book is 350 - refer to ##)
27. 19
28. 10301(? see ** below and ##)
29. 15
30. 109
31. 4
32. 98
33. 30
34. 4022
35. 10
*Answers for Qn 14 and Qn 19 are provided by sz and wmdsg, respectively. Thanks.
** Lim Li: as pointed out by GeNiUs in comments, there may be something wrong with Qn 28. The answer is unknown at the moment.

National Average Statistics

SMO (Junior) Previous Years' Cut-off Points (Inclusive of Round 2 scores)
2010 Gold (24), Silver (9), Bronze (8), HM (5)
2009 Gold (11), Silver (7), Bronze (6), HM (5)
2008 Gold (23), Silver (14), Bronze (11), HM (10)
2007 Gold (20), Silver (14), Bronze (11), HM (10)

Update:
2011 Gold (12), Silver (9), Bronze (7), HM (6), Cut-off for Round 2: 11, Cut-off for Top 30: about 34

SMO 2011 (Senior Section) Answers

SMO 2011 Senior Special Round Participants List
1. B
2. A
3. D
4. C
5. E
6. A
7. E
8. B
9. A
10. C
11. 400
12. 12
13. 14
14. 300
15. 8001
16. 1006
17. 54
18. 1005
19. 1011
20. 1
21. 40
22. 3
23. 93
24. 1120
25. 1
26. 180
27. 9
28. 28
29. 168
30. 276
31. 20
32. 5
33. 61
34. 45 (correct answer is 16, as in solution book)
35. 12
*Correct answers to Qn. 29 and Qn. 35 are provided by goran.

National Average Statistics

SMO (Senior) Previous Years' Cut-off Points (Inclusive of Round 2 scores)
2010 Gold (26), Silver (10), Bronze (7), HM (6)
2009 Gold (19-23), Silver (10), Bronze (7), HM (6)
2008 Gold (27-28), Silver (15), Bronze (10), HM (9)
2007 Gold (29-30), Silver (16), Bronze (12), HM (10)

Update:
2011 Gold (21), Silver (15), Bronze (10), HM (9), Cut-off for Round 2: about 15, Cut-off for Top 30: about 27
My Score: 28+50

APMOPS 2011

This is posted by Lim Li☺
From left: Mrs Chua (our principal), Zheng Han, me, Wei Jue, Step, Mr Ng.

Today we took the Asia Pacific Mathematical Olympiad for Primary Schools (APMOPS which is the 2nd Round of SMOPS) in the morning and also attended the prize giving ceremony held in the afternoon.

Zheng Han and I were in group 2, and there were only 2 girls (out of 30 people in my group). The other girl won a SPSO Top 30, and is also in NUS High's Einstein Club, just like me. I also met another boy called Eugene, who told me that he visited this blog before.

The school, Hwa Chong Institution, provided us packet lunch after the competition, which they did not give the teachers (too bad). There were rice, brocoli, tofu, fish and meat. Zheng Han spilled the food on the table and then he ate it (so unhygienic and disgusting). Some time later, they gave each of us a McDonald french fries and apple pie. Zheng Han dropped a french fry on the grass and he ate it (more disgusting). After the prize giving ceremony, there was a buffet (bee hoon, bao, cream puff, very spicy carrot cake, cheese tarts, hot dog pastry, chicken wing, fruit punch etc.) for all students and guests. I forgot to bring lunch boxes to "da-bao".

We have won the following awards:
SMOPS Platinum Award - Zheng Han, me
SMOPS Gold Award - Stephen, Wei Jue
Honourable Mention Team Award - Queenstown Primary School: Zheng Han, Wei Jue, me
APMOPS 11th to 40th Position (Gold Medal) - me

The top in SMOPS is Clarence Chew from Tao Nan. The top few in APMOPS are from Shanghai.

Maths Talent Quest

This is posted by LL ☺

Hello. ☺☻. This afternoon, I played truant with Step, Wei Jue, Wei Wei and Ji Xuan. This time, we played truant for 15 min more than last time (30 mins). During that time, we had our lunch in our school canteen. We then took the school bus to Clementi Town Secondary School for the Maths Talent Quest competition.

We played some games while waiting for our turns to take the competition, which was on the computer. First, we played the Rubik's Cube and I totally failed. After that, we played Sudoku. Then, we went to play some games on the stage (without audience) - each person from each school can play one kind of game. I played sliding blocks. I had 5 mins to complete the puzzle but there was something wrong with the computer, I had only 1 min instead of 5 mins so I did not manage to complete it. Then I played another game that I could remember the name. At the end of the games, I only accumulated 4 points and could exchange the points for an 8-point star puzzle (see below).

Then, it was our turn to take the competition. It was challenging and I got 12 marks out of a total of 25 marks (1/2 more mark to pass!). During the competition, there was someone from another school hollering very loudly at the invigilator. Step got 11 marks, Wei Jue got 10 marks, Wei Wei got 9 and I do not know how many marks Ji Xuan got.

Following that, we went for our refreshments. There were some black thingy (carrot cake?), yellow stuff, cream puff, sandwiches, chicken wings ... The food was scrumptious and mouthwatering, especially the cream puff, which was luscious and cooling. The lemon drink was also very refreshing.

Next, we proceeded to the hall for the prize presentation ceremony. Step, Wei Jue and Wei Wei got Silver awards. I got Individual 5th (a trophy) and Gold award (another trophy). Step needed 1 more mark to get Gold. The Individual 2nd and 3rd got something like a tablet, but the Individual 1st won an iPad 2 (so lucky!!). My school also won 2nd for Team Award (a medal), same as last time (St Andrews Maths & Science Competition).

SNGMC

This is posted by Lim Li.

Today, more than 12 hours but less than 15 hours ago, I took part in a math competition called Singapore National Girls' Mathematics Competition (SNGMC). It is organized by RGS. When I reached my school at 7:30 am, I was the latest as usual. Then, we waited what seemed like eternity for Mr Ng to come, who gave the excuse that he bought a toy transformer at 12 midnight the day before and went home at 3 am. The 6 of us girls and Mr Ng took school bus to RGS.

When we reached RGS, they gave us a nice bag with Rubik's cube keychain, sliding puzzle keychain and 2 small metal puzzles inside. They also gave us a bottle of mineral water with RGS logo. I think there were 60 schools and about 400 girls taking part in SNGMC. We were divided into groups, mine was group E2. After that, we took the competition comprising about 25 questions. I left 4 blanks because I forgot to guess their answers. I found a mistake about 5 mins before time was up but I did not have time to change it. After that, we went for the Amazing Race Competition and someone commented that I must be Lim Jeck's sister (strangely, she did not remark that I am Lim Min's sister since I was in RGS compound). I hated the Amazing Race because I am very (very) unfit.

After the Amazing Race, we went for free food which was chicken rice with nuggets and chicken wings. It was delectable. The queue was very (very) long. After the refreshment we went to the hall for the results announcement. I got the 11th to 20th position (the individual prizes were: 1st, 2nd, 3rd, 4th to 10th and 11th to 20th) and won $50 (the prize money will be sent to my school).

NTST 2011 Results

The results are out - 3 from RI (Ding Yue, Ryan Kor and Joseph Kuan), 1 from ACSI (Ang Jie Jun) and 2 from NUS High (Ang Yan Sheng and I) will be representing Singapore in the 52nd International Mathematical Olympiad (IMO), which will be held from 18 to 25 July in Amsterdam, The Netherlands.

Training will start next Saturday. I think just like previous years, we will be training every day during the June holidays and I am going to miss 4.5 weeks of classes when school reopens.

Hope we can better last year's results of 4 Silvers, 1 Bronze and 1 Honourable Mention!

NTST 2011

We took the NTST yesterday and today. It was ok. I managed to do 5.9 questions.

Yet Another iPad

It is unbelievable. We have just won for ourselves another iPad (the one in the centre)! This time, it is won by Lim Min, who took part in the DSO Quiz which was open to current students of Raffles Institution (RI JC) during the career fair.

Again, it is not iPad2 .. it is a 32G with 3G.

Excused from Lessons

This is posted by LJ's mum
In preparation for the SIMO National Team Selection Test (NTST) on 30 Apr and 1 May (4.5 hrs each day, 9 am to 1.30 pm), Lim Jeck has been excused from lessons and CCA commitments this week (25 Apr to 1 May).

As stated in the letter, the arrangement is to allow students from the National Team to fully concentrate on a 5-day intensive training, to increase the chance of qualifying for the IMO National Team 2011. Alternative arrangements will be made for lessons missed.

I appreciate NUS High's support of her students in their aspirations to become part of the 6-member Singapore IMO team.

In my opinion, it is not really necessary for students to be pulled out from all classes to fully focus on either the selection tests or (if selected) the intensive preparation for the competition itself (which could last 6-7 weeks). Consistent, on-going work (for instance, doing a few IMO question(s) on a daily/weekly basis) is probably more important. Unless you are really competent in the subjects missed, taking a long leave may be detrimental to your studies, and you are bound to have a tough time catching up. It won't be easy to make alternative arrangements for most lessons missed, since you are probably busy attending classes. Extension for assessment deadlines may not help much, since you will be overwhelmed with new homework and assessment for current classes. For group projects, it may not be fair for your group members to cover your area in your absence.

I think it is good that students are given the flexibility to attend any particular lessons. They can decide on missing those lessons which have the least impact on them. These may include subjects that they are already strong at (e.g. Maths), lessons that are inconsequential (e.g. PE, CCA).

If Lim Jeck is selected again, it would be the 3rd time that he is representing Singapore in IMO. If he is not selected, it is okay as he has 2 more chances, in 2012 and 2013.

May the most deserving students (from whichever schools) from the national team get selected into the IMO Singapore Team 2011! :)

Direct School Admission

This is posted by LL's mum. The Direct School Admission – Secondary Exercise (DSA-Sec) for Primary 6 students has started. Lim Li has applied for the NUS High DSA. The selection test will be held on 25 June, which is about 2 months away. I do not think it is necessary to prepare for the selection test – it is hard to prepare anyway, since there are no past year questions for reference. Both Lim Jeck and Lim Min took the NUS High selection tests some 4 or 5 years ago, respectively. According to them, the Maths questions were easy (as they had been exposed to Maths Olympiad competitions like SMOPS, RI World Maths Contests) but the Science questions comprising Physics, Chemistry and Biology components were more challenging, though they could not remember what kind of questions were being asked.
While both Lim Min and Lim Jeck attempted two DSAs each during their times, Lim Li is going to try only NUS High. In my opinion, it is not advisable to try more than 3 DSAs. It may be emotionally draining for the kids as there will be a series of selection tests and camps (and possibly interviews too) - this could happen from June to August, which coincides with the all important preliminary exam and PSLE preparation period. I would think that students should only attempt DSA for schools of their first-choice (i.e. their dream school(s)), and not their second-choice or even third-choice schools. Why? There is a flip side to the DSA exercise – if you are successful in your second/third-choice school but not the first-choice school, are you going to accept the school? Once you accept the school, you will not be allowed to participate in the S1-posting exercise. What if your PSLE results turn out quite well, qualifying you for the first choice school? Yes, it may be possible to appeal to your dream school after the PSLE results are out. However, there is no guarantee that a place will be offered. Your dream school may request you to sit for tests, or call you up for an interview, and there may be a long agonizing wait for the appeal results (which could be soon after the appeal, or as late as end December, or even early January, after the school sorts out all the acceptances and rejections). There will be emotional upheavals while waiting for and receiving that important call.
Some top secondary schools will give priority to students from the MOE primary gifted education programme (GEP), and these students will apply under a GEP track. Mainstream students may apply under sports/art/music/performing arts, or academic track (math/science/english/mother tongue). For mainstream students, they have to prove that they are very outstanding in sports/art/music/etc., or way above their peers in the academic subject that they are applying. Some other schools like NUS High do not give preference to GEP students, but students who did very well in Maths and Science competitions (e.g. Platinum in SMOPS, Gold in SPSO) will have a higher chance of being selected. I have heard many parents lamenting that their above-average children who are non-GEP and do not have any special talent (in sports/art/academic area) do not stand a good chance in DSAs. I kind of agree with them. I think it is fine to try 1 or 2 DSAs, but don't take it to heart if the DSA is unsuccessful, and parents should encourage their child to focus on the PSLE and do well enough to qualify for his/her dream school.

Good luck to all the P6s who are applying for DSAs this year!

My Second iPad

I took part in the Cryptography Quiz jointly organised by DSO and Temasek Laboratories @ NUS, on 18 March. This afternoon was the prize presentation. Yay, I have won a 64G iPad with 3G. I think they should have given us iPad2, instead of iPad. I heard that the organiser had wanted to get iPad2 as prizes but unfortunately it has not been launched in Singapore yet. I already have a 16G iPad, but with this 64G iPad, we can download more games :)

Math Qn on Black and White hexagonal tiles

This is posted by LL♪♫. The following is a question from cbox: A very large floor is tiled with black and white regular hexagonal tiles. Each black tile is surrounded by 6 white tiles and each white tile is surrounded by 3 white tiles and 3 black tiles. Find the approximate ratio of the number of black tiles to the number of white tiles. Solution is below: The picture above is self-explanatory. The approx. ratio of the number of black tiles to the number of white tiles is 1:2.

2011 Harvard-MIT Mathematics Online Tournament

This is posted by LJ's mum. The Harvard-MIT Mathematics Tournament (HMMT) is an annual math tournament for high school students, held at MIT and at Harvard in alternate years. It is held in February and November of each year. With about 900 local participants, HMMT is one of the largest math contests in the United States. Six individual tests (each participant is to pick 2 out of 4 Subject Tests: Algebra, Geometry, Calculus, and Combinatorics) and two team events (the Team Round and the Guts Round) are the major events of the Tournament.

As the HMMT is restricted to teams within 75 miles of Cambridge, there are many high school students within US but outside the 75 miles radius, and outside of US, who are unable to attend the competitions to share in the challenge and excitement of the contest. Hence, the informal and unofficial Harvard-MIT Online Tournament is created. For the online tournament, no prizes are awarded, but top-performing teams and individuals are recognised on the HMMT website.

A group of 8 NUS High School students were among 81 high school students from all around the world who participated in the 2011 HMMT Online Competition held on 13 February (Sunday) from 1 - 7 am, Singapore time. The NUS High students did well, emerging tops in a number of categories, as seen below:

Individual (Overall)
1st - Lim Jeck
5th - Wayne Lin
6th - Ryan Chan
8th - Ang Yan Sheng

Algebra/Calculus
3rd - Ang Yan Sheng

Algebra/Combinatorics
10th - Ling Yan Hao

Algebra/Geometry
1st - Ryan Chan

Calculus/Geometry
2nd - Shen Dai
3rd - Yuan Chenyang
6th - Cheng Herng Yi

Combinatorics/Geometry
1st - Lim Jeck
3rd - Wayne Lin

Team Round
1st - NUS High

For full results, check here.

Inter-Primary Maths and Science Competition

This is posted by LL ☺☻

Yesterday, Wei Jue, Stephen and I went to St. Andrew's Secondary School to take part in the Inter-Primary Mathematics and Science Competition.

There were 40 MCQ questions, 20 of which were Math questions and 20 Science questions. We were given 40 minutes. The Maths questions were do-able but I could not answer most of the Science questions (I put 'C' for those which I had no inking of the answers). After the competition, we proceeded to the refreshments, comprising beehoon, fishballs, hard-boiled egg halves, nuggets and fruit punch. I did not have much time to eat as the special event was slated to commence 30 minutes later. The special event was more like a running event where we were given questions and had to find the answers (about God?!) from the walls and flooring in the school hall.

Before the prize presentation, we were elated to be informed that our school was one of the top 3 schools (out of 32 participating schools) which got into the grand finals, the buzzer round. It was held on the stage. There were 6 tables separated into 3 groups, with one computer for each group. The mouse of the computer was the buzzer but it had no sound; the word 'Team A/B/C' would appear on the display depending on which team pressed the buzzer first. Then, the team members would use the microphone on the table to say the answer. The 1st team to answer would get 5 points if the answer was correct, and 2 points would be deducted for a wrong answers. For wrong answer, the remaining 2 teams could answer - if they answered correctly, they would get 3 points, if answered wrongly, they would lose 1 point. My team could only do the Math questions but we were usually too slow with our answer. Whenever any Science question was posed, we would wait for the other teams to answer hoping they would get marks deducted for giving incorrect answers. At the end of the buzzer round, Team A had 23 points, Team B (my team) had 10 points and Team C had -2 points. We emerged Team 2nd and won a trophy each! Wei Jue also won another trophy for being the Individual 3rd. Haha, now our teacher Mr Ng could brag about our achievements again ☺ :P

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.