Friday, 28 May 2010
Our New Toy
My father bought an iPad. It was shipped from US and we received it yesterday. I think it costs US$7xx (about S$1000). We downloaded many free games and utilities from the Internet (Apple iTunes Store).
Friday, 21 May 2010
Year 3 Semester 1 Results
My semestral GPA is 4.6 (max is 5). I did badly for Fine Art. I look forward to dropping this subject in 1.5 years' time. For Year 5 & 6, I would like to take Maths Major with Honours (already taking it now), Physics Major with Honours, Chemistry Major with Honours and Computer Science Major.
Saturday, 15 May 2010
Singapore Team to 51st IMO
The results for the Singapore National Team for 51st International Mathematical Olympiad were released today. Out of the 6 participants selected, 2 are from RI-JC (Ivan Loh and Vincent Tseng), 1 from ACS(I) (Ang Jie Jun) and 3 from NUSH (Ang Yan Sheng, Gabriel Wong and I).
The 51st IMO will be held in Astana, the Republic of Kazakhstan. I do not know much about the country so I googled it - the Republic of Kazakhstan is in Eurasia and ranked as the ninth largest country in the world, and its location is below:
Training for the Singapore IMO national team will start next Thu (20/5) at NUS Maths Dept, and will stretch all the way to the competition itself, which is from 4 Jul to 15 Jul. Just like last year, my 1-month June holidays will be spent on training and I am going to miss many lessons again when school reopens ...
The 51st IMO will be held in Astana, the Republic of Kazakhstan. I do not know much about the country so I googled it - the Republic of Kazakhstan is in Eurasia and ranked as the ninth largest country in the world, and its location is below:
Training for the Singapore IMO national team will start next Thu (20/5) at NUS Maths Dept, and will stretch all the way to the competition itself, which is from 4 Jul to 15 Jul. Just like last year, my 1-month June holidays will be spent on training and I am going to miss many lessons again when school reopens ...
Sunday, 9 May 2010
Art of Problem Solving
I think The Art of Problem Solving is the best resource for Maths problem solving. You can also train your quick thinking by playing Maths games with other people. Try FTW! to pit your Maths skills in solving AMC kind of questions against other Maths enthusiasts. At the end of a game, you will be rated against other registered players.
If you have any Maths problems, go to mathlinks.ro and post your problems there (instead of spamming my cbox :) ), and hopefully someone else will answer it for you. It has forums for primary school kind of Maths questions, to high school types, to Maths Olympiad questions, college/university Maths and even Arts and Sciences.
http://www.artofproblemsolving.com/Forum/index.php
If you have any Maths problems, go to mathlinks.ro and post your problems there (instead of spamming my cbox :) ), and hopefully someone else will answer it for you. It has forums for primary school kind of Maths questions, to high school types, to Maths Olympiad questions, college/university Maths and even Arts and Sciences.
http://www.artofproblemsolving.com/Forum/index.php
Sunday, 2 May 2010
SIMO NTST 2010
I took the Singapore IMO National Team Selection Test yesterday and today. It was like the IMO format i.e. 3 questions to be done in 4.5 hrs each day. The type of questions were: 1. Geometry, 2. Algebra, 3. Combinatorics, 4. Combinatorics, 5. Number Theory, 6. Inequalities. They were taken from the IMO 2009 Shortlist questions (in the IMO, there are Longlist questions and Shortlist questions, and the 6 questions for IMO are selected from the Shortlist questions). I am not supposed to reveal the questions as some other countries may also be using some of these Shortlist questions which were not selected for IMO questions, for their own national selection tests.
Too bad there was only 1 Geometry qn, usually in the IMO there are 2, one for each day. Anyway, I could only solve qn 1, 2, 4, 5 and 6. I think the ever pro Ivan could solve all 6 questions!
*note: this is in fact the 2nd selection test. The 1st selection test with a lower weightage was held about a month ago.
Too bad there was only 1 Geometry qn, usually in the IMO there are 2, one for each day. Anyway, I could only solve qn 1, 2, 4, 5 and 6. I think the ever pro Ivan could solve all 6 questions!
*note: this is in fact the 2nd selection test. The 1st selection test with a lower weightage was held about a month ago.
Tuesday, 27 April 2010
Another Math Qn
Another question posted on the cbox:
A travelled from Town P to Q. B travelled from Town Q to P. They started at the same time. They met each other 80km from Q. When A reached Town Q, he immediately travelled back to Town P. When B reached Town P, he also immediately travelled back to Town Q. They met each other 60km from P. What was the distance from Town P to Town Q?
Solution (not drawn to scale) by Lim Li:
A travelled from Town P to Q. B travelled from Town Q to P. They started at the same time. They met each other 80km from Q. When A reached Town Q, he immediately travelled back to Town P. When B reached Town P, he also immediately travelled back to Town Q. They met each other 60km from P. What was the distance from Town P to Town Q?
Solution (not drawn to scale) by Lim Li:
Monday, 26 April 2010
Qn from SMOPS 2010
Someone posted the following question from SMOPS 2010 in the cbox:
s=1/((1/2001)+(1/2002)+(1/2003)+(1/2004)+(1/2005)+(1/2006)+(1/2007)+(1/2008)+(1/2009)+(1/2010)). Find the largest whole number smaller than s.
Soln:
Clearly, 10/2001 > (1/2001)+(1/2002)+(1/2003)+(1/2004)+(1/2005)+(1/2006)+(1/2007)+(1/2008)+(1/2009)+(1/2010) > 10/2010
Hence 2001/10 < s < 2010/10
Therefore the largest whole number smaller than s is 200.
s=1/((1/2001)+(1/2002)+(1/2003)+(1/2004)+(1/2005)+(1/2006)+(1/2007)+(1/2008)+(1/2009)+(1/2010)). Find the largest whole number smaller than s.
Soln:
Clearly, 10/2001 > (1/2001)+(1/2002)+(1/2003)+(1/2004)+(1/2005)+(1/2006)+(1/2007)+(1/2008)+(1/2009)+(1/2010) > 10/2010
Hence 2001/10 < s < 2010/10
Therefore the largest whole number smaller than s is 200.
Tuesday, 20 April 2010
Excuse from Lessons & Mid Year Exams Coming
The 2010 SIMO National Team Selection test is here again. It will be held on 1 May (Sat, Labour Day where our brains have to labour much) and 2 May (Sun), the day we emo. I can skip as many lessons/test/quiz/exams/lectures as I want and get away with it :-). I think I will still be attending some lessons (e.g. science lectures/lab, computer programming lab which I like).
My school mid year exams will be from 30 April to 7 May. I will also be taking AP Calculus BC exam on 5 May. Yay, my principal gave me permission to be exempted from the English exam on 30 April :D
Sunday, 18 April 2010
Ala Carte Buffet Dinner at Dragon Gate Restaurant
Yesterday was my paternal grandmother's birthday. We had ala carte buffet dinner at the Dragon Gate Restaurant. I was slightly late as I helped out at the NUS High Open House (Physics booth at the Concourse) till 4 pm, went home to change and then met my family at the Harbourfront Centre. The dinner was not that cheap, about $30 per person, and the food not really to my liking. I only liked fried man-tou, lobster ball, cheese beancurd, beancurd wrapped chicken and mixed fruit with sago dessert.
My paternal grandmother has 7 grandchildren.
My sisters and cousins watching me playing games on iphone (my uncle's, not mine - I don't even own a handphone).Sunday, 11 April 2010
NJC Secondary Maths Challenge 2010
I took part in the NJC maths challenge yesterday. I met some people from the national training team - 4 from RI, 1 from RGS and 2 from HCI. I got first in individual and third in team, and also got 2 more prizes in the audience round. In total, I got 2 medals, 2 graphic calculators and 2 random prizes.
Thursday, 8 April 2010
妈妈的感触
This post is written by my mother.
从妈妈的生病到她的逝世，我深深地体会到“人生不如意之事，常之八九”这句话的含义。一个人的一生中，不知要伤心欲绝和痛苦难耐多少次。我指的伤心事是，当亲人逝世（你能想象有几次吗？父母、叔伯婶姨、朋友、兄姐。。。）离你而去，指的痛苦事是，当你病入膏肓时身体的煎熬，而不是和朋友争吵、失去工作、考试不及格等的“芝麻绿豆”小事。
我想，如此的人生，难怪有些人需要精神寄托，也可能就是这个原因，才有那么多不同的宗教被发起。本来有宗教信仰是好的,只可惜，很多人用宗教的名义来干不道德的事，更可笑的是，有些人利用宗教杀了人后，还振振有词说“杀人是为了要警戒人们，杀人是不对的！”
从妈妈的生病到她的逝世，我深深地体会到“人生不如意之事，常之八九”这句话的含义。一个人的一生中，不知要伤心欲绝和痛苦难耐多少次。我指的伤心事是，当亲人逝世（你能想象有几次吗？父母、叔伯婶姨、朋友、兄姐。。。）离你而去，指的痛苦事是，当你病入膏肓时身体的煎熬，而不是和朋友争吵、失去工作、考试不及格等的“芝麻绿豆”小事。
我想，如此的人生，难怪有些人需要精神寄托，也可能就是这个原因，才有那么多不同的宗教被发起。本来有宗教信仰是好的,只可惜，很多人用宗教的名义来干不道德的事，更可笑的是，有些人利用宗教杀了人后，还振振有词说“杀人是为了要警戒人们，杀人是不对的！”
Wednesday, 7 April 2010
In Memory of My Maternal Grandma
This post is written by my mother, to my maternal grandmother who passed away peacefully on Good Friday (2 Apr 10).
Mum, I miss you very much. This morning, we brought father to NCC for CT Scan. I couldn’t control my tears when I was there, as just not too long ago I was with you in the same room, waiting for your turn to have the radiation sessions. I had to walk away from father and my sisters as I didn’t want them to see my tears. I fear visiting places flooded with lots of memories, like the shophouse, your bed and the sofa bed in the hall of 2nd brother’s house, it just hurts …
Mum, you are greatest mum, grandma and wife in the whole wide world! Though you have 9 children, you took great care of every single one of us, not showing any favouritism. When we were young, most of us did not do any housework while you had to cook, wash, clean, tend to grandma, help in father’s shop – you were like a superwoman! Like what brother-in-law said, you seemed to have a mini computer in your brain and knew everyone’s likes and dislikes. You knew all our favourite dishes and would cook for us - father, 9 of us plus our spouses, your 21 grandchildren, our 3 cousins from Malacca and even the employees of the shop. As I live near the shop, you would often phone me to go to the shop whenever you cooked my favourite dishes and you would specially reserve many pieces of yam for me in a separate bowl. Unfailingly, you would ring me every Saturday (when we have our weekly family affair, where 20-30 of us would gather at the shophouse) at about 6 pm, to ask when we were going over, and I would always say “yeah, we’re coming over soon ...” Sadly, I do not know your favourite dishes … I only know you love to play Bubbles on the Palm PDA which I bought from ebay for you (but you were so addicted to the game that I secretly removed the game from the PDA, but later put it back again), solve Sudoku, and you also love to play jackpot in Genting (1-cent kind); you said that before you were sick, even plain water tasted good, and when you were very sick and did not have much appetite, even a cup of instant hot Kopi-O could make your day!
Mum, even when you were very sick and feeling uncomfortable, you still thought of us, and constantly worried about us. You said that Lim Jeck was intelligent but he must not neglect making friends and should learn to speak more; and you also reminded me to get Lim Min (whom I told you I have the least worries, in her studies) and Lim Jeck to guide Lim Li in her school work …
Mum, most couples would squabble but I don’t remember you and father had ever quarreled. You had never laid hands on us, and you had never raised your voice before, to anyone. You seemed sad when you heard us having disputes/disagreements over your treatment options …
Mum, though you were gone, I think you are very blessed as all of us love you so much!! And, you are no longer suffering, and do not have to force yourself to take so many kinds of tablets (English medicine), herbs (Chinese medicine) and supplements …
Mum, if there is a next life, I am certain that I want you and father to be my parents again …
I miss you mum … so much … so much …
father's birthday celebration in 2007
father's birthday celebration in 2008
mum's birthday celebration in 2008
mum's favourite game which she played incessantly before she was diagnosed with breast cancer in January this year.
Mum, I miss you very much. This morning, we brought father to NCC for CT Scan. I couldn’t control my tears when I was there, as just not too long ago I was with you in the same room, waiting for your turn to have the radiation sessions. I had to walk away from father and my sisters as I didn’t want them to see my tears. I fear visiting places flooded with lots of memories, like the shophouse, your bed and the sofa bed in the hall of 2nd brother’s house, it just hurts …
Mum, you are greatest mum, grandma and wife in the whole wide world! Though you have 9 children, you took great care of every single one of us, not showing any favouritism. When we were young, most of us did not do any housework while you had to cook, wash, clean, tend to grandma, help in father’s shop – you were like a superwoman! Like what brother-in-law said, you seemed to have a mini computer in your brain and knew everyone’s likes and dislikes. You knew all our favourite dishes and would cook for us - father, 9 of us plus our spouses, your 21 grandchildren, our 3 cousins from Malacca and even the employees of the shop. As I live near the shop, you would often phone me to go to the shop whenever you cooked my favourite dishes and you would specially reserve many pieces of yam for me in a separate bowl. Unfailingly, you would ring me every Saturday (when we have our weekly family affair, where 20-30 of us would gather at the shophouse) at about 6 pm, to ask when we were going over, and I would always say “yeah, we’re coming over soon ...” Sadly, I do not know your favourite dishes … I only know you love to play Bubbles on the Palm PDA which I bought from ebay for you (but you were so addicted to the game that I secretly removed the game from the PDA, but later put it back again), solve Sudoku, and you also love to play jackpot in Genting (1-cent kind); you said that before you were sick, even plain water tasted good, and when you were very sick and did not have much appetite, even a cup of instant hot Kopi-O could make your day!
Mum, even when you were very sick and feeling uncomfortable, you still thought of us, and constantly worried about us. You said that Lim Jeck was intelligent but he must not neglect making friends and should learn to speak more; and you also reminded me to get Lim Min (whom I told you I have the least worries, in her studies) and Lim Jeck to guide Lim Li in her school work …
Mum, most couples would squabble but I don’t remember you and father had ever quarreled. You had never laid hands on us, and you had never raised your voice before, to anyone. You seemed sad when you heard us having disputes/disagreements over your treatment options …
Mum, though you were gone, I think you are very blessed as all of us love you so much!! And, you are no longer suffering, and do not have to force yourself to take so many kinds of tablets (English medicine), herbs (Chinese medicine) and supplements …
Mum, if there is a next life, I am certain that I want you and father to be my parents again …
I miss you mum … so much … so much …
father's birthday celebration in 2007
father's birthday celebration in 2008
mum's birthday celebration in 2008
mum's favourite game which she played incessantly before she was diagnosed with breast cancer in January this year.Good Resource for Math Olympiad Enthusiasts
Mathlinks (http://www.mathlinks.ro/index.php) is one of the best resources for high school students who are Maths Olympiad enthusiasts. You can find past year questions, answers, and forum discussions on all sorts of Maths competitions, such as IMO, APMO, AMC, USAMO as well as local Maths olympiads held within different countries.
My favourite is the following thread:
Forum » Olympiad Section » Geometry » Geometry Unsolved Problems
My favourite is the following thread:
Forum » Olympiad Section » Geometry » Geometry Unsolved Problems
Wednesday, 31 March 2010
Number Patterns
This week's Columbus State University's Math contests are about number patterns.
Problem of the Week:
0, -2, -2, 0, 4, 10, ___, ___
Algebra in Action:
1.5, 1.0, 0.83, 0.75, 0.7, ___, ___
Middle School Madness:
1, 4, 9, 61, 52, 63, 94, ___, ___
Elementary Brain Teaser:
2, 5, 11, 17, 23, 31, 41, 47, ____, ____
Algebra in Action's pattern is more challenging than the rest as only about 1/4 of participants got the answer correct. You should be able to get the other 3 answers quickly. Just in case you can't solve the challenging one, check the solution here by highlighting the text -> 1.5 (3/2), 1.0 (4/4), 0.83 (5/6), 0.75 (6/8), 0.7 (7/10), 0.67 (8/12), 0.64 (9/14)
Problem of the Week:
0, -2, -2, 0, 4, 10, ___, ___
Algebra in Action:
1.5, 1.0, 0.83, 0.75, 0.7, ___, ___
Middle School Madness:
1, 4, 9, 61, 52, 63, 94, ___, ___
Elementary Brain Teaser:
2, 5, 11, 17, 23, 31, 41, 47, ____, ____
Algebra in Action's pattern is more challenging than the rest as only about 1/4 of participants got the answer correct. You should be able to get the other 3 answers quickly. Just in case you can't solve the challenging one, check the solution here by highlighting the text -> 1.5 (3/2), 1.0 (4/4), 0.83 (5/6), 0.75 (6/8), 0.7 (7/10), 0.67 (8/12), 0.64 (9/14)
Thursday, 25 March 2010
Question from AMC10A 2010
Someone posted a question (#18) from AMC10A on the cbox. It's easier and less messy to explain it here rather than on the cbox:
Qn: Bernardo randomly picks distinct numbers from the set (1,2,3,4,5,6,7,8,9) and arranges them in descending order to form a 3-digit number. Silvia randomly picks distinct numbers from the set (1,2,3,4,5,6,7,8) and also arranges them in descending order to form a 3-digit number. What is the probability that Bernardo's number is larger than Silvia's number?
Solution:
Consider two scenarios: (a) Bernardo picks a '9' among the 3 numbers that she picks from her set of 9 numbers (b) Bernardo does not pick any '9'
Bernardo picks ‘9’:
When picking 3 numbers from the set (1,2,3,4,5,6,7,8,9), probability that Bernardo would pick a ‘9’ is 3/9 or 1/3. When this happens, Bernardo’s number (which has to be 9**, since the 3-digit number is to be arranged in descending order) will always be greater than Silvia’s number (obvious, since Silvia's greatest possible 3-digit number can only be 876!).
Bernardo does not pick ‘9’:
Number of different 3-digit numbers: 8C3 = 56
Probability that both Bernardo and Silvia pick the same 3-digit number is 1/56
Probability that both Bernardo and Silvia do not pick the same 3-digit number is 55/56
If both Bernardo and Silvia pick different number, probability that Bernardo’s number is bigger than Silvia’s number is ½ (similarly, probability that Bernardo’s number is smaller than Silvia’s number is also ½)
Therefore the probability that Bernardo’s number is larger than Silvia’s number is:
(Bernardo picks ‘9’) 1/3 + (Bernardo does not pick ‘9’) 2/3 x ½ x (55/56)
= 37/56
Qn: Bernardo randomly picks distinct numbers from the set (1,2,3,4,5,6,7,8,9) and arranges them in descending order to form a 3-digit number. Silvia randomly picks distinct numbers from the set (1,2,3,4,5,6,7,8) and also arranges them in descending order to form a 3-digit number. What is the probability that Bernardo's number is larger than Silvia's number?
Solution:
Consider two scenarios: (a) Bernardo picks a '9' among the 3 numbers that she picks from her set of 9 numbers (b) Bernardo does not pick any '9'
Bernardo picks ‘9’:
When picking 3 numbers from the set (1,2,3,4,5,6,7,8,9), probability that Bernardo would pick a ‘9’ is 3/9 or 1/3. When this happens, Bernardo’s number (which has to be 9**, since the 3-digit number is to be arranged in descending order) will always be greater than Silvia’s number (obvious, since Silvia's greatest possible 3-digit number can only be 876!).
Bernardo does not pick ‘9’:
Number of different 3-digit numbers: 8C3 = 56
Probability that both Bernardo and Silvia pick the same 3-digit number is 1/56
Probability that both Bernardo and Silvia do not pick the same 3-digit number is 55/56
If both Bernardo and Silvia pick different number, probability that Bernardo’s number is bigger than Silvia’s number is ½ (similarly, probability that Bernardo’s number is smaller than Silvia’s number is also ½)
Therefore the probability that Bernardo’s number is larger than Silvia’s number is:
(Bernardo picks ‘9’) 1/3 + (Bernardo does not pick ‘9’) 2/3 x ½ x (55/56)
= 37/56
Thursday, 18 March 2010
APMO 2010 (Revealed)
My sister and I took the APMO today. We were told not to reveal anything about it, not the name, not the number of questions, how long is it, whether it is a test or not, and how many questions I did. The APMO is held at RI from 0800 to 1200, which is about geometry, number theory, combinatorics and algebra. We ate alot of food at RI. There are five questions in the test and we can only discuss the APMO 7 days later.
APMO - Asia Pacific Maths Olympiad
today - 9 March 2010
APMO - Asia Pacific Maths Olympiad
today - 9 March 2010
Tuesday, 16 March 2010
AIME I 2010
This morning I took the AIME I at NUS High Theatrette. I did 13 questions out of 15, but I may have made careless mistakes because I did not have time to check my answers.
I think this year's AIME is about as tough as AMC 12B. AMC 12B is considered tough because there is very little time (75 minutes for 25 questions). For AIME, we were given 3 hrs to do 15 questions. The questions were of course harder than AMC 12, but I did more percentage of questions in AIME than in AMC 12 since I was given more time to solve the problems. I would rather find the product of 2 10-digit numbers than find 100 products of 2 1-digit numbers.
Update on 21 March - answers for AIME I are found here. I think I have made 3 careless mistakes and got only 10 correct answers. I got the hardest question (#15) correct but the easiest question (#1) wrong :-(
I think this year's AIME is about as tough as AMC 12B. AMC 12B is considered tough because there is very little time (75 minutes for 25 questions). For AIME, we were given 3 hrs to do 15 questions. The questions were of course harder than AMC 12, but I did more percentage of questions in AIME than in AMC 12 since I was given more time to solve the problems. I would rather find the product of 2 10-digit numbers than find 100 products of 2 1-digit numbers.
Update on 21 March - answers for AIME I are found here. I think I have made 3 careless mistakes and got only 10 correct answers. I got the hardest question (#15) correct but the easiest question (#1) wrong :-(
Tuesday, 9 March 2010
**** 2010
My sister and I took the **** today. We were told not to reveal anything about it, not the name, not the number of questions, how long is it, whether it is a test or not, and how many questions * did. The **** is held at ** from **** to ****, which is about ********, ****** ******, ************* and *******. We ate alot of food at **. There are **** questions in the test/not test and we can only discuss the **** * day(s) later.
My sister will decrypt the above message 1 week later.
My sister will decrypt the above message 1 week later.
Saturday, 6 March 2010
SIMO training
We did some combi questions today led by our new IMO gold medalist trainer from Bulgaria. His name is Vladimir Barzov, and he has won 3 gold medals in the IMO 2000 to 2002. He has an accent and his handwriting is sometimes hard to read. But at least he taught us, unlike some other trainers who just left us alone to do the pr0blems and then asked one of us to present it.
I heard that this year there will be two rounds of selection tests to select the IMO team, one in April and one in May. In previous years, there was only one selection test in May.
I heard that this year there will be two rounds of selection tests to select the IMO team, one in April and one in May. In previous years, there was only one selection test in May.
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