It does not have to get here within 48 hours, But you have to post it by the end of the day (So there should be a date on the stamp).

Question will be available between 8-9am. Those sending solution by Internet will have 24 hours (upto 9am on November 3rd). You can scan your handwritten solution if you want. But if it's unclear then you will not get points - so I prefer LaTeX. If you type your solution, it must be in LateX.

Those sending solution by post must post it today. So they do not have 24 hours. They only have time upto the post office closes. So if you want 24 hours, use internet.

## বাংলাদেশ অনলাইন ক্যাম্প - ২০১১

### Re: বাংলাদেশ অনলাইন ক্যাম্প - ২০১১

Exam question and rules

http://www.matholympiad.org.bd/forum/vi ... =14&t=1350

http://www.matholympiad.org.bd/forum/vi ... =14&t=1350

### Re: বাংলাদেশ অনলাইন ক্যাম্প - ২০১১

প্রথম অনলাইন গণিত ক্যাম্পকে আনুষ্ঠানিকভাবে সমাপ্ত ঘোষণা করছি। ক্যাম্পের পরীক্ষার প্রশ্ন নিয়ে ফোরামে এখন আলোচনা করা যেতে পারে। অংশগ্রহণকারী সবাইকে ধন্যবাদ এবং অভিনন্দন।

"Je le vois, mais je ne le crois pas!" - Georg Ferdinand Ludwig Philipp Cantor

### Re: বাংলাদেশ অনলাইন ক্যাম্প - ২০১১

I have graded all the problems. Most of you did very well. However, there were some very common mistakes everyone made.

1. Many of you made the mistake of saying things like "Without loss of generality assume $a \geq b \geq c$" even though that was not general. You have to very careful when you say things like that. $a^2b + b^2c + c^2a$ is cyclic but not symmetric. So, you cannot assume $a \geq b \geq c$ here. You also have to consider $a \geq c \geq b$, because there are two possible arrangements of three things upto cyclic permutations. Almost all of you lost points for this.

2. Only one of you (Sourav Das) successfully recognised a mistake in the statement of problem-8. The problem statement says $a,b,c$ are real numbers. All of you used AM-GM and other similar inequalities in this problem. AM-GM is not applicable to negative numbers. Similarly you need to be careful with any other theorem or result that you use. You must know when theorems are applicable and when they are not. If you think a theorem is applicable in more than the well-known case, then you have to prove it for your case before using it. The statement of this problem does not hold in general for real numbers. In this cases you need to also find out when it holds and when it does not. Only Sourav did this.

3. When divide or multiply both sides of an inequality by something (which must be nonzero) you must make sure whether that thing is positive or negative. The sign matters in inequality.

4. When you add/multiply two inequalities, or subtract one from another, or divide one by another you have to be careful that it makes sense. Many of you made this mistake. For example $a>b$, $c>d$ does not directly imply that $ac >bd$ or $a/d > b/c$. You have to be careful with sign (and division by zero). And it also does not imply that $a/c > b/d$; some of you made this mistake; if the absolute value the denominator is big then the absolute value of the ratio is small. Similar logic applies for subtraction. There are no set rules for these, you have to think the logic before you do it.

5.None of you were careful about special cases. In IMO ,if you forget to consider a special case (even if it is completely trivial) you will lose points. In many of the problems in this exam you needed to consider cases where something is zero. None of you did this. As a result you lost 1 or 2 points in many problems. In IMO, 1 or 2 points can be the difference between a medal and nothing (you will not even get an honourable mention if you lose 1 point from each problem).

6. Most of you were careless about division and multiplicative inverses. Whenever you divide or write the multiplicative inverse of something you must make sure that you are not dividing by zero or the denominator is not zero. If that is a possible case, you must consider that case separately. Many of you wrote things like Let $a=1/x$ where $a=0$ was a possible case. In IMO, you might lose more than one points for this. In the case $a=0$ you cannot say $a=1/x$; so you must mention that case specifically. You should also mention that here $x$ is nonzero, and also whether $x$ is positive or negative etc. if relevant.

7. None of you wrote any explanations for any of your solutions. This is a very bad practice. You are taught to write side notes in school mathematics. You need to do the same here. In particular, when any of the above points or other similar things are involved, you need to write a note explaining why you are correct. When you use a theorem you need to mention it. When you do some operation that might not be completely obvious, you need to explain what you are doing. When you do something where there might be special cases that need to be done differently, you need to mention those. When you do something that can be wrong in cases other than the ones applicable to that problem, you need to explain why it is correct in this problem. For example, when you multiply both sides of an inequality by, say, $a$ you need to mention why it is correct (for example, if the problem statement mentions that $a >0$ then you need to say this when you multiply by $a$). This is of course a stupid example, but things like these are more important for division, taking square roots, taking squares etc.

1. Many of you made the mistake of saying things like "Without loss of generality assume $a \geq b \geq c$" even though that was not general. You have to very careful when you say things like that. $a^2b + b^2c + c^2a$ is cyclic but not symmetric. So, you cannot assume $a \geq b \geq c$ here. You also have to consider $a \geq c \geq b$, because there are two possible arrangements of three things upto cyclic permutations. Almost all of you lost points for this.

2. Only one of you (Sourav Das) successfully recognised a mistake in the statement of problem-8. The problem statement says $a,b,c$ are real numbers. All of you used AM-GM and other similar inequalities in this problem. AM-GM is not applicable to negative numbers. Similarly you need to be careful with any other theorem or result that you use. You must know when theorems are applicable and when they are not. If you think a theorem is applicable in more than the well-known case, then you have to prove it for your case before using it. The statement of this problem does not hold in general for real numbers. In this cases you need to also find out when it holds and when it does not. Only Sourav did this.

3. When divide or multiply both sides of an inequality by something (which must be nonzero) you must make sure whether that thing is positive or negative. The sign matters in inequality.

4. When you add/multiply two inequalities, or subtract one from another, or divide one by another you have to be careful that it makes sense. Many of you made this mistake. For example $a>b$, $c>d$ does not directly imply that $ac >bd$ or $a/d > b/c$. You have to be careful with sign (and division by zero). And it also does not imply that $a/c > b/d$; some of you made this mistake; if the absolute value the denominator is big then the absolute value of the ratio is small. Similar logic applies for subtraction. There are no set rules for these, you have to think the logic before you do it.

5.None of you were careful about special cases. In IMO ,if you forget to consider a special case (even if it is completely trivial) you will lose points. In many of the problems in this exam you needed to consider cases where something is zero. None of you did this. As a result you lost 1 or 2 points in many problems. In IMO, 1 or 2 points can be the difference between a medal and nothing (you will not even get an honourable mention if you lose 1 point from each problem).

6. Most of you were careless about division and multiplicative inverses. Whenever you divide or write the multiplicative inverse of something you must make sure that you are not dividing by zero or the denominator is not zero. If that is a possible case, you must consider that case separately. Many of you wrote things like Let $a=1/x$ where $a=0$ was a possible case. In IMO, you might lose more than one points for this. In the case $a=0$ you cannot say $a=1/x$; so you must mention that case specifically. You should also mention that here $x$ is nonzero, and also whether $x$ is positive or negative etc. if relevant.

7. None of you wrote any explanations for any of your solutions. This is a very bad practice. You are taught to write side notes in school mathematics. You need to do the same here. In particular, when any of the above points or other similar things are involved, you need to write a note explaining why you are correct. When you use a theorem you need to mention it. When you do some operation that might not be completely obvious, you need to explain what you are doing. When you do something where there might be special cases that need to be done differently, you need to mention those. When you do something that can be wrong in cases other than the ones applicable to that problem, you need to explain why it is correct in this problem. For example, when you multiply both sides of an inequality by, say, $a$ you need to mention why it is correct (for example, if the problem statement mentions that $a >0$ then you need to say this when you multiply by $a$). This is of course a stupid example, but things like these are more important for division, taking square roots, taking squares etc.

### Re: বাংলাদেশ অনলাইন ক্যাম্প - ২০১১

Thanks... I'll try to learn from my mistakes.

Please

**Install $L^AT_EX$ fonts**in your PC for better looking equations,**Learn****how to write equations**, and**don't forget**to read**Forum Guide and Rules.****"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes**### Re: বাংলাদেশ অনলাইন ক্যাম্প - ২০১১

I scored the problems on a 10 point scale. So there were 120 points in total.

Sourav Das (sourav das) was the highest scorer with 96 points. Other people who scored 80 or more are Mahi Nur Muhammad (*Mahi*), Tripto, ধনঞ্জয় বিশ্বাস (Corei13), Tahmid Hasan (Tahmid Hasan). Well done!

The average scores on the problems were (in order) 6.86, 8.31, 6.79, 9.17, 8.6, 7.81, 8.93, 6.4, 7.3, 3.5, 8.13 and 0.38

If you want to know your score for each problem or your rank send me a message/email.

Sourav Das (sourav das) was the highest scorer with 96 points. Other people who scored 80 or more are Mahi Nur Muhammad (*Mahi*), Tripto, ধনঞ্জয় বিশ্বাস (Corei13), Tahmid Hasan (Tahmid Hasan). Well done!

The average scores on the problems were (in order) 6.86, 8.31, 6.79, 9.17, 8.6, 7.81, 8.93, 6.4, 7.3, 3.5, 8.13 and 0.38

If you want to know your score for each problem or your rank send me a message/email.