Don't help contest cheaters, please

darij grinberg

In the last time a sadly large number of people have posted problems from ongoing (!) competitions on MathLinks in the hope to obtain solutions to these problems "for free". Particularly, problems from the Vietnamese Mathematics&Youth magazine seem to be popular among these cheaters.

Here: http://www.nxbgd.com.vn/toanhoctuoitre/?p=7&id=6&ReportID=289&ph=25 you can find the latest few problems of Mathematics&Youth. The deadline for them is 15 October 2007. Please don't help anyone with any of these problems until that date!

Don't believe everyone who tells you that "the deadline is over". The user nmtvn has made false claims of this kind.

There has also been some cheating going on with problems from the Polish MO and with the Indian IMO TSTs. It would be nice if someone would post a link to the problems of such competitions in time before cheaters post the problems here. It would also be great if someone posts a link to the respective Mathematics&Youth problems when they come out so that cheating can be prevented in future.

To everyone who posted solutions to ongoing contest problems: when I see such solutions, I move them into a hidden forum in order to move them back. Some other moderators delete them instead. To all such moderators: Please, if you delete them, save them on your computer so that you can repost them later when the deadline is over! Otherwise, the authors of the solutions (who often didn't know that they were solving a problem from a running contest) get their posts deleted for apparently no reason, what is not quite a motivating experience.

Darij

**Posted:** Tue Oct 02, 2007 6:10 am

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Now the die is cast, the first step taken, a glimmer of hope lights up our lives
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pardesi

Thanks Darij
the users who have been posting the indian postal test problems are
chessfreak ,mnrc_2
and another one is suppose whom i am not getting
who has been warned sufficiently many times .
so please don't answer any of their questions before proper clarifications.

**Posted:** Tue Oct 02, 2007 10:34 am

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FUBAR -KVS

darij grinberg

Another nickname of probably the same Vietnam cheater: pavarotti.

dg

**Posted:** Sat Oct 06, 2007 1:38 am

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Now the die is cast, the first step taken, a glimmer of hope lights up our lives
Visions of the past, dreams forsaken forming right under our eyes
We are alive...

pardesi

another one is hoasua

**Posted:** Sat Oct 06, 2007 1:51 am

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FUBAR -KVS

hungkhtn

They are young kids, and actually, the "contest" in MY magazine of Vietnam is not so serious... so I think they will think back. Don't treat them too seriously too, since we are mature.

I am pretty sad because all the mentions here are about Vietnamese members. Hope that such a thing ends.

**Posted:** Sat Oct 06, 2007 2:05 am

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Vol 2 was officially come out

quangpbc

Some different members used to post M&Y problems : toan hoc , friendlist , Harry Potter... Mad

**Posted:** Sat Oct 06, 2007 5:36 am

darij grinberg

**Posted:** Sat Oct 06, 2007 5:43 am

_________________
Now the die is cast, the first step taken, a glimmer of hope lights up our lives
Visions of the past, dreams forsaken forming right under our eyes
We are alive...

darij grinberg

GUIDELINE FOR POLISH MO PROBLEMS

Polish MO problems: http://www.om.edu.pl/index2.php?poziom=9&main=zadania.php
Current Polish MO: http://www.om.edu.pl/zadania/om/om59_1.pdf

Even without knowledge of the language, you can identify most questions by the mathematical formulas included. You can translate the names of the months using the Polish wikipedia. The first series (I seria) is over now (deadline was 8 October 2007). I have moved some of the topics back. I am starting to delete some cheater topics which have received no reply.

RECOGNIZING CHEATERS

There is no common rule to recognize cheaters, but here are some observations I have done on some of them.

Cheaters don't hesitate to post the same problem over and over, opening up a new topic each time the older one is locked or deleted.

Sometimes they post their problems in regional fores where they hope that nobody will detect their cheating: Kisiu111 posted a Polish MO problem in the Georgia forum ( http://www.artofproblemsolving.com/Forum/viewtopic.php?t=167330 ; please delete the topic). Stupidly enough for them, problems are seldomly solved on regional fores, while there are still many watchful eyes.

Sometimes they claim false sources for their problems (Rand0m claims his problem comes from "USA california math classes", http://www.artofproblemsolving.com/Forum/viewtopic.php?t=165238 ; Hoasua claimed his - ongoing M&Y - problem was from Uzbekistan MO 1998, http://www.artofproblemsolving.com/Forum/viewtopic.php?t=169275 ).

What I found particularly cool was Kisiu111 posting a running contest problem, getting an answer from Loup Blanc and then starting another topic where he presented that answer as his own and asked for a proof.

If you see a problem posted in JPEG format rather than text, it is pretty likely that it is from an ongoing Mathematics&Youth problem sections. Some cheaters are even too lazy to write the problem in LaTeX and just cut it out of the JPEG file of the magazine.

Deleting one's post after it has been recognized as cheating has been practiced, too (I have just deleted such a topic).

Most of the cheaters seem to have a very poor understanding of mathematics and scrutinize every not completely trivial step in proofs ( http://www.artofproblemsolving.com/Forum/viewtopic.php?t=167995 ).

Cheaters are impatient because they have a deadline. If they don't get the help they want in time, or they can't understand the proofs because they are not detailed enough, they start crying around ("Can anybody help me, please?", "can anybody help me with this problem, please? I cannot do it anyway....", "So what about the answer?", "Noone can do it?", "For all: Do you have a more simple solution for this problem? The solution of mszew is very long and very difficult to understand!"), bumping up their topics.

Some get aggressive when their posts are revealed as cheating ( http://www.artofproblemsolving.com/Forum/viewtopic.php?t=165235 ), claiming nonsense like that the contest is open and anyone is allowed to help, but also attacking others who rightfully claim that the topic has to be locked ("You're very impolite? You think that you're good, do you? I don't need your solution!" - http://www.artofproblemsolving.com/Forum/viewtopic.php?t=168943 ).

Some claim that the deadline is over and thus the problem can be discussed when it is not so.

Some completely ignore posts revealing their problems as ongoing contest problems. Nmtvn has made himself a name here: Being told several times that his problem is from a current magazine contest, he continued reposting it answering "But there isn't any true and full solution in that topic! All of solutions are false or not full!" and "Where's the solution for your problem? Don't you have it, do you?". ( http://www.artofproblemsolving.com/Forum/viewtopic.php?t=167965 )

Almost as good: Knowing exactly why one's old topic was locked and then "returning" it. ( http://www.artofproblemsolving.com/Forum/viewtopic.php?t=168712 )

Don't expect cheaters to post exactly the same problem they got in the contest. Some will try to generalize the problem, often yielding complete nonsense; others will change notations (Kisiu111 posted the same Polish MO geometry question with 3 different ways to label the points).

Darij

**Posted:** Wed Oct 10, 2007 4:36 am

_________________
Now the die is cast, the first step taken, a glimmer of hope lights up our lives
Visions of the past, dreams forsaken forming right under our eyes
We are alive...

besmart · P versus NP Offline Joined: 18 Nov 2007 Posts: 29

thanks for the reminder

**Posted:** Wed Nov 21, 2007 5:10 pm

darij grinberg

thesunflower is another M&Y cheater. Thanks ZetaX for the info.

darij

**Posted:** Sun Jan 20, 2008 4:02 pm

_________________
Now the die is cast, the first step taken, a glimmer of hope lights up our lives
Visions of the past, dreams forsaken forming right under our eyes
We are alive...

darij grinberg

Can some Vietnamese here post a link to the official problem pages of Maths&Youth (the link in my first post only gives one issue) AND tell us the deadlines for the issues?

darij

**Posted:** Mon Feb 25, 2008 4:27 am

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Now the die is cast, the first step taken, a glimmer of hope lights up our lives
Visions of the past, dreams forsaken forming right under our eyes
We are alive...

darij grinberg

Hello,

I need your help:

From which sources (contests or journals) do the following problems come, and when are the respective deadlines? I have to decide whether to unhide them (they are currently in the hidden forum).

**Posted:** Fri Mar 07, 2008 3:42 pm

_________________
Now the die is cast, the first step taken, a glimmer of hope lights up our lives
Visions of the past, dreams forsaken forming right under our eyes
We are alive...

April

There are problems from the newest Mathematics and Youth Magazine (7/2008)

FOR LOWER SECONDARY SCHOOLS

T1/373. (For $6^{th}$ grade) Write the numbers $1$ , $2$ , $3$ , $\ldots$ , $2007$ in an arbitrary order and let $A$ be the resulting number. Can $A + 2008^{2007} + 2009$ be a perfect square?

T2/373. (For $7^{th}$ grade) Consider the following two polynomials $f(x) = (x - 2)^{2008} + (2x - 3)^{2007} + 2006x$ and $g(y) = y^{2009} - 2007y^{2008} + 2005y^{2007}$ . Let $s$ be denote the sum of all the coefficients of $f(x)$ (after expansion). Find $s$ , and the value of $g(s)$ .

T3/373. Find all positive integer solutions of the following system of two equations
$\begin{cases} x + y + z = 15 \\ x^3 + y^3 + z^3 = 495\end{cases}$
T4/373. Let $a$ , $b$ , $c$ be non-negative real numbers such that $a^2 + b^2 + c^2 = 1$ . Find the maximum value of the expression:

(a + b + c)^3 + a(2bc - 1) + b(2ca - 1) + c(2ab - 1)

T5/373. Given a triangle $ABC$ where $\angle ABC$ is not a right angle. Let $AH$ and $AM$ denote, respectively, the altitude and the median through vertex $A$ . Choose a point $E$ on the ray $AB$ and $F$ on the ray $AC$ such that $ME = MF = MA$ . Let $K$ be reflection point of $H$ over $M$ . Prove that four points $E$ , $M$ , $K$ and $F$ lie on a single circle.

FOR UPPER SECONDARY SCHOOLS

T6/373. Solve for $x$
$\sqrt {x + \sqrt {x^2 - 1}} = \frac {9\sqrt 2}{4}(x - 1)\sqrt {x - 1}$
T7/373. Prove that in any acute triangle $ABC$ , the following inequality holds
$\frac {\tan A}{\tan B} + \frac {\tan B}{\tan C} + \frac {\tan C}{\tan A}\ge\frac {\sin 2A}{\sin 2B} + \frac {\sin 2B}{\sin 2C...$
T8/373. The incircle of a triangle $ABC$ meets $BC$ , $CA$ , $AB$ respectively at $A_1$ , $B_1$ , $C_1$ . Let $p$ , $S$ , $R$ be respectively, half of the perimeter, the area and the circumradius of $\triangle ABC$ . Let $p_1$ be half of perimeter of $\triangle A_1B_1C_1$ . Prove the inequality $p_1^2\le\frac {pS}{2R}$ . When does equality occur?

TOWARDS MATHEMATICAL OLYMPIAD

T9/373. Let $A$ ( $A\subset \mathbb{N}$ ) be a non-empty set satisfying the condition: If $a\in A$ then $4a$ and $[\sqrt a]$ are also in $A$ (where $[x]$ denotes the integer part of $x$ ). Prove that $A = \mathbb{N}$ .

T10/373. Let $a$ be a natural number which is greater than $3$ and consider the sequence $(u_n)$ ( $n = 1, 2, \ldots$ ) defined inductively by $u_1 = a$ and $u_{n + 1} = u_n - \left[\frac {u_n}{2}\right] + 1$ for all $n = 1, 2, \ldots$ (where $\left[x\right]$ denotes the greatest integer that is $\leq x$ ). Prove that there exists $k\in\mathbb{N}^{*}$ such that $u_n = u_k$ for all $n\ge k$ .

T11/373. Find all polynomials with real coefficients $P(x)$ , $Q(x)$ and $R(x)$ such that $\sqrt {P(x)} - \sqrt {Q(x)} = R(x)$ for all $x\in\mathbb{R}$ .

T12/373. Let $ABCD$ be a tetrahedron with the centroid $G$ and the circumradius $R$ . Prove that
$GA + GB + GC + GD + 4R\ge\frac {2}{\sqrt 6}(AB + AC + AD + BC + CD + DB)$
And the dealine for submitting solutions is 15 September, 2008.

**Posted:** Sun Jul 20, 2008 5:43 am

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kunny

See here! http://www.artofproblemsolving.com/Forum/search.php?search_author=friendlist

**Posted:** Sun Jul 20, 2008 7:27 am

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Today's calculation of Integral Digest

zeikii · Hodge Conjecture Offline Joined: 05 Sep 2006 Posts: 66

http://www.nxbgd.com.vn/toanhoctuoitre/?p=7&id=6&ReportID=413&ph=37
the latest problems ^^. The deadline is two months from the day they were published.
It's not good for Vietnamese guys because this fact. I feel so sorry because i'm a Vietnamese student, too.

**Posted:** Fri Jul 25, 2008 3:29 am

mathwizarddude

Excuse me, but for this problem

T10/373. Let $a$ be a natural number wich is greater than $3$ and consider the sequence $(u_n)$ ( $n = 1, 2, \ldots$ ) defined inductively by $u_1 = a$ and $u_{n + 1} = u_n - \left[\frac {u_n}{2}\right] + 1$ for all $n = 1, 2, \ldots$ . Prove that there exists $k\in\mathbb{N}^{*}$ such that $u_n = u_k$ for all $n\ge k$ .

Why would there be a square bracket around $\frac {u_n}{2}$ and what does the asterisk as a superscript of $\mathbb{N}$ mean?

**Posted:** Sat Jul 26, 2008 11:04 pm

hsiljak

Brackets denote the floor function (if I'm not mistaken, i.e. $[a]=\lfloor a \rfloor$ ), and the asterisk should just be a thing of convention, denoting the fact that zero is not included in $\mathbb{N}$ .

**Posted:** Sat Jul 26, 2008 11:31 pm

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Engineer outside [mathematician inside].

April

There are problems from the newest Mathematics and Youth Magazine (8/2008)

FOR LOWER SECONDARY SCHOOLS

T1/374. (For $6^{th}$ grade) Find all triple of natural numbers $a$ , $b$ , $c$ less than $20$ such that $a(a + 1) + b(b + 1) = c(c + 1)$ , where $a$ is a prime number and $b$ is a multiple of $3$ .

T2/374. (For $7^{th}$ grade) Let $f(n) = \left(n^2 + n + 1\right)^2 + 1$ , where $n$ is a positive integer and let
$P_n = \frac {f(1)\cdot f(3)\cdot f(5)\cdots \f(2n - 1)}{f(2)\cdot f(4)\cdot f(6)\cdots f(2n)}$
Prove the inequality: $P_1 + P_2 + \cdots + P_n < \frac {1}{2}$

T3/374. Find the maximum value of the expression $T = \frac {\left(y + z\right)^2}{y^2 + z^2} - \frac {\left(x + z\right)^2}{x^2 + z^2}$ , where $x$ , $y$ , $z$ are real numbers such that $x > y$ , $z > 0$ and $z^2\ge xy$ .

T4/374. Solve for $x$ :
$\sqrt [3]{14 - x^3} + x = 2\left(1 + \sqrt {x^2 - 2x - 1}\right)$
T5/374. An acute triangle $ABC$ is inscribed in a fixed circle with center at $O$ . Let $AI$ , $BD$ , and $CE$ denote the altitudes through $A$ , $B$ , and $C$ respectively. Prove that the perimeter of he triangle $IDE$ does not change when $A$ , $B$ , and $C$ move on the circle $(O)$ such that the area of the triangle $ABC$ is always equal to $a^2$ .

FOR UPPER SECONDARY SCHOOLS

T6/374. Solve the system of equations $\begin{cases} \sqrt {x^2 + 91} = \sqrt {y - 2} + y^2 \\ \sqrt {y^2 + 91} = \sqrt {x - 2} + x^2\end{cases}$

T7/374. Let $a$ , $b$ , $c$ be real numbers such that $4\left(a + b + c\right) - 9 = 0$ . Find the maximum value of the expression:
$S = \left(a + \sqrt {a^2 + 1}\right)^b\left(\sqrt {b + \sqrt {b^2 + 1}\right)^c\left(c + \sqrt {c^2 + 1}\right)^a$
T8/374. Let $I$ and $O$ denote respectively the incenter and the circumcenter of a triangle $ABC$ . Given that $\measuredangle AIO = 90^{\circ}$ , prove that the area of the triangle $ABC$ is less than $\frac {3\sqrt 3}{4}AI^2$ .

TOWARDS MATHEMATICAL OLYMPIAD

T9/374. Let $a$ , $b$ , $n$ be positive integers, $b > 1$ and $a$ is a multiple of $b^{n} - 1$ . Rewritten $a$ to the base $b$ , prove that the resulting contains at least $n$ non-zero digits.

T10/374. Let $x$ , $y$ , $z$ be real numbers such that $0 < z\le y\le x\le 8$ and $3x + 4y\ge\max\left\{xy; \frac {1}{2}xyz - 8z\right\}$ . Find the maximum value of $A = x^5 + y^5 + z^5$ .

T11/374. Find all functions $f: \mathbb{R}\to \mathbb{R}$ such that $f\left(f(x) + y^2\right) = f^2(x) - f(x)f(y) + xy + x$

T12/374. Let $K$ denote the intersection of the two diagonals of a quadrilateral $ABCD$ where $\measuredangle ABC = \measuredangle ADC = 90^{\circ}$ and $AC = AB + AD.$ Prove that the radii of the inscribed of the triangles $ABK$ and $ADK$ are equal.

The dealine for submitting solutions is 15 October, 2008.

**Posted:** Fri Aug 15, 2008 4:33 pm

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"Mathematics, mathematics, mathematics. This much mathematics? No, more!" - Grigore Moisil

Allnames

**Posted:** Fri Aug 15, 2008 7:33 pm

great math

Anybody knows how to be ashamed when receiving any reminded information. Actually, I think we should have positive attitutes to keep a right and competitive environment of Mathematics where each ability is confirmed and achieved.

**Posted:** Fri Aug 15, 2008 11:00 pm

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$\left(\frac{a_{1}+a_{2}+...+a_{n}}{n} \right) \geq \sqrt[n]{a_1a_{2}a_{3}....a_{n}}$