# Recently Active Olympiad Stuff Questions

• For n >=4 points in a plane , such that distance between any 2 points is an integer, prove that there are at least 1/6 distances , which are divisible by 3 ...
• Let AN be any line drawn through A in a Triangle ABC. Let BM, CN perpendiculars are drawn from B and C to AN and let D be the mid-point of BC, prove that MD = ND. ...
replied2012-06-03 01:30:11
• Consider a n*n chessboard. A person moves along the lines of the chessboard such that the sum in the y axis is greater than or equal to the sum in the x axis. Find the number of ways of going from one corner to the other corn ...
replied2012-06-03 00:59:57
• 1) Find the last 3 digits of 9999... ...
replied2012-05-29 03:03:55
replied2012-05-20 07:27:13
• *Image* Ans a *Image* Ans d ...
replied2012-05-03 20:26:40
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replied2012-02-16 07:56:39
replied2012-02-05 09:44:05
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replied2012-02-02 15:29:23
• G.C.D of (m,n)=1 1) x â‰¡3 (mod n) x â‰¡2 (mod m) Find x. Got it from a frnd. ...
replied2012-01-31 10:17:31
• *Image* Find the mistake.... ...
replied2012-01-24 23:32:44
• 1) Show that [5x]+ [5y] is greater than or equal to [3x+y] + [3y+x] where x,y greater than or equal to 0.. ...
replied2012-01-20 08:29:37
• Determine the largest number in the infinite sequence 1^1/1 , 2^1/2 , 3^1/3 , 4^1/4 , ............ n^1/n ...
replied2012-01-18 08:44:16
• here is a 3 x 3 square.... *Image* how many triangles can be formed with the dots being the three vertices of the triangle?? ...
replied2012-01-18 04:42:47
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replied2012-01-10 19:45:44
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replied2012-01-10 05:01:17
• 1) Find the last digit of ((5!+9)(6!+4))100! How do we do these types of sums? i think we can't do this by taking modulo 10... ...
replied2012-01-09 21:30:35
• 1)Find the number of isosceles triangles with integer sides if no side exceeds 1994. ...
replied2012-01-08 07:08:03
• Src: AOPS *Image* ...
replied2012-01-05 07:33:28
• P is an interior point of an equilateral \Delta ABC so that *Image* , and BP and CP meet AC and AB at D and E respectively. Suppose that PB : PC = AD : AE. Find \angle BPC . ...
• Here are the problems of RMO 2011 *Image* Source: Mathlinks. ro ...
replied2011-12-26 07:23:09
• Prove that for $$a,b,c>0$$ $$\frac{1}{2a^{2}+bc}+\frac{1}{2b^{2}+ca}+\frac{1}{2c^{2}+ab}\leq \left( \frac{a+b+c}{ab+bc+ca}\right) ^{2}.$$ ...
replied2011-12-25 03:44:01
• Start with the set S - { 3 , 4 , 12 } . In each step , you may chose two numbers " a " and " b " from S and replace " ( . 6 a - . 8 b) " by " ( . 8 a + . 6 b ) " . Can you form a set P - { 4 , 6 , 12 } by finitely many steps ...
replied2011-12-02 20:54:26
• You have bought n chocolates from a shop. Now the shopkeeper offers that if you return the wrappers, then for every 3 wrappers, he will give you 1 more chocolate. And you can continue this exchange offer until you run out of ...
replied2011-11-25 10:15:56
• Find all functions p:\mathbb{Z}\Rightarrow\mathbb{Z} such that p(x^2+1)=p(x)^2+1 . ...
replied2011-11-16 23:33:31
• \lfloor\dfrac{r+19}{100}\rfloor+\lfloor\dfrac{r+20}{100}\rfloor+....+\lfloor\dfrac{r+91}{100}\rfloor=546 Find \lfloor r \rfloor ...
replied2011-11-16 10:37:48
• A natural number is called "nice" if it is the product of its distinct proper divisors. Find the sum of first 10 nice numbers. ...
replied2011-11-16 08:14:33
• ABC is a triangle. The tangent to the circumcircle at A meets the line BC at D. The perpendicular to BC at B meets the perpendicular bisector of AB at E, and the perpendicular to BC at C meets the perpendicular bisector of AC ...
replied2011-11-13 06:35:08
• Let A = \sum_{n=1}^{10000} \dfrac{1}{\sqrt{n}} Determine [A]. Here [.] denotes the greatest integer function. ...
replied2011-11-09 05:09:37
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