Unanswered Olympiad Stuff Questions

suppose there are 997 points given in a plane. if every two points are joined by a line segment with its mid point coloured in red, show that there are atleast 1991 red points in the plane. can u find a special case with exac ...

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A town has several clubs. Given any two residents there is exactly one club that both belong to. Given any two clubs, there is exactly one resident who belongs to both. Each club has at least 3 members. At least one club has ...

Find all positive integral solutions (a,b,c) to the equation (a+1)(b+1)(c+1)=2(abc + 1) ...

Find all positive integral solutions (a,b,c) to the equation (a+1)(b+1)(c+1)=2(abc + 1) ...

Twenty-one girls and twenty-one boys took part in a mathematics competition. It turned out that (i) each contestant solved at most six problems, and (ii) for each pair of a girl and a boy, there was at least one problem that ...

A device consists of 4n elements, any two of which are joined by either a red or a blue wire. The numbers of red and blue wires are the same. The device is disabled by removing two wires of the same color connecting four di e ...

sveral numbers are written in a row. in each move, john choses any 2 adjacent numbers in which one on the left is greater than one on the right, doubles each of them and switches around. prove that roberts cn make only a fini ...

Could anyone please post a copy of all B.Stat Subjective Questions? ...

For any natural number n≥2, find out which of the real positive numbers a and b is greater, knowing that an=a+1 and b2n=b+3a. ...

Prove that there are infinitely many primes congruent to 9 mod 10. ...

Prove that: \begin{vmatrix}\frac{1}{p+1}&\frac{1}{p+2}&\ldots &\frac{1}{p+n}\\ \frac{1}{p+2}&\frac{1}{p+3}&\ldots &\frac{1}{p+n+1}\\ \vdots &\vdots &\ddots &\vdots\\ \frac{1}{p+n}&\frac{1}{p+n+1}&\ldots &\frac{1}{p+2n-1}\end{ ...

prophet sir .. have a try at this one :) Each of the boys A and B tells the teacher a positive integer but neither of them knows the other`s number.The teacher writes 2 distince positive integers on the blackboard and announc ...

Well, Actually I don't know anything on how to solve such type of problems. Can anyone suggest any article or make a post for better understanding on how to approach such problems. Thanks! ...

*Image* ABCD is a prallelogram. Vertex D meets the side BC when produced to E such that LDEC = 90° and LDCB = 150°. A person starts from E and reaches C with some speed in time t seconds and then from C to B and again from ...

i am from 10 std. i got 35 marks in rmo and was selected for inmo on 6th feb 2011.how should i prepare?please help ...

please tell me about any olympiads which undergraduates may appear for. ...

Find the number of 4-digit numbers(in base 10) having non-zero digits and which are divisible by 4 but not by 8. ...

Find three distinct positive integers with the least possible sum such that the sum of the reciprocals of any two integers among them is an integral multiple of the reciprocal of the third integer. ...

1. In a race course there are 5 tracks .In how many minimum number of chances can you find out the fastest three horses, if there were 25 horses initially. 2. Can you use all 9 numerals - 1, 2, 3, 4, 5, 6, 7, 8 and 9 - above ...

Two of the squares of a 7X7 checkboard are painted yellow. and the rest are painted green..two color schemes are said to be equivalent if one can be obtained from the other by a rotation of the board...how many inequivalent s ...

Given four points A_{1}, A_{2}, A_{3}, A_{4} in the plane, no three collinear, such that \ A_{1}A_{2}\cdot A_{3}A_{4}= A_{1}A_{3}\cdot A_{2}A_{4}= A_{1}A_{4}\cdot A_{2}A_{3} denote by O_i the circumcenter of \triangle A_{j}A_ ...

*Image* sine rule can help too... ...

In a regular pentagon, if the length of each side is a and that of each diagonal is b then find the numerical value of a2/b2 + b2/a2 Note : you are not allowed to use trigonometry in this..!! maybe complex can help ...

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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 . ...

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 ...