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i am excited to see the solution: (a-b)(b-c)(c-a)=a^{2}+b^{2}+c^{2} ...
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solve the following: tanx-sinx=\frac{x^{3}}{2} ...
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Six people sit around a circular table. In how many ways can three pairs of people shake hands so that no arms cross (nobody shakes hands with two people at the same time)? ...
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Provided n^3 unit cubes, n > 1 which are numbered from 1 to n^3. All these unit cubes are put together to form a cube with side length n. In this cube two unit cubes will be neighbors if they share at least one vertex. As ...
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http://www.ajorza.org/wimo/images/mathfiles/files/resources/intseq.pdf ...
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After elections, each senator in the CaliMass Congress has an absolute rating (the number of voters for example - anyway a positive number). Each of these senators enters in a committee in which he obtains a relative rating. ...
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[we're 2005 while writing] According to a legend there is a monster that awakes every now and then to swallow everyone who is solving this problem, and then falls back asleep for as many years as the sum of the digits of that ...
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Is it possible to number the 8 vertices of a cube from 1 to 8 in such a way that the value of the sum on every edge is different? ...
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Prove that there are no perfect squares in the array below: 11 111 1111 ... 22 222 2222 ... 33 333 3333 ... 44 444 4444 ... .. .. .. 99 999 9999 ... ...
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Four couples play chess together. For the match, they're paired as follows: ("man Clara" indicates the husband of Clara, etc.) Bea ≡ Eddy An≡ man Clara Freddy ≡woman Guy Debby ≡ man An Guy ≡ woman Eddy Who is Hubert ...
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Given a cube in which you can put two massive spheres of radius 1. What's the smallest possible value of the side - length of the cube? Prove that your answer is the best possible. ...
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Let a and b be two primes having at least two digits, such that a > b. Show that 240 divides a4-b4. ...
