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What is the number of ways can you cover a Nx2 board using 1x2 tiles....?? ...
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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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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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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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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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Your friend has two children. You meet one of them and find out that he is a boy. What is the probability that the other child is a girl? P.S. - A child can only be a boy or girl ...
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Is it possible to construct a continuous and differentiable curve in the cartesian plane such that both the co- ordinates can never be simultaneously rational ? take 0 < x,y <1 ...
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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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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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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. ...
