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1. For which positive integer values of n, the set {1, 2, 3, 4, ... 4n} can be split into n distinct 4 elements subsets {a, b, c, d} such that a = (b +c + d)/3.
 

2.Given any four positive distinct real numbers, show that, one can choose 3 numbers A, B, C from among them such that, all the three quadratic equations have only real roots or all the three equations have only imaginary roots, where the equations are
Bx^2+x+C=0, Cx^2 +x+A=0, Ax^2 +x+B=0.

 

3.Given the 7-element set A = {a, b, c, d, e, f, g}. Find a collection T of 3-element subsets of A such that each pair of elements from A occurs exactly in one of the subsets of T.

 Jan 22, 2021
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1. This is possible for all even positive integers n.

 Jan 22, 2021

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