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With Casino Royale hitting the theatres, we thought it's time we followed the footsteps of Mr. Bond, and treat you with something that requires more style and oompph than the regular stuff.
So here we got four questions for you. Each question can be solved in many ways and might have solutions which can be lengthy. However, the deal is that the people with the best and the most stylish (a.k.a shortest) solution will walk away with cool goIIT T-shirts. So in order to solve the question, click on the attached forum/post link, and post your answers there for everyone else to see. So here we go..
ABC is a triangle and the equation of the sides AB, BC, CA are
a1 x + b1 y + c1 = 0 ….. (1)
a2 x + b2 y + c2 = 0 ….. (2)
a3 x + b3 y + c3 = 0 ….. (3)
Find the eqn. of the medians of the triangle, without solving for the vertices. [click here to answer]
Sixteen people are arranged around a circular table. Find the number of ways of selecting seven people so that no two of them are consecutive. [click here to answer]
Find the number of ways of distributing 30 identical balls in the three identical boxes, such that no box remains empty. [click here to answer]
From a point P (x1 , y1 ), tangents PA and PB are drawn to the circle x2 +y2 +2gx +2fy +c = 0
If P' and Q' are mid points of PA and PB respectively, find the equation of P'Q'. [click here to answer]
Moderator [dated 23-Jan-2007]: The contest is closed for action. Only one answer qualified for the prize. To see answer click here