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For The Mathematically Inclined

Anil Saigal
10/16/2007

FOR CHILDREN

PROBLEM # 1
If you expand (a + b)^4, what is the coefficient of a^2 b^2?

FOR GROWNUPS 

PROBLEM # 2
Find the equation of a plane through P(5,1,4) and parallel to the plane with equation x + y -2z = 0.

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Please send your solutions to anil@lokvani.com.

Use Problem Solutions M-101807 as the subject line. Please include your full name in the text of the main message. Everyone with the right answer will be acknowledged in the next issue of Lokvani.

Please do not post your solution in Post Comments. No credit will be given for solutions not sent to anil@lokvani.com.

If you need clarification on any problem, please contact anil@lokvani.com.

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Problem Solutions 10/04/07

PROBLEM # 1
Your house has 3 bedrooms. Each bedroom is 12 feet long, 10 feet wide and 8 feet high. You must paint the walls of all the bedrooms. Doorways and windows will not be painted occupy 60 square feet in each bedroom. How many square feet of wall must be painted?

Solution:
876 sq.ft.
 

FOR GROWNUPS 

PROBLEM # 2

A pyramid with a square base is cut by a plane that is parallel to the base and is 2 units from the base. The surface area of the smaller pyramid that is cut from the top is half the surface are of the original pyramid. What is the height of the original pyramid?

Solution: 
4 + 2 sqrt(2). 


Congratulations to
Janani Baskaran, Aseem Chandawarkar, Nihal Gowravaram, Niket Gowravaram, Prabhakar Nadkarni, Dhruv Ramanujan and Mukund Seshadri, who were winners of the last set of puzzles.





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