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| For The Mathematically Inclined |
Anil Saigal
09/28/2007
FOR CHILDREN
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?
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?
Please send your solutions to anil@lokvani.com.
Use Problem Solutions M-100407
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 # 1
A circle of radius 1 is surrounded by 4 circles of radius r, the centers of which form a square. What is r?
Solution:
1+ sqrt(2).
FOR GROWNUPS
Let n denote the smallest positive integer that is divisible by both 4 and 9, and whose base 10 representation consists of only 4's and 9's, with at least one of each. What are the last four digits of n?
Solution:
4944.
Congratulations to Aseem Chandawarkar, R. Dileepan, Shailesh Goregaonkar, Prabhakar Nadkarni and Rohit Malrani, who were winners of the last set of puzzles.
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