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Anil Saigal 07/09/2008 FOR STUDENTS PROBLEM # 1 What is the approximate ratio of the area of the shaded square compared to the area of the large square? (See Fig. 1) FOR GROWNUPS PROBLEM # 2  Please send your solutions to anil@lokvani.com.
 Problem Solutions 06/26/08PROBLEM # 1 If 4 apples and 2 oranges equals $1 and 2 apples and 3 orange equals $0.70, how much does each apple and each orange cost? There are no quantity discounts. Solution: Apple cost 20 cents and oranges cost 10 cents. FOR GROWNUPS The sequence a_{1}, a_{2},... is geometric with a_{1} = a and commom ratio r, where a and r are positive integers. Given that log_{ 8} a_{1} + log_{ 8} a_{2} + ... + log_{ 8} a_{12} = 2006, find the number of possibleordered pairs (a, r). Solution: Congratulations to Anindya Basu, Aseem Chandawarkar, Sitaram Chandawarkar, Mahesh Danke, Shailesh Goregaokar, Roopesh Mathur, Prabhakar Nadkarni and Ashwin ShivaShankar, who were winners of the last set of puzzles.
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Fig. 1  
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