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| For The Mathematically Inclined |
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. ------------------------------------------------------------------------------------------------------------- Solution: The sequence a1, a2,... is geometric with a1 = a and commom ratio r, where a and r are positive integers. Given that log 8 a1 + log 8 a2 + ... + log 8 a12 = 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.
Show that 10^2008 − 10^8 is divisible by 2008.
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PROBLEM # 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.
Apple cost 20 cents and oranges cost 10 cents.
FOR GROWNUPS
46 pairs.
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Fig. 1