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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
Show that 10^2008 − 10^8 is divisible by 2008.

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Please send your solutions to anil@lokvani.com.

Use Problem Solutions M-071008 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 06/26/08

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. 

Solution: 
Apple cost 20 cents and oranges cost 10 cents.

FOR
GROWNUPS 

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:
46 pairs.

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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