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For The Mathematically Inclined

Anil Saigal
02/01/2005

FOR CHILDREN

PROBLEM # 1

If you add the consecutive counting numbers starting with one, what number will make the sum be equal to or more than 1,000?

FOR GROWNUPS

PROBLEM # 2
If cos(10x) + cos(5x) = 0, 0< x < 2.2 pi, find the exact average of all solution for x.

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Please send your solutions to anil@lokvani.com.

Use Problem Solutions M-021005 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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SOLUTIONS TO PROBLEMS ON 01/27/05

FOR CHILDREN

PROBLEM # 1
I am looking for a 5-digit number where the sum of the ones and tens digits is half of the ten-thousands digit, the thousands digit is half of the ten-thousands digit, and the tens digit is half of the hundreds digit. What is the number?

SOLUTION
 84422 or 84631.

FOR GROWNUPS

PROBLEM # 2
Given sec(A) = 41/40 and sin(A)< 0, express cot (A - 90) as a fraction in lowest terms.

SOLUTION
 9/40.

Congratulations to Aneesh Anand, Giridhar Anand, Anirudh Arun, Sandeep Bansal, Mahesh Danke, Dattaraya Joshi, Nidhee Krishnan, Rohan Kulkarni, Sameer Mehta, Hareesh Mitra, Pooja Murali, Sarthak Pani, Kunaal Patel, Rajiv Ramaratnam, Arun Saigal, Manan Thakkar and Bharath Venkataraman, who were winners of the last set of puzzles



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