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?

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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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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