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For The Mathematically Inclined

Anil Saigal
02/18/2005

FOR CHILDREN

PROBLEM # 1
A number is called a pretty number if it has exactly 3 different whole number factors. For example, the factors of 4 are 1, 2, and 4 since 1 x 4 =4 and 2 x 2 = 4. The factor 2 is not counted twice. What is the sum of all the pretty numbers between 0 and 50?

FOR GROWNUPS

PROBLEM # 2
A video tape can record two hours on short play (SP), four hour on long play (LP) and six hours on extra long play (ELP). After recording 32 minutes on SP and 44 minutes on LP, how many minutes can it record on ELP?

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Use Problem Solutions M-022405 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 02/10/05

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?

SOLUTION
45.

FOR GROWNUPS

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

SOLUTION
Cos(5x) = 1/2 or -1, so 5x = (1/3, 1, 5/3)pi, so average 5x=pi and
average x=pi/5.

Congratulations to Sandeep Bansal, Mahesh Danke, Srikanth Gopalan, Nidhee Krishnan, Swathi Krishnan, Hareesh Mehta, Mahesh Murali, Sarthak Pani, Preeti Rangaraj, Arun Saigal, Neha Sharma, Ramya Tammisetti and Manan Thakkar, who were winners of the last set of puzzles



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