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For The Mathematically Inclined

Anil Saigal
04/22/2004

FOR CHILDREN

PROBLEM # 1

What is the least odd number you can obtain from the product of four prime numbers?

PROBLEM # 2

If the diameter of a circle is increased by forty percent, by what percent is the area of the circle increased?

FOR GROWNUPS

PROBLEM # 3
Let A(1), A(2), ... be a sequence with the following properties.

i) A(1) = 1, and
ii) A(2N) = N x A(N), for any positive interger N.

What is the value of A(2^100))?

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Please send your solutions to anil@lokvani.com.

Use "Problem Solutions M-050604" as the subject line. Please include your full name in the text of the main message. The first one to submit the right answer will be profiled 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 04/22/04

FOR CHILDREN

PROBLEM # 1

Find the smallest two-digit prime numbers whose digits are also prime?

SOLUTION
23.

PROBLEM # 2

Write 1,000,000,000 as the product of two positive integers, neither of which contains any zeros.

SOLUTION
1953125 x 512 = 1000000000.
FOR GROWNUPS

PROBLEM # #

A sequence of three real numbers forms an arithmetic prgression with a first term of 9. If 2 is added to the second term and 20 is added to the third term, the three resulting numbers form a geometric progression. What is the smallest possible value for the third term of the geometric progression? SOLUTION
49.

Congratulations Raca Banerjee, Sandeep Bansal, Ruby Dhillon, Prem Kapoor, Samita Mohanasundaram and Pooja Mutalik who were winners of the last set of puzzles.



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