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For The Mathematically Inclined

Anil Saigal
01/14/2005

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?

FOR GROWNUPS

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

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Please send your solutions to anil@lokvani.com.

Use Problem Solutions M-012705 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 01/13/05

FOR CHILDREN

PROBLEM # 1
Start with a square piece of paper. Draw the largest circle possible inside the square, cut it out and discard the trimmings. Draw the largest square possible inside the circle, cut the square out and discard the trimmings. What fraction of the original square piece of paper has been cut off and thrown away?

SOLUTION
1/2.

FOR GROWNUPS

PROBLEM # 2
Observe the cube (Figure 1). Find the measure of angle ABC that is formed by the dashed segments.

SOLUTION
60 degrees.

Congratulations to
Mahesh Danke, Amar Gupta, Kirti Khandelwal, Nidhee Krishnan, Rohan Kulkarni, Shashank Mallick, Samir Mehta, Rishendra Naidoo, Rajiv Ramaratnam, Mukund Seshadri, and Ramya Tammisetti, who submitted correct solutions to  the last set of puzzles.



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In this Issue
For The Mathematically Inclined


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Figure 1

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