For The Mathematically Inclined


Anil Saigal 01/14/2005
FOR CHILDREN
PROBLEM # 1
I am looking for a 5digit number where the sum of the ones and tens
digits is half of the tenthousands digit, the thousands digit is half
of the tenthousands 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. 
Please send your solutions to anil@lokvani.com.
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If you need clarification on any problem, please contact anil@lokvani.com.
 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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