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For The Mathematically Inclined


Anil Saigal 08/31/2004
PROBLEM # 1
How old would you be in years if you lived 1,000,000 hours? FOR GROWNUPS
PROBLEM # 2
One angle of a traingle has a measure of x. The sides are
sin(x), cos(x) and tan (x) and the product of the sides is
1/4. Determine the cosine of the largest angle. 
Please send your solutions to anil@lokvani.com.
Use Problem Solutions M090904 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.
 SOLUTIONS TO PROBLEMS ON 08/26/04
FOR CHILDREN
PROBLEM # 1
A man decides to buy a nice horse. He pays $60 for it, and he is very content with the strong animal. After a year, the value of the horse has increased to $70 and he decides to sell the horse. But already a few days later he regrets his decision to sell the beautiful horse, and he buys it again. Unfortunately he has to pay $80 to get it back, so he loses $10. After another year of owning the horse, he finally decides to sell the horse for $90. What is the overall profit the man makes?
SOLUTION
$ 20.
FOR GROWNUPS
PROBLEM # 2
There are 12 coins. One of them is false; it weights differently. It is not known, if the false coin is heavier or lighter than the right coins. How do you find the false coin by three weighs on a simple scale?
SOLUTION
1. Divide the coins into 3 groups of 4, say A,B, C
2. Weigh A and B
Case I: A and B are equal.
Now weigh 3 coins of A and C, Lets call them
A1 and C1
(a)If they are equal, then the remaining coin
in C (not in C1)is the odd one
(b)If they are different, say A1 weighs more
than C1, weigh two coins in C1.If these
weigh the same , the remaining coin in c1
is the odd man out. If they are different
then the lighter coin in c1 is the odd man
out.
Congratulations to Beena Krishnan, Nidhee Hrishnan, Anupa M. and Rajiv Ramaratnam, who were winners of the last set of puzzles.

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