For The Mathematically Inclined


Anil Saigal 07/22/2009
PROBLEM # 1 Using a balance scale and four weights you must be able to balance
any integer load from 1 to 40. How much should each of the four
weights weigh?
PROBLEM #2 A circle whose center is (1,r) is tangent to xaxis and to the curve y = x^2 in the first quadrant. Determine r to the nearest hundredth.
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 Problem Solutions 07/09/09
PROBLEM # 1 A bartender has a three pint glass and a five pint glass. A customer walks in and orders four pints of coke. Without a measuring cup but with an unlimited supply of coke how does he get four pints in either glass?
Solution: Call the two glasses A (5 pints) and B (3). Fill B and pour into A twice leaving A and B with 5 and 1 pint resp. Now empty A. Pour out contents of B (1 pint) into A. Now fill out B and empty its contents (3 pints) into glass A. Now Glass A contains 4 pints as required.
PROBLEM #2 Let x be in radians with 0<x<pi/2. If sin(2sin(x)) = cos(2cos(x)), then tan(x) + cot(x) can be written as a / (b  pi^c) where a, b, and c are positive integers. Compute the sum (a+b+c).
Solution: 50.
Congratulations to Suman Luthra, Prabhakar Nadkarni andNikhil Nathwani, who were the winner of the last set of puzzles.

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