For The Mathematically Inclined

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 x-axis 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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