For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
11/09/2010

PROBLEM # 1

Four men want to cross a bridge.  The bridge is of a width such that a 
maximum of 2 people may cross at a time. 

One man takes 10 minutes to cross, another takes 5 minutes to cross,
another takes 2 minutes to cross, and the last takes 1 minute to 
cross.
 
Let's call these men A, B, C, and D, respectively.

Here is the catch.  If two people cross the bridge together, they must 
walk at the pace of the slower one. So if A and B cross, they take 10 
minutes. Also, it is night. Each trip requires a flashlight.  There 
is only one flashlight. The men are not allowed to toss the light over 
the river.

How fast can you get all 4 men over the bridge?

PROBLEM #2

John has a miniature Pyramid of Egypt. It is 4 inches in height. John was invited to display it at an exhibition. John felt it was too small and decided to build a scaled-up model of the Pyramid out of material whose density is (1 / 3) times the density of the material used for the miniature. He did a "back-of-the-envelope" calculation to check whether the model would be big enough.

If the mass (or weight) of the miniature and the scaled-up model are to be the same, how many inches in height will be the scaled-up Pyramid?

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Problems from 10/28/10

PROBLEM # 1

What comes in place of the question mark(s) in the sequence below?
> < = = + > ? ? = +

SOLUTION
< =.

PROBLEM #2

Given f(2) = 3, g(3) = 2, f(3) = 4 and g(2) = 5, evaluate the composite function

(f _o g)(3)

SOLUTION
3.

Congratulations to Aseem Chandawarkar, Akshay Gowrishankar and Bharath Venkataraman, who were winners of the last set of puzzles.

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