PROBLEM # 1

Three tennis balls snugly fit in a cylindrical can. The balls touch the side, top and bottom of the can. What is the ratio of the volume of the balls to the volume of the space in the can that is around the tennis balls.

PROBLEM # 2

How many rectangles and squares are there in a standard 8x8 chessboard? Please include all possible rectangles and squares, not just the smallest ones. Also, try to think of a shortcut way to do this - don't just manually count all possibilities.

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Please send your solutions to both problems to anil@lokvani.com.

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SOLUTIONS TO PROBLEMS ON 4/10/03

PROBLEM # 1

There are two trains hurtling towards each other on a straight piece of track. They are 100 miles apart at the time of this puzzle. A dragonfly starts off from the headlamp of train A and flies towards train B at a speed of 225 miles per hour; when it reaches train B it immediately reverses course and flies towards train A. It keeps doing this (i.e. fly back and forth) till the two trains collide and it passes away to the netherworld.

The trains are each traveling at a speed of 50 miles per hour. What is the total distance traveled by the dragonfly?

Lifestyle hint: If you are summing infinite series to get the answer, you are working too hard.

SOLUTION

225 miles

PROBLEM # 2

What is the greatest number of pieces of pizza you can get if you cut a circular pizza with 5 straight cuts?

SOLUTION

16

About the Winner(s)

Abhijit Bhadra is a networking software professional working in Marlboro area. His hobbies include music, cricket and literature.

Rahul Shukla is an engineer turned business analyst from New Delhi with a great passion for music, dance and brain teasers :-) and enjoys meeting new people.

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