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For The Mathematically Inclined


Anil Saigal 08/21/2006
FOR CHILDREN
PROBLEM # 1 There is
a pole in a lake. Onehalf of the pole is in the ground, another
onethird of it is covered by water, and 12 ft is out of the water.
What is the total length of the pole in ft? FOR GROWNUPS
PROBLEM # 2 Consider
a road with two cars, at a distance of 100 kilometers, driving towards
each other. The left car drives at a speed of 40 kilometers per hour
and the right car at a speed of 60 kilometers per hour. A bird starts
at the same location as the right car and flies at a speed of 80
kilometers per hour. When it reaches the left car it turns its
direction, and when it reaches the right car it turns its direction
again to the opposite, etcetera. What is the total distance that the
bird has traveled at the moment that the two cars have reached each
other?

Please send your solutions to anil@lokvani.com.
Use Problem Solutions M082406
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If you need clarification on any problem, please contact anil@lokvani.com.
 SOLUTIONS TO PROBLEMS ON 08/10/06
FOR CHILDREN
PROBLEM # 1 In the Tour de France, what is the position of a rider, after he passes the second placed rider? SOLUTION Second!
FOR GROWNUPS
PROBLEM # 2 A
rectangular room measures 7.5 meters in length and 3 meters in width.
The room has a height of 3 meters. A spider sits 25 centimeters down
from the ceiling at the middle of one of the short walls. A sleeping
fly sits 25 centimeters up from the floor at the middle of the opposite
wall. What is the shortest distance the spider has to walk (i.e., move
along the walls, floor, and ceiling only) to the fly to catch it? SOLUTION This is a tough one!
The
shortest path between the spider and the fly is the straight line AC.
Since AB has a length of 1.5+3+1.5 = 6 meters and BC has a length of
0.25+7.5+0.25 = 8 meters, AC has a length of 10 meters. Congratulations to Sandeep
Bansal, Ryan Bhattacharyya, Dinesh Dalal, Nari Deboo, Dattatraya Joshi,
Samita Mohan, Indira Nouduri, Sarthak Pani, Arun Saigal, Ramya
Tamisetti, Manan Thakkar and Bharati Venkatraman, who were winners of the last set of puzzles.

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