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For The Mathematically Inclined

Anil Saigal
08/21/2006

FOR CHILDREN

PROBLEM # 1
There is a pole in a lake. One-half of the pole is in the ground, another one-third 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?

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Please send your solutions to anil@lokvani.com.

Use Problem Solutions M-082406 as the subject line. Please include your full name in the text of the main message. Everyone with the right answer will be acknowledged in the next issue of Lokvani.

Please do not post your solution in Post Comments. No credit will be given for solutions not sent to anil@lokvani.com.

If you need clarification on any problem, please contact anil@lokvani.com.

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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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