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For The Mathematically Inclined

Anil Saigal
06/05/2007

FOR CHILDREN AND GROWNUPS

PROBLEM # 1
Greengrocer C. Carrot wants to expose his oranges neatly for sale. Doing this he discovers that one orange is left over when he places them in groups of three. The same happens if he tries to place them in groups of 5, 7, or 9 oranges. Only when he makes groups of 11 oranges, it fits exactly. How many oranges does the greengrocer have at least?

PROBLEM # 2
Farmer Ram has a chicken farm. On a certain day, Ram calculates in how many days he will run out of chicken-food. He notices that if he would sell 75 of his chickens, he could feed the remaining chickens twenty days longer with the chicken-food he has, and that if he would buy 100 extra chickens, he would run out of chicken-food fifteen days earlier.

The Question: How many chickens does farmer Ram have?

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Please send your solutions to anil@lokvani.com.

Use Problem Solutions M-061407 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 05/31/07

FOR CHILDREN

PROBLEM # 1
In how many ways can a student pick 7 questions from 10?

SOLUTION
120. 

FOR GROWNUPS

PROBLEM # 2
In an exam a student needs to answer 7 questions out of 10. The student should pick   atleast 3 from first 5 questions.  How many ways can the student pick 7 questions?

SOLUTION 
110.

Congratulations to Sandeep Bansal, Anindya Basu, Somnath Chattopadhyay, Shailesh Goregaokar, Suhas Joglekar, Dattatraya Joshi, Mukkai Krishnamoorthy and Samir Mehta, who were winners of the last set of puzzles.



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