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For The Mathematically Inclined

Anil Saigal
01/27/2012

PROBLEM # 1
What are the next two numbers in this series?
1, 4, 8, 13, 21, 30, 36, 45, 54, 63, 73, ?, ?


PROBLEM # 2
What is Sin3θ in terms of Sinθ ?  (symbol is theta)


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Please send your solutions to mr.asaigal@gmail.com.

Use Problem Solutions M-020212 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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Problems from 1/19/12

PROBLEM # 1
A car travels downhill at 72 mph (miles per hour), on the level at 63 mph, and uphill at only 56 mph  The car takes 4 hours to travel from town A to town B.  The return trip takes 4 hours and 40 minutes.

Find the distance between the two towns.

SOLUTION 1
The distance between the two towns is 273 miles

 

PROBLEM #2
The sum of three numbers is 6, the sum of their squares is 8, and the sum of their cubes is 5.  What is the sum of their fifth powers?
 
That is, the sum of the fourth powers of the numbers is 0. 

SOLUTION 2

That is, the sum of the fourth powers of the numbers is 0.

Congratulations to Kishore Balsara, who was the winner of the last set of puzzles.



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