Problem 7:
You can very easily check that sum of three consecutive integers is three times the second number. Similarly, sum of five consecutive numbers is five times the third number, sum of seven consecutive numbers is seven times the fourth number and so on. What is the smallest even number that can be expressed as sum of three consecutive integers, sum of five consecutive integers and also sum of eleven consecutive integers?
BdMO National Primary 2011/7
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learn how to write equations, and don't forget to read Forum Guide and Rules.
Re: BdMO National Primary 2011/7
The answer is 330
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Tahmid Hasan
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Re: BdMO National Primary 2011/7
$k-1+k+k-1=3k$
$k-2+k-1+k+k+1+k+1=5k$
$k-6+.......k+6=11k$
so we have to find the smallest even number divisible by $3,5,11$
so the answer is $2.3.5.11=330$
$k-2+k-1+k+k+1+k+1=5k$
$k-6+.......k+6=11k$
so we have to find the smallest even number divisible by $3,5,11$
so the answer is $2.3.5.11=330$
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