Narayanganj Higher Secondary 2014 P5
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Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
 samiul_samin
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 Joined: Sat Dec 09, 2017 1:32 pm
Narayanganj Higher Secondary 2014 P5
Every participants of a picnic are given a lottery coupon. The coupons are numbered from $1$ and consequently. The winner’s coupon number, and the all coupons number are added and the sum is $2610$. What is the number of coupon which was winner?

 Posts: 62
 Joined: Sun Mar 30, 2014 10:40 pm
Re: Narayanganj Higher Secondary 2014 P5
$1+...+10=55$
$11+...+20=100+55$
$21+...+30=200+55$
$31+...+40=300+55$
$41+...+50=400+55$
$51+...+60=500+55$
$61+...+70=600+55$
Adding=> $100(1+...+6)+55\times7=2485$
Now, $26102485=125$, which is not possible.
Adding $71$ to $2485$, the summation of all the coupon numbers become $2556$.
Therefore, the winning coupon number is $54$.
$11+...+20=100+55$
$21+...+30=200+55$
$31+...+40=300+55$
$41+...+50=400+55$
$51+...+60=500+55$
$61+...+70=600+55$
Adding=> $100(1+...+6)+55\times7=2485$
Now, $26102485=125$, which is not possible.
Adding $71$ to $2485$, the summation of all the coupon numbers become $2556$.
Therefore, the winning coupon number is $54$.