Could someone give me an easier IMO 6 ?

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nafistiham
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Could someone give me an easier IMO 6 ?

Unread post by nafistiham » Sat Mar 10, 2012 12:11 am

A father gave his sons a bunch of gold identical gold coins in his will.
the rule was such, the eldest son will get $1$ coin and $\frac {1}{7}$ of the remaining.
the next son will get $2$ coins and $\frac {1}{7}$ of the remaining.
the $3^{rd}$ son will get $3$ coins and $\frac {1}{7}$ of the remaining.
.
.
.
this goes on.
how many were the sons and how many gold coins did they get ?
:lol: :lol: :lol:
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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rakeen
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Re: Could someone give me an easier IMO 6 ?

Unread post by rakeen » Sun Mar 11, 2012 12:05 am

if it is only one then its correct.

the second son should get $\frac{62+6n}{49}$ coins(n is the total coin). Ive checked that for n=1 - 104 there is no such second son.
r@k€€/|/

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Re: Could someone give me an easier IMO 6 ?

Unread post by nafistiham » Sun Mar 11, 2012 12:14 pm

well, the only solution is $36$ coins
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
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rakeen
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Re: Could someone give me an easier IMO 6 ?

Unread post by rakeen » Sun Mar 11, 2012 1:26 pm

o yes..I made a mistake in my calc.
the first son would get $\frac{6+n}{7}$ coins and the second one would get $\frac{78+6n}{49}$ and so on untill we get #6 son! but that's also too messier.
r@k€€/|/

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Sazid Akhter Turzo
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Re: Could someone give me an easier IMO 6 ?

Unread post by Sazid Akhter Turzo » Sun Mar 11, 2012 4:03 pm

I can't believe that the 6th problem of IMO is so easy.

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nafistiham
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Re: Could someone give me an easier IMO 6 ?

Unread post by nafistiham » Sun Mar 11, 2012 5:49 pm

it is of the $7^{th}$ IMO
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Introduction:
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CSE Dept. SUST -HSC 14'
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*Mahi*
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Re: Could someone give me an easier IMO 6 ?

Unread post by *Mahi* » Sun Mar 11, 2012 7:00 pm

nafistiham wrote:it is of the $7^{th}$ IMO
That's why.
Please read Forum Guide and Rules before you post.

Use $L^AT_EX$, It makes our work a lot easier!

Nur Muhammad Shafiullah | Mahi

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sm.joty
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Re: Could someone give me an easier IMO 6 ?

Unread post by sm.joty » Sun Mar 11, 2012 7:45 pm

Sazid Akhter Turzo wrote:I can't believe that the 6th problem of IMO is so easy.
Just see IMO-1960 problem no-2 or IMO-1964 problem no-1 :)
I had a IMOphobia (phobia about IMO problems).
But one day I discover that IMO problems are not always SO HARD. :lol:
হার জিত চিরদিন থাকবেই
তবুও এগিয়ে যেতে হবে.........
বাধা-বিঘ্ন না পেরিয়ে
বড় হয়েছে কে কবে.........

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nafistiham
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Re: Could someone give me an easier IMO 6 ?

Unread post by nafistiham » Mon Mar 12, 2012 2:17 pm

Most the earlier IMO problems are really easy.
beginners like me should always start with them, I think
and then step up ahead.
It grows the confidence within
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Introduction:
Nafis Tiham
CSE Dept. SUST -HSC 14'
http://www.facebook.com/nafistiham
nafistiham@gmail

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sm.joty
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Re: Could someone give me an easier IMO 6 ?

Unread post by sm.joty » Mon Mar 12, 2012 2:49 pm

nafistiham wrote:Most the earlier IMO problems are really easy.
beginners like me should always start with them, I think
and then step up ahead.
It grows the confidence within
You're not beginner. ;)
হার জিত চিরদিন থাকবেই
তবুও এগিয়ে যেতে হবে.........
বাধা-বিঘ্ন না পেরিয়ে
বড় হয়েছে কে কবে.........

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