## Could someone give me an easier IMO 6 ?

For discussing Olympiad Level Combinatorics problems
nafistiham
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### Could someone give me an easier IMO 6 ?

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 ?
$\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0$
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rakeen
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### Re: Could someone give me an easier IMO 6 ?

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€€/|/

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

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.

rakeen
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### Re: Could someone give me an easier IMO 6 ?

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€€/|/

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

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

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

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.

*Mahi*
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### Re: Could someone give me an easier IMO 6 ?

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

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

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.
হার জিত চিরদিন থাকবেই
তবুও এগিয়ে যেতে হবে.........
বাধা-বিঘ্ন না পেরিয়ে
বড় হয়েছে কে কবে.........

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

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.

sm.joty
Posts: 327
Joined: Thu Aug 18, 2011 12:42 am
Location: Dhaka

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

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.........