## Could someone give me an easier IMO 6 ?

- nafistiham
**Posts:**829**Joined:**Mon Oct 17, 2011 3:56 pm**Location:**24.758613,90.400161-
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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 ?

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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### 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.

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
**Posts:**829**Joined:**Mon Oct 17, 2011 3:56 pm**Location:**24.758613,90.400161-
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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.

Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.

### 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.

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
**Posts:**69**Joined:**Sat Feb 18, 2012 9:15 am**Location:**Sirajganj-
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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
**Posts:**829**Joined:**Mon Oct 17, 2011 3:56 pm**Location:**24.758613,90.400161-
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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.

Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.

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

That's why.nafistiham wrote:it is of the $7^{th}$ IMO

Please read Forum Guide and Rules before you post.

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

Nur Muhammad Shafiullah | Mahi

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

Nur Muhammad Shafiullah | Mahi

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

Just see IMO-1960 problem no-2 or IMO-1964 problem no-1Sazid Akhter Turzo wrote:I can't believe that the 6th problem of IMO is so easy.

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.........তবুও এগিয়ে যেতে হবে.........

বাধা-বিঘ্ন না পেরিয়ে

বড় হয়েছে কে কবে.........

- nafistiham
**Posts:**829**Joined:**Mon Oct 17, 2011 3:56 pm**Location:**24.758613,90.400161-
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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

beginners like me should always start with them, I think

and then step up ahead.

It grows the confidence within

Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.

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

You're not beginner.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

*হার জিত চিরদিন থাকবেই*

তবুও এগিয়ে যেতে হবে.........

বাধা-বিঘ্ন না পেরিয়ে

বড় হয়েছে কে কবে.........তবুও এগিয়ে যেতে হবে.........

বাধা-বিঘ্ন না পেরিয়ে

বড় হয়েছে কে কবে.........