Could someone give me an easier IMO 6 ?
- nafistiham
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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
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Re: Could someone give me an easier IMO 6 ?
well, the only solution is $36$ coins
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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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.
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
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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Re: Could someone give me an easier IMO 6 ?
That's why.nafistiham wrote:it is of the $7^{th}$ IMO
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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
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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
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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 ?
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.........