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Could someone give me an easier IMO 6 ?

Posted: Sat Mar 10, 2012 12:11 am
by nafistiham
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:

Re: Could someone give me an easier IMO 6 ?

Posted: Sun Mar 11, 2012 12:05 am
by rakeen
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.

Re: Could someone give me an easier IMO 6 ?

Posted: Sun Mar 11, 2012 12:14 pm
by nafistiham
well, the only solution is $36$ coins

Re: Could someone give me an easier IMO 6 ?

Posted: Sun Mar 11, 2012 1:26 pm
by rakeen
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.

Re: Could someone give me an easier IMO 6 ?

Posted: Sun Mar 11, 2012 4:03 pm
by Sazid Akhter Turzo
I can't believe that the 6th problem of IMO is so easy.

Re: Could someone give me an easier IMO 6 ?

Posted: Sun Mar 11, 2012 5:49 pm
by nafistiham
it is of the $7^{th}$ IMO

Re: Could someone give me an easier IMO 6 ?

Posted: Sun Mar 11, 2012 7:00 pm
by *Mahi*
nafistiham wrote:it is of the $7^{th}$ IMO
That's why.

Re: Could someone give me an easier IMO 6 ?

Posted: Sun Mar 11, 2012 7:45 pm
by sm.joty
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:

Re: Could someone give me an easier IMO 6 ?

Posted: Mon Mar 12, 2012 2:17 pm
by nafistiham
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

Re: Could someone give me an easier IMO 6 ?

Posted: Mon Mar 12, 2012 2:49 pm
by sm.joty
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. ;)