Gopalgang higher hisec 2011 08
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Mehfuj Zahir
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S={1,2,3,.........,441}&X is a subset of S that no two member of X is a square less or equal to 21^2.What is the largest number of elements can X have?
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nafistiham
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Re: Gopalgang higher hisec 2011 08
this may go thus:
in $S$ there are $21$ squares.which all are less or equal to $21^2$ . again, we can have a square number like that. so the answers is $441-21+1=420$ which is the highest number of elements of $X$
in $S$ there are $21$ squares.which all are less or equal to $21^2$ . again, we can have a square number like that. so the answers is $441-21+1=420$ which is the highest number of elements of $X$
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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Re: Gopalgang higher hisec 2011 08
This solution is not correct...
eg 2+7=9... A SQUARE!!
The solution might be 221... But need a full solution!!
eg 2+7=9... A SQUARE!!
The solution might be 221... But need a full solution!!
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nafistiham
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Re: Gopalgang higher hisec 2011 08
vaia, i could not get where the problem is 
because the problem says "X is a subset of S that no two member of X is a square less or equal to 21^2"
the meaning of this i got is such "there is only one number in X which is less or equal to $21^2$ at most"
as it doesn't say 'summation or total of two numbers less or equal to $21^2$'
because the problem says "X is a subset of S that no two member of X is a square less or equal to 21^2"the meaning of this i got is such "there is only one number in X which is less or equal to $21^2$ at most"
as it doesn't say 'summation or total of two numbers less or equal to $21^2$'
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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Re: Gopalgang higher hisec 2011 08
আচ্ছা এখানে X এর ২টি সদস্যকে কি যোগ করতে বলেছে? যদি না বলে তাহলে নাফিসেরটা সঠিকLabib wrote:This solution is not correct...
eg 2+7=9... A SQUARE!!
The solution might be 221... But need a full solution!!
টা না হলে আরো ঝামেলা আচে।অম্লান সাহা
Re: Gopalgang higher hisec 2011 08
শিশির ভাই এর কম্পোজিং ভুল!
Please Install $L^AT_EX$ fonts in your PC for better looking equations,
Learn how to write equations, and don't forget to read Forum Guide and Rules.
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes
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"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes
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nafistiham
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Re: Gopalgang higher hisec 2011 08
আগে বলবেন না ! এখন তো অনেক জটিল হয়ে গেল । 
এখন, প্রতিটা বর্গ সংখ্যার partition বের করে সেগুলো বাদ দিতে হবে ।
অর্থাৎ,
$x^2=y+z$ হলে $y$ আর $z$ একসাথে থাকা যাবে না । আমি brute force ছাড়া তো পথ দেখতেছি না।
এখন, প্রতিটা বর্গ সংখ্যার partition বের করে সেগুলো বাদ দিতে হবে ।
অর্থাৎ,
$x^2=y+z$ হলে $y$ আর $z$ একসাথে থাকা যাবে না । আমি brute force ছাড়া তো পথ দেখতেছি না।
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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nafistiham
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Re: Gopalgang higher hisec 2011 08
may be this is the solution :
as it is said that summation of no two numbers can be $\leq 21^2$ and the largest member of $S$ id $441$
so the answer will be
\[\left \lfloor \frac{21^2}{2} \right \rfloor+1=221\]
i think there is some incompleteness of the solution .but, probably the way is right.
the incompleteness is we can add another number.which is $441$
so, the answer is
\[222\]
as it is said that summation of no two numbers can be $\leq 21^2$ and the largest member of $S$ id $441$
so the answer will be
\[\left \lfloor \frac{21^2}{2} \right \rfloor+1=221\]
i think there is some incompleteness of the solution
.but, probably the way is right.the incompleteness is we can add another number.which is $441$
so, the answer is
\[222\]
Last edited by nafistiham on Tue Dec 06, 2011 12:46 am, edited 1 time in total.
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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Mehfuj Zahir
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Re: Gopalgang higher hisec 2011 08
No compose was right . I have copied it from the original question
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nafistiham
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Re: Gopalgang higher hisec 2011 08
তাহলে তো সমাধানটা নিশ্চয়ই ওভাবেই হবে । তাই না ?
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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.