Search found 172 matches

by Zzzz
Fri Jan 28, 2011 6:53 pm
Forum: Social Lounge
Topic: Dhaka Divisional
Replies: 5
Views: 2406

Re: divisional

Can't wait !!
by Zzzz
Fri Jan 28, 2011 6:51 pm
Forum: Junior Level
Topic: 5=4 ! ! ! ! !
Replies: 13
Views: 15535

Re: 5=4 ! ! ! ! !

আমরা ১০ ভিত্তিতে সাধারণত গণনা করি। এর অর্থ আমরা যদি লিখি ২৩, এর মানে বুঝায় ২ বার ১০ যোগ করে আরো ৩ যোগ করা হইছে। ছোটবেলায় যেমন পড়ছি ২ দশ ৩ =২৩. আবার ৫৪৬ বলতে বুঝায় ৫ বার $১০^২$ যোগ করে ৪ বার ১০ যোগ তার সাথে ৬ যোগ। একইভাবে $৭২৩৪৬= ৭\times ১০^৪+২\times ১০^৩+৩\times ১০^২+৪\times ১০ + ৬$ যদি বলা হইত ...
by Zzzz
Fri Jan 28, 2011 2:27 pm
Forum: Junior Level
Topic: 5=4 ! ! ! ! !
Replies: 13
Views: 15535

Re: 5=4 ! ! ! ! !

The question was :
"If $\frac {10}{2}=4$, then $5 \times 2=?$"
by Zzzz
Thu Jan 27, 2011 6:28 pm
Forum: Higher Secondary Level
Topic: Find Combinatorial Interpolation
Replies: 3
Views: 1704

Re: Find Combinatorial Interpolation

Just got another proof that doesn't need that identity. Let $A$ be set of $n$ elements. Now, how many subsets are there which contain $3$ or $4$ elements? Let $m$ be the answer. If we take any $2$ subsets of $2$ elements, their union will be either a $3$-element subset or a $4$-element subset. $\bin...
by Zzzz
Thu Jan 27, 2011 1:34 pm
Forum: Secondary: Solved
Topic: Dhaka Secondary 2010/6
Replies: 7
Views: 3211

Re: Dhaka Secondary 2010/6

We should prove that 3 is only such prime. If $N+1=k^2$ then $N=k^2-1 \Rightarrow N=(k-1)(k+1)$ as $N$ is prime, $k-1=1\ \ \therefore k=2$ how did it become? $(k-1)(k+1)=N as N is a prime, so (k-1)=1 . . . ? k+1 and k-1 both are factors of a prime number. Each prime number has only two factors - 1 ...
by Zzzz
Thu Jan 27, 2011 1:22 pm
Forum: Site Support
Topic: নীল রঙের আধিক্য :(
Replies: 12
Views: 5492

Re: নীল রঙের আধিক্য :(

অনেক দিন পর আসলাম। এই মুহূর্তে দেখতে তো ভালই লাগে ...
by Zzzz
Thu Jan 27, 2011 1:11 pm
Forum: Secondary: Solved
Topic: Dhaka Secondary 2009/4
Replies: 3
Views: 4500

Re: Dhaka Secondary 2009/4

Nice problem ..
$(1- \frac {1}{n^2})= \frac {(n+1)(n-1)}{n^2}$ Now where can we find a $(n-1)$ and a $(n+1)$ as denominator? ;)
by Zzzz
Thu Jan 27, 2011 12:58 pm
Forum: Algebra
Topic: Calculate value of expression.
Replies: 1
Views: 1146

Re: Calculate value of expression.

\[\left(\frac{a}{b-c}+\frac{b}{c-a}+\frac{c}{a-b}\right).\left(\frac{b-c}{a}+\frac{c-a}{b}+\frac{a-b}{c}\right) \] \[= \frac {a(c-a)(a-b)+b(a-b)(b-c)+c(b-c)(c-a)}{(a-b)(b-c)(c-a)}\cdot \frac {bc(b-c)+ca(c-a)+ab(a-b)}{abc}\] \[= \frac {a(c-a)(a-b)+b(a-b)(b-c)+c(b-c)(c-a)+ 9abc - 9abc}{(a-b)(b-c)(c-a)...
by Zzzz
Thu Jan 27, 2011 12:05 pm
Forum: H. Secondary: Solved
Topic: Dhaka Higher Secondary 2010/11
Replies: 1
Views: 1699

Re: Dhaka Higher Secondary 2010/11

The solution was posted here (it was a regular n gon with m points on each side). (From the post) If we choose any two points that are not on same side of the $n\ gon$ then we will find a straight line. Lets number the sides of $n\ gon$ with $1,2,3,...,n$. Start with side $1$. For each of the $m$ po...
by Zzzz
Thu Jan 27, 2011 11:18 am
Forum: Higher Secondary Level
Topic: Find Combinatorial Interpolation
Replies: 3
Views: 1704

Re: Find Combinatorial Interpolation

Can I use this identity:\[\binom {n}{r}=\binom {n-1}{r} +\binom {n-1}{r-1}\] ?
I can prove this identity using combinatorial interpolation :roll: