Search found 25 matches

by Mahfuz Sobhan
Sun Aug 02, 2015 6:06 pm
Forum: Secondary Level
Topic: combinatorics
Replies: 20
Views: 3168

combinatorics

There are 9 committees with each committee having 20 members and any two committee have 5 members in common then find the minimum number of distinct members in this group.....
by Mahfuz Sobhan
Wed Jul 15, 2015 12:19 pm
Forum: Secondary Level
Topic: number theory
Replies: 1
Views: 1048

number theory

Let us define $$S_n$$ to be the set of all integers divisible by $$2014^n$$ but not $$2014^n+^1$$ where $$n$$ is a non-negative integer. What is the value of $$n$$ (if any) so that $$500!$$ belongs to $$S_n$$. :?:
by Mahfuz Sobhan
Fri Jul 10, 2015 2:04 am
Forum: Secondary Level
Topic: 2014-national
Replies: 15
Views: 4802

Re: 2014-national

no bhai. i did not solve it. i need help
by Mahfuz Sobhan
Wed Jul 08, 2015 7:20 pm
Forum: Secondary Level
Topic: Sylhet - 2014
Replies: 2
Views: 1217

Sylhet - 2014

A book has some page missing consecutively. The sum of the page number of
missing pages is ${976}$. How many pages are missing there?
:?: :roll:
by Mahfuz Sobhan
Wed Jul 08, 2015 6:14 pm
Forum: Secondary Level
Topic: 2014-national
Replies: 15
Views: 4802

2014-national

Closing his eyes Towsif begins to place knights on a Chess board of $ {19} \times {21}$. After placing how many knights Towsif will be sure that on the next move at least one knight will attack another one. (In one move knight goes straight for ${2}$ steps and the 3rd step should be at right angle t...
by Mahfuz Sobhan
Tue Jul 07, 2015 2:45 am
Forum: Secondary Level
Topic: Sylhet - 2014
Replies: 3
Views: 7455

Sylhet - 2014

$${x} = {m} \times ({m} + 1) \times ({m} + 2) \times ({m} + 3) \times ........ ....\times ({3m} - 1) \times {3m}$$. Here ${x}$ is divisible by ${3}^{k}$, if
m=1000 then find the maximum possible value of k.
by Mahfuz Sobhan
Fri Jun 12, 2015 12:39 am
Forum: Secondary Level
Topic: Find XYZ
Replies: 10
Views: 3422

Re: Find XYZ

here $x = 3, y = 3, z = 3$
$x = y = z = 3$
$3^2 + 3^2 + 3^2 = 27$
$3 ^ 3 = 27$
by Mahfuz Sobhan
Sat May 30, 2015 7:27 pm
Forum: Algebra
Topic: cos(sin(... sin(x) ...))
Replies: 0
Views: 857

cos(sin(... sin(x) ...))

If $x$ is small enough that $\sin x\to x$. An operator $\mbox{S}_n$ is defined such that $\mbox{S}_n\left(x\right)=\sin\left(\mbox{S}_{n-1}\left(x\right)\right)$ and $\mbox{S}_1\left(x\right)=\sin x$. For sufficiently large $n$, $\mbox{S}_n\left(x\right)\to \mbox{S}_{n-1}\left(x\right)$. Express $\c...
by Mahfuz Sobhan
Thu May 28, 2015 8:29 pm
Forum: Secondary Level
Topic: Chittagong-2014
Replies: 1
Views: 1164

Chittagong-2014

Everyday, a fox catches 5 crocodiles and locks them in a cave. Every day, he takes one of the crocodile randomly, and tells, “If you can part the crocodiles into seven, I will free you and eat the rest of the crocodiles. But if you can’t, I will eat you and leave the rest alive but captive.” If the ...
by Mahfuz Sobhan
Tue May 19, 2015 6:45 pm
Forum: Secondary Level
Topic: Find XYZ
Replies: 10
Views: 3422

Re: Find XYZ

bhaiya what should i do to solve this problem?
from which sector of math it is?