Search found 138 matches
- Fri Feb 01, 2013 2:33 pm
- Forum: National Math Olympiad (BdMO)
- Topic: Let us help one another preparing for BdMO national 2013
- Replies: 12
- Views: 13246
Re: Let us help one another preparing for BdMO national 2013
$x_1 = 3 + 2 \sqrt {2}$ & $x_2 = 3 - 2 \sqrt {2}$ $(3 + 2 \sqrt {2})^n + (3 - 2 \sqrt {2})^n$ $(1 + \sqrt {2})^{2n} + (1 - \sqrt {2})^{2n}$ $2*(1 + ^{2n} C_2 \times 2^2 + ^{2n} C_4 \times 2^4 +.. .. ..+ 2^n)$ We will not get any irrational number $[ \sqrt {2} ]$ here because they are getting cancell...
- Thu Jan 31, 2013 6:11 pm
- Forum: Combinatorics
- Topic: Rubik's Cube Comb
- Replies: 4
- Views: 4662
Re: Rubik's Cube Comb
@sakibtanvir. You're right. I did the permutation for only one piece and forgot to do for others. Thanks to correct me..
So finally we get
$12! \times 2^{12} \times 8! \times 3^{8}$
So finally we get
$12! \times 2^{12} \times 8! \times 3^{8}$
- Thu Jan 31, 2013 12:34 pm
- Forum: Higher Secondary Level
- Topic: Secondary and Higher Secondary Marathon
- Replies: 128
- Views: 299650
Re: Secondary and Higher Secondary Marathon
No. Notice that I said 'ends in "all the same" as n'.
I meant the last $5$ digits of $n^2$ is $n$.
Suppose, when $n$ is a two digit number, take $76$ as example. $76^2=5776$. Here the last two digits are same as $n$ or $76$.
Now find 5 digit numbers of this property.
I meant the last $5$ digits of $n^2$ is $n$.
Suppose, when $n$ is a two digit number, take $76$ as example. $76^2=5776$. Here the last two digits are same as $n$ or $76$.
Now find 5 digit numbers of this property.
- Thu Jan 31, 2013 12:52 am
- Forum: Higher Secondary Level
- Topic: Secondary and Higher Secondary Marathon
- Replies: 128
- Views: 299650
Re: Secondary and Higher Secondary Marathon
Problem $\boxed{35}$
Find all $5$-digit natural numbers $n$ such that $n^2$ ends in all the same as $n$.
Source: Book 'Olympiad Somogro'(Bangla)
Find all $5$-digit natural numbers $n$ such that $n^2$ ends in all the same as $n$.
Source: Book 'Olympiad Somogro'(Bangla)
- Wed Jan 30, 2013 12:45 am
- Forum: Divisional Math Olympiad
- Topic: Rajshahi MO 2013, Secondary 1
- Replies: 9
- Views: 6411
Re: Rajshahi MO 2013, Secondary 1
I have just drawn a regular nonagon perfectly & also 27 diagonals and observed that there is not a single same point of intersection. It works for the odds. $^{2013}C_4$ is the answer. Thanks..
- Tue Jan 29, 2013 11:23 pm
- Forum: Divisional Math Olympiad
- Topic: Rajshahi MO 2013, Secondary 1
- Replies: 9
- Views: 6411
Re: Rajshahi MO 2013, Secondary 1
But Mahi vai, it does not work at all. If we do according to that we get 6 sided polygon having 15 intersections. But actually it is 13.
3 intersections are same point here. It is not working for the polygons having even number(greater than 4) of sides.
3 intersections are same point here. It is not working for the polygons having even number(greater than 4) of sides.
- Tue Jan 29, 2013 8:47 pm
- Forum: Divisional Math Olympiad
- Topic: Rajshahi MO 2013, Secondary 1
- Replies: 9
- Views: 6411
Rajshahi MO 2013, Secondary 1
Here is a regular polygon having $2013$ sides. Find the number of intersections of its diagonals. I tried for about 15 minutes to solve it there. But couldn't...still not. Is there any formula for finding number of intersections of diagonals for $n$ -sided polygon ? That was the first question and I...
- Tue Jan 29, 2013 8:28 pm
- Forum: Social Lounge
- Topic: Any Way
- Replies: 11
- Views: 9781
Re: Any Way
I'll send it as you said. If they select according to regional result (which should be ) I'll have no chance. Last year I was regional champ when in class 9 and this year though being older, became 2nd Runner-up. And I think 2nd runners-up are not eligible. :-( Let me see what happens... or I have t...
- Tue Jan 29, 2013 2:24 am
- Forum: Social Lounge
- Topic: Any Way
- Replies: 11
- Views: 9781
Re: Any Way
If anyone knows something about S.S.C. camp, kindly inform me. Perhaps the ex-campers can easily go there,but if I have to give a test (after SSC) to enter into it I'm ready. Perhaps like many others I'm not going to participate in NMO. I have the form & still thinking whether I should fill it up or...
- Mon Jan 28, 2013 4:13 pm
- Forum: Social Lounge
- Topic: Negative Marking
- Replies: 7
- Views: 5921
Re: Negative Marking
@Adib. It happens what you said. Yesterday @MO, in first 20 minutes I solved 2 probs, a logarithm and a problem on number theory. I noticed the student sitting beside me of same category(actually the other student in the middle was absent) copying my two answers. Then I looked at his rough paper. Th...