Search found 53 matches

by Shifat
Sun Aug 21, 2011 6:20 pm
Forum: Number Theory
Topic: Perfect Number Is Sum Of Cube
Replies: 9
Views: 3326

Re: Perfect Number Is Sum Of Cube

we know \[1^3+2^3+3^3+............(2n-1)^3= n^2(2n^2-1)\] eta asholei induction diye prove kora jai, Inter er math boi er dharay eta aseo.....akhon n er value boshalei ans chole ashe.......... BTW amar ques holo nth odd number cube jodi perfect hoy tahole $n=2^{\frac{p-1}2}$.. eta ki kore prove kora...
by Shifat
Sun Aug 21, 2011 12:27 am
Forum: National Math Olympiad (BdMO)
Topic: BdMO National Higher Secondary 2011/8
Replies: 18
Views: 7148

Re: BdMO National Higher Secondary 2011/8

Rakeen vai ADC and BGC konotai shomobahu triangle hobe na......., hoile AF=FO impossible..
by Shifat
Sat Aug 20, 2011 6:20 pm
Forum: H. Secondary: Solved
Topic: Dhaka Higher Secondary 2010/9
Replies: 7
Views: 6507

Re: Dhaka Higher Secondary 2010/9

I think I have a solution, the total number of increasing numbers is and decreasing is 20. Here it is:- While we are writing them as decreasing numbers, then either the first one should be 5,4,3... Now there is three cases First Value five:- the second value can be 4,3 or 2 .if the second value is 4...
by Shifat
Sat Aug 20, 2011 4:33 am
Forum: H. Secondary: Solved
Topic: Dhaka Higher Secondary 2010/2 (Secondary 2010/9)
Replies: 17
Views: 12216

Re: Dhaka Higher Secondary 2010/2 (Secondary 2010/9)

By the way I am posting another solution, this time the result is different though... but more convincing to me.please check it if it is right or not:- The point and the lines are mentioned before..but we let the area of AOE is x and the area of COD is y. Now we saw.. AO:OD=2:1, and also AF:FB=4:3.....
by Shifat
Sat Aug 20, 2011 1:10 am
Forum: H. Secondary: Solved
Topic: Dhaka Higher Secondary 2010/2 (Secondary 2010/9)
Replies: 17
Views: 12216

Re: Dhaka Higher Secondary 2010/2 (Secondary 2010/9)

Cevian mane ki?? yes I get my mistakes, 2:1 holei je median hote pare na eta mathai ashe nai... sorry
by Shifat
Sat Aug 20, 2011 1:05 am
Forum: National Math Olympiad (BdMO)
Topic: BdMO National Higher Secondary 2011/8
Replies: 18
Views: 7148

Re: BdMO National Higher Secondary 2011/8

Ceva's theorem chara ki eta prove kora jabe na!!!! :o
by Shifat
Sat Aug 20, 2011 12:34 am
Forum: National Math Olympiad (BdMO)
Topic: BdMO National Higher Secondary 2011/4
Replies: 7
Views: 3574

Re: BdMO National Higher Secondary 2011/4

I used a basic (x+p)(x-p)<x^2.... 2011! = 1.2.3..........2011 =(1.2.3.4.........1005).1006.(1007.1008.1009.........2011) 2011.1<1006^2 2010.2<1006^2 2009.3<1006^2...............so 1005.1007<1006^2 we see now, 1.2.3.4.............1005.1007..........2009.2010.2011<1006^2010 each side we multiply 1006 ...
by Shifat
Thu Aug 18, 2011 5:22 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO National Primary 2011/7
Replies: 2
Views: 1778

Re: BdMO National Primary 2011/7

The answer is 330
by Shifat
Tue Aug 16, 2011 4:15 am
Forum: H. Secondary: Solved
Topic: Dhaka Higher Secondary 2010/2 (Secondary 2010/9)
Replies: 17
Views: 12216

Re: Dhaka Higher Secondary 2010/2 (Secondary 2010/9)

Moon vaia I think I have a solution but not sure about it.. here it is shown. But first, let the point is O and the lines are AD, BE and CF. From the figure we can see Triangle AOB and BOD have the same height. So AOB:BOD= AO:OD=2:1(same height means the area is propotionate to their bases), which i...
by Shifat
Tue Aug 16, 2011 1:46 am
Forum: H. Secondary: Solved
Topic: Rangpur Higher Secondary 2011/7
Replies: 14
Views: 9823

Re: Rangpur Higher Secondary 2011/7

amar mone hoi question e r sequence e vul ase..... y+z er value hobar kotha 25..... so amar value ashse 13.. agreed tahmid bro