Search found 12 matches
- Thu Apr 27, 2023 12:44 am
- Forum: Junior Level
- Topic: Czech and Slovak Republics 1997
- Replies: 4
- Views: 64143
Re: Czech and Slovak Republics 1997
Let us label the vertices as $A_1,A_2,A_3, \dots ,A_{2n+1}$. Every vertex has $2n$ edges. Let $D_i$ be the number of blue edges incident to $A_i$ (For all $0<i\le 2n+1$). Then $2n -D_i$ is the number of green edges incident to $A_i$. It's obvious that $D_i$ and $2n -D_i$ have the same parity. Every ...
- Thu Apr 27, 2023 12:38 am
- Forum: Junior Level
- Topic: Czech and Slovak Republics 1997
- Replies: 4
- Views: 64143
Re: Czech and Slovak Republics 1997
Let us label the vertices as $A_1,A_2,A_3, \ots ,A_{2n+1}$. Every vertex has $2n$ edges. Let $D_i$ be the number of blue edges incident to $A_i$ (For all $0<i\e 2n+1$). Then $2n -D_i$ is the number of green edges incident to $A_i$. It's obvious that $D_i$ and $2n -D_i$ have the same parity. Every ve...
- Sat Mar 12, 2022 5:59 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Higher Secondary 2020 P6
- Replies: 10
- Views: 13998
BdMO National Secondary 2022 P3
Prove that if the numbers $3,4,5 \ndots ,3^5 $ are partitioned into two disjoint sets, then in one of the sets the numbers $a,b,c$ can be found such that $ab=c$.
- Wed Aug 18, 2021 11:53 am
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2021 Junior Problem 9
- Replies: 2
- Views: 12334
Re: BdMO National 2021 Junior Problem 9
We can only use Composite numbers in our pairs. There are 34 composite numbers between 1-50. But the Square of 2,3,5&7 exist Between 1-50. So we can use Them also in our pairs. So we get a total of 38 numbers. So the highest number of pairs possible is 19. Here is a example (50,28), (49,7), (48,46),...
- Mon Jul 26, 2021 2:26 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2021 Junior Problem 10
- Replies: 3
- Views: 9640
Re: BdMO National 2021 Junior Problem 10
Bbbbbbbbbbbb
- Sat Jun 05, 2021 11:32 pm
- Forum: Junior Level
- Topic: Draw a Circle
- Replies: 2
- Views: 12560
Draw a Circle
There are 2019 points in a plane. Prove that a circle be drawn in such way that 1009 points lie Outside and inside the cricle respectively. And the last point is on the circumference.
- Tue Apr 06, 2021 1:01 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Higher Secondary 2020 P6
- Replies: 10
- Views: 13998
Re: BdMO National Higher Secondary 2020 P6
So that's why we made f(101)=5
So that is the lowest possible value.
I got it now.
So that is the lowest possible value.
I got it now.
- Tue Apr 06, 2021 12:48 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Higher Secondary 2020 P6
- Replies: 10
- Views: 13998
Re: BdMO National Higher Secondary 2020 P6
What if we assume that f(n) = 1
For all positive integers.
??
For all positive integers.
??
- Tue Apr 06, 2021 12:33 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Higher Secondary 2020 P3
- Replies: 3
- Views: 9212
Re: BdMO National Higher Secondary 2020 P3
But here S doesn't contain all rectangles.
Like it doesn't contain the rectangles of base > 0.25
It only contains all possible squares.
Like it doesn't contain the rectangles of base > 0.25
It only contains all possible squares.
- Sat Apr 03, 2021 7:15 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National Junior 2020 P9
- Replies: 3
- Views: 3248
Re: BdMO National Junior 2020 P9
1010
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