s={1,2,3,...,2021}
1.In how many ways can you form a triangle by taking 3 numbers from the series?
2.How many different triangles can you form by taking 3 numbers from the series?
[NOTE: Think of each digit as length of an arm of the triangle]
Search found 13 matches
- Fri Apr 09, 2021 10:47 pm
- Forum: National Math Olympiad (BdMO)
- Topic: Triangle formation
- Replies: 0
- Views: 3016
- Fri Apr 09, 2021 10:41 pm
- Forum: National Math Olympiad (BdMO)
- Topic: set, subset
- Replies: 0
- Views: 2902
set, subset
s ={1,2,3,.....,2021} . r ={x, y, z} which is a subset of s. If x + y>z, then how many such subsets are there?
- Fri Apr 09, 2021 5:50 pm
- Forum: National Math Olympiad (BdMO)
- Topic: Number theory problem
- Replies: 1
- Views: 1196
Number theory problem
x is a random factor of the number 10^99. What is the probability that x is divisible by 10^88?
- Thu Apr 08, 2021 10:11 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BDMO 2019 national - junior/9
- Replies: 0
- Views: 2897
BDMO 2019 national - junior/9
In the cartesian coordinate system, four points (0, 0),(20, 0),(20, 19) and (0, 19) are used as vertices to draw a rectangle. At first, a ball with negligible size is at the (0, 0) point. It then started to move towards the point (2, 1). Every second, the ball passes the amount of distance between (...
- Tue Apr 06, 2021 2:18 pm
- Forum: Junior Level
- Topic: Please help me solve this problem!!
- Replies: 7
- Views: 4238
Re: Please help me solve this problem!!
There might be a straightforward approach to the problem. But counting the tuples is an important part of the solution which is given. Yes, obviously it is . By not counting tuples like {a,m,m,m} , I have meant tuples where a=b=c=d, a=b=c, b=c=d, a=b , c= d etc. Because the question says that a,b,c...
- Tue Apr 06, 2021 11:31 am
- Forum: Junior Level
- Topic: Please help me solve this problem!!
- Replies: 7
- Views: 4238
Re: Please help me solve this problem!!
Well, here's the solution: Number of tuples $(a,b,c,d)$ is $2020\choose 3$ [Stars and bars theorem maybe] Remember, while doing this calculation, we have some tuples where they are not pairwise distinct and also here, the positions are important. Now let's calculate the number of tuples where at le...
- Tue Apr 06, 2021 10:33 am
- Forum: Junior Level
- Topic: Please help me solve this problem!!
- Replies: 7
- Views: 4238
Re: Please help me solve this problem!!
Well, here's the solution: Number of tuples $(a,b,c,d)$ is $2020\choose 3$ [Stars and bars theorem maybe] Remember, while doing this calculation, we have some tuples where they are not pairwise distinct and also here, the positions are important. Now let's calculate the number of tuples where at le...
- Mon Apr 05, 2021 2:18 pm
- Forum: Junior Level
- Topic: Please help me solve this problem!!
- Replies: 7
- Views: 4238
Please help me solve this problem!!
a + b + c + d = 2021. How many possible solutions of (a, b ,c, d) are there if a , b , c , d are 4 different positive integers ? Position of (a , b, c , d) doesn't matter . Ex: (a ,c , b ,d) = (d, a, b, c).
- Sat Apr 03, 2021 11:39 pm
- Forum: Junior Level
- Topic: BDMO Regional Junior P8
- Replies: 14
- Views: 7866
Re: BDMO Regional Junior P8
we can creat what you are saying in $\{1,2,3,4,5\} subset. But we cannot do the same for $\{3,4,5,6,7\}$. We cannot make combinations with $\{6,7,8,9\}$ because 6,7 is already on the main subset. Yes, we can't, but as result we can create new combinations using 1,2 . As you can see for each main su...
- Sat Apr 03, 2021 8:20 pm
- Forum: Junior Level
- Topic: BDMO Regional Junior P8
- Replies: 14
- Views: 7866
Re: BDMO Regional Junior P8
we cannot create combinations of 4 numbers on all those 5 subsets. And the answer should be 48. Why can't we create combinations of 4 numbers on all those subsets? Would you please explain :?: we can creat what you are saying in $\{1,2,3,4,5\} subset. But we cannot do the same for $\{3,4,5,6,7\}$. ...