# combinatorics

1. ### [Help] The number of possible k-sided polygons in an m by n grid of dots

Hello. :spin: This is my first post, so sorry for the potential mistakes below. A grid of dots has the dimensions m by n, where m is greater than or equal to n. Pick k dots from this grid in such a way that they form a polygon with k sides. In other words, no three dots can be collinear...
2. ### Combinatorics

On how many ways Vlad, Alex and Mike can share 5 books, whereby can happen that someone didn't get a single book if books are same? _ (7) The answer is P(5,2) or 7! / (5! * 2!) = 21. I'm not sure where did these numbers came from, so if someone could explain it.
3. ### Induction question about partitioning with a condition

We have n students which are in k classes. We know that between each two classes, there exist two persons A and B who know each other. Prove that we can put students in nâˆ’k+1 groups such that all the persons in a group know each other. (the proof is probably with induction) (I think it is safe...
4. ### Some fundamental question in combinatorics

Hey. We started to study all this subject of combinatorics integrated with the subject of functions. 1. I don't actually understand how to integrate between combinatorics and function, those functions which represent our possibilities and etc... And why at all we need to represent our...
5. ### One problem in combinatorics

I know thet number is divisible by 3 if the sum of its digits is divisible by 3, but have no idea what to do next.
6. ### Combinatorics with several conditions

Hello. I have a math problem that I need to solve, however I'm really stuck and also kind of depressed now. We have 30 balls: 6 red, 7 white, 9 green and 8 blue. We want to separate them to 4 different boxes. â€¢ First box can only contain 13 or less balls, which can be either red or white...
7. ### Combinatorics with several conditions

Hello. I have a math problem that I need to solve, however I'm really stuck and also kind of depressed now. We have 30 balls. 6 red, 7 white, 9 green and 8 blue. We want to separate them to 4 different boxes. â€¢ First box can only contain 13 or less balls, which can be either red or white...
8. ### Is this part of combinatorics?

Hi I need your help to figure the following out. Thanks in advance. So, letâ€™s say Iâ€™m given 10 elements (numbers, for example) and I need to select 3 of these elements (the order doesnâ€™t matter, and I can select the same element more than once) to obtain a fixed result. So for...
9. ### Help on Combinatorics

Hey guys I am struggling to understand what the difference is between ordered and unordered selection between a set of elements. Could anyone please give me an example which i might find helpful to understand them? Thanks again and sorry for the spam!
10. ### Number of ways to connect vertices of n squares with line segments

Hello. Could you please help me with the following: What is the number of ways to connect the vertices of n squares with non-intersecting line segments ? (These line segments should not cross the edges of the given squares as well). Just a few of possible different configurations...
11. ### Challenging Combinatorics Question

In how many different ways can six unique coins - a penny, a nickel, a dime, a quarter, a half dollar, and a silver dollar - be distributed among three people, such that each person receives at least one coin?
12. ### Combinatorics : counting

Hi, We have a grid 6x6. We want to place on each square one of 36 tokens. 18 tokens are red : 6 copies of tokens numbered from 1 to 3. 18 tokens are blue : 6 copies of tokens numbered from 1 to 3. In how many different ways could we place them all? Thank you. Ps : It is not a...

There are 2 buckets and 100 balls. A man throws the balls one at a time and it always falls in one of the two buckets. At which point(how many balls thrown) the difference between the number of balls in the two buckets is statistically likely to be the greatest? // My solution When you...
14. ### 12 knights are seated in a circular table, each one consider her neighbors as an enem

12 knights are seated in a circular table, each one consider her neighbors as an enemy. We need to form a group with 5 knights, in this group we will not have enemies, how many ways we have to do it? Thank you.
15. ### In a chess tournament we have 10 participants....

In a chess tournament we have 10 participants and want to do 5 games simultaneously such that ever player play once. How many ways we have to do this? Thank you. I think the maximum possible ways is: 45 * 30 * 15 * 7 *1 (my thought was: i have 45 ways to the first pair, after this i...
16. ### Combinatorics

A castle is built like a grid nxn. Each room have 4 walls. At most one door is opened on each wall. Each room have exactly 2 doors. Depending on the value of n how many configurations m are possible? Example : n=1 m=6 If we note the walls A,B,C,D then we have 6 possibilities : A,B A,C...
17. ### Combinatorics question

In how many ways can we place r indistinguishable balls into n boxes numbered 1 to n, where the number of balls in each box can be zero or more than one? If there is no empty box allowed for r >= n? I started with the second question as it seemed easier. I've tried partitioning the balls into n...
18. ### Very hard combinatorics

3-5-7-8-9 1-2-3-4-5 1-2-6-7-8 1-3-6-9-10 2-4-7-9-10 4-5-6-8-10 All the 6 quintuplets share exactly 2 numbers pairwise. 6 is the maximal number of quintuplets with the condition above you could extract from C(10,5)=252. You can not find more than 6. Now assume that instead of 10...
19. ### Is it possible to create a circle with all Domino tiles?

Is it possible, according to Domino rules, to create a circle with all Domino tiles from the set, when the symbols: a) 1, 2, 3, 4, 5, 6 b) 0, 1, 2, 3, 4, 5, 6 are allowed? What I was trying to do first is brute force it with a computer program, but that kinda got out of hand, I have a...
20. ### Interesting Combinatorics

I find the answer is 285, but the right answer is 825 What is my mistake? My solution is 1 + 2^2 + 3^2 +... 9^2