Number of ways a certain event will occur in a game

  • Thread starter JimBob81345
  • Start date
  • Tags
    Game
In summary, the game involves 2n people assigned numbers from 1 to x and arranged randomly in a line. Each round, the person at the front goes to the corner and if two people with the same number are in the corner, they both exit and do not return to the line. The question is how many orderings of the people in the line have a corner with at most 2 people after each round. To satisfy this condition, there cannot be two people with the same number next to each other unless one is already in the corner. After 2m people, if the corner is empty, the numbers in the row must have a specific pattern that satisfies the condition. The number of possible patterns where the corner is empty
  • #1
JimBob81345
Each of 2n people are assigned a number from 1 to x so that every number is assigned to exactly 2 people. The people are then arranged randomly in a line. Every round of the game, the person at the front of the line goes to the corner. If two people with the same number are in the corner, both people immediately exit the place and DO NOT go to the end of the line. The round ends after the two people exit the corner. Out of all the possible orderings of the people in a line, how many have the following property: After every round, the corner consists of at most 2 people.

My Work:
- If there are two people of the same number next to each other in the line, then the permutation of people cannot satisfy the previous condition unless one person is already in the corner.
- If there are 2 people of the same number one person apart, then the condition is not satisfied if a person is already in the corner.
 
Physics news on Phys.org
  • #2
What can you say about the numbers in the row if the corner is empty after 2m people?
How many patterns can you find such that the corner is empty after 2m people but not before?
 
  • #3
Start with some simple examples of the game and work through them. First with 2 people and 1 number (seems trivial but may give you some insight into a pattern for higher numbers), then with 4 people and 2 unique numbers. Then 6 people and 3 numbers. See if you can then figure out a general case.
 

FAQ: Number of ways a certain event will occur in a game

1. How do you calculate the number of ways a certain event will occur in a game?

The number of ways a certain event can occur in a game is calculated by using the formula nPr = n! / (n-r)!, where n is the total number of possibilities and r is the number of items selected. This formula is used for calculating permutations, which are ordered arrangements of objects.

2. What is the difference between permutations and combinations?

Permutations and combinations are both methods used to calculate the number of ways a certain event can occur. The main difference is that permutations take into account the order of the objects, while combinations do not. For example, choosing a first, second, and third place winner in a race would require using permutations, while selecting three people to be on a team would use combinations.

3. Can the number of ways a certain event will occur change during a game?

Yes, the number of ways a certain event can occur in a game can change depending on the circumstances. For example, in a card game, the number of possible hands that can be dealt changes with each card that is drawn. This is because the total number of possibilities is reduced with each card that is dealt.

4. How can the number of ways a certain event will occur be used in game strategy?

The number of ways a certain event can occur can be used in game strategy by helping players make informed decisions. For example, knowing the number of possible outcomes can assist players in choosing the best move or predicting the likelihood of a certain event happening.

5. Are there any limitations to using the number of ways a certain event will occur in a game?

There are some limitations to using the number of ways a certain event can occur in a game. This method assumes that all possibilities are equally likely, which may not always be the case in a game. Additionally, it does not take into account external factors such as luck or chance. Therefore, it should be used as one tool in game strategy rather than the sole determining factor.

Similar threads

Probability of girls on a team getting shirts with pair numbers
Replies
3
Views
1K
Find the number of ways the cake can be shared among two people
Replies
4
Views
762
MHB Probabilities of certain events in a lucky wheel game
Replies
2
Views
2K
A A game of seemingly mutually independent events
Replies
7
Views
2K
Permutations (with repetitions) problem
Replies
5
Views
2K
Bishops and permutations on chessboard
Replies
23
Views
2K
Planning Tournament with p People & g Games: Algorithm Needed
Replies
1
Views
1K
Help understanding proof that a winning strategy exists for Chomp
Replies
2
Views
4K
Calculating Standard Deviation for Margin of Victory in a Game of Chance
Replies
1
Views
1K
Probability: Dice Game between 20- and 12-sided dice with re-rolls
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top