Give the required conditions for a stalemate to occur

A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 6 freshmen, 7 sophomores, 9 juniors, and 7 seniors are eligible to be on the committee, in how many ways can the committee be chosen? Your answer is:

We are given three ropes with lengths n₁, n2, and n3. Our goal is to find the smallest value k such that we can fully cover the three ropes with smaller ropes of lengths 1,2,3,...,k (one rope from each length). For example, as the figure below shows, when n₁ = 5, n₂ 7, and n3 = 9, it is possible to cover all three ropes with smaller ropes of lengths 1, 2, 3, 4, 5, 6, that is, the output should be k = 6. = Devise a dynamic-programming solution that receives the three values of n₁, n2, and n3 and outputs k. It suffices to show Steps 1 and 2 in the DP paradigm in your solution. In Step 1, you must specify the subproblems, and how the value of the optimal solutions for smaller subproblems can be used to describe those of large subproblems. In Step 2, you must write down a recursive formula for the minimum number of operations to reconfigure. Hint: You may assume the value of k is guessed as kg, and solve the decision problem that asks whether ropes of lengths n₁, n2, n3 can be covered by…

In a recent court case, a judge cited a city for contempt and ordered a fine of $2 for the first day. Each subsequent day, until the city followed the judge's order, the fine was squared (i.e., the fine progressed as follows: $2, $4, $16, $256, $65,536, .). a, What would be the fine on day N? b. How many days would it take for the fine to reach D dollars (a Big-Oh answer will do)? 2.6

Consider the following parlor game to be played between two players. Each player beginswith three chips: one red, one white, and one blue. Each chip can be used only once.To begin, each player selects one of her chips and places it on the table, concealed.Both players then uncover the chips and determine the payoff to the winning player.In particular, if both players play the same kind of chip, it is a draw; otherwise, thefollowing table indicates the winner and how much she receives from the other player.Next, each player selects one of her two remaining chips and repeats the procedure,resulting in another payoff according to the following table. Finally, each player playsher one remaining chip, resulting in the third and final payoff.Winning Chip Payoff ($)Red beats white 250White beats blue 100Blue beats red 50Matching colors 0(a) Formulate the payoff matrix for the game and identify possible saddle points.(b) Construct a linear programming model for each player in this game.(c)…

Consider the following parlor game to be played between two players. Each player beginswith three chips: one red, one white, and one blue. Each chip can be used only once.To begin, each player selects one of her chips and places it on the table, concealed.Both players then uncover the chips and determine the payoff to the winning player.In particular, if both players play the same kind of chip, it is a draw; otherwise, thefollowing table indicates the winner and how much she receives from the other player.Next, each player selects one of her two remaining chips and repeats the procedure,resulting in another payoff according to the following table. Finally, each player playsher one remaining chip, resulting in the third and final payoff.Winning Chip Payoff ($)Red beats white 250White beats blue 100Blue beats red 50Matching colors 0(a) Formulate the payoff matrix for the game and identify possible saddle points.(b) Construct a linear programming model for each player in this game.(c)…

I just need the proof for the puzzle problem being NP-Complete.

TOPIC: MARKOV CHAINS A book club has 3 mailing lists: A special list M of the most senior active members. Another list R containing the regular members, and A list of regular members and names of individuals who have shown interest in club activities in the past. For each new publication, it is necessary to decide which list should be used to mail the sale announcements.sale.If after the last mailing there was a request for too few copies, the secretary uses list R with probabilityof ¼ and P with a probability of ¾.If after the last mailing there was a satisfactory response, the secretary uses the R list and the P list with equalprobabilities.If, after the preceding shipment, there was an excessive number of orders or over demand, the secretary uses list M with probability 1/3 and list P with probability ¾.list M with probability 1/3 and R with probability 2/3.If list M is used, there will be poor sales or satisfactory sales with equal probabilities; if list R is used, there will be…

A movie theater offers showings of a movie each day. A total of 500 people come to see the movie on a particular day. The theater is interested in the number of people who attended each of the six showings. 81 +82 +83 +84 +85 +86 = 500. How many possibilities are there for the tallies for each showing for that day if... a ... there are no restrictions? b ... none of the showings can be an empty theater? c...81 2, 82 ≥3, 83 4, 84 ≥5, 85 ≥6, 86 ≥ 7?

A movie theater offers showings of a movie each day. A total of 500 people come to see the movie on a particular day. The theater is interested in the number of people who attended each of the six showings. 81 +82 +83 +84 +85 +86 = 500. How many possibilities are there for the tallies for each showing for that day if... a...there are no restrictions? b ... none of the showings can be an empty theater? c... S12, 82 ≥ 3, 83 ≥ 4, 84 ≥ 5, 85 ≥ 6, 86 ≥ 7?