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- The game of Chomp is played by two players. In this game, cookies are laid out on a rectangular grid. The cookie in the top left position is poisoned. The two players take turns making moves; at each move, a player is required to eat a remaining cookie, together with all cookies to the right and/or below (that is all the remaining cookies in the rectangle, in which the first cookie eaten is the top left corner). The loser is the player who has no choice but to eat the poisoned cookie. Prove that if the board is square (and bigger than 1 × 1) then the first player has a winning strategy.State University is about to play Ivy College for the statetennis championship. The State team has two players (A andB), and the Ivy team has three players (X, Y, and Z). Thefollowing facts are known about the players’ relative abilities: X will always beat B; Y will always beat A; A will alwaysbeat Z. In any other match, each player has a12chance ofwinning. Before State plays Ivy, the State coach mustdetermine who will play first singles and who will play secondsingles. The Ivy coach (after choosing which two players willplay singles) must also determine who will play first singlesand second singles. Assume that each coach wants tomaximize the expected number of singles matches won bythe team. Use game theory to determine optimal strategies foreach coach and the value of the game to each team.I don't need to know the value of the game I need to know the optimal strategies for R and C please
- There are two players who simultaneously call out one of the numbers oneor two. Player I’s name is James; he wins if the sum of the numbers is odd. Player II’s name is Louis; she wins if the sum of the numbers is even. The amount paid to the winner by the loser is always the sum of the numbers in pesos. Find the table for the payoff function P, and analyze the game to find the value and optimal strategies of the players. Is the game fair?Cully Furniture buys two products for resale: big shelves (B)and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. Which of the following is not a feasible purchase combination? Group of answer choices 100 big shelves and 82 medium shelves 150 big shelves and 0 medium shelves 100 big shelves and 100 medium shelves 100 big shelves and 0 medium shelvesGiven question is A basket of fruit is being assembled from apples, bananas, and oranges. What is the fewest number of fruit pieces that should be placed in the basket to ensure that there are at least 8 apples, 6 bananas, or 9 oranges?Your answer: The question is asking you to prepare for a worst-case scenario, not a best-case scenario. Imagine a game where you're not the one in charge of choosing the fruits - your opponent is in charge, and they don't want you to win. The opponent can get away with choosing 20 fruits (7 apples, 5 bananas, and 8 oranges) before the 21st fruit finally forces your condition to be satisfied. Therefore total required the fewest number of fruit pieces =(7+5+8)+1=21.My question:Why did you add 7+5+8 , instead of 8 apples, 6 bananas, or 9 oranges? The given is 8+6+9 not 7+5+8. Also why did you add +1? Here, you add 1: (7+5+8) +1 =21. Also, Is it pigeonhole formula? The pigeonhole is ⌈n/m⌉ not like this as far as i know. Thank you