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A rectangular array of mn numbers arranged in n rows, each consisting of m columns, is said to contain a saddlepoint if there is a number that is both the minimum of its row and the maximum of its column. For instance, in the array
ith row, jth column of the array. Now suppose that the array contains a saddle point—say the number in the row r and column k call this number
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Chapter 6 Solutions
A First Course in Probability
- A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in the front and 3 in the back a. How many arrangements are possible with no restrictions? b. How many arrangements are possible if the parents must sit in the front? C. How many arrangements are possible if the parents must be next to each other?arrow_forwardThe game Capture is played by two players, First and Second, who take turns to move towards one another on a narrow bridge. Initially, the two players are at opposite ends of the bridge, at a distance of n feet from each other. (Here n is an arbitrary positive integer.) When it is their turn, they are allowed to jump 1, 2, or 3 feet toward each other. The game starts by First making a move first; the game is over when one player is able to capture (jump on top of) the other player. Generalize the problem further to the case when the initial distance is n feetand the players are allowed to jump any (positive) integer number of feet up to k feet. (Here n and k are arbitrary natural numbers.)arrow_forwardSubject: Discrete Mathematics 1carrow_forward
- The game Capture is played by two players, First and Second, who take turnsto move towards one another on a narrow bridge. Initially, the two players areat opposite ends of the bridge, at a distance of n feet from each other. (Here nis an arbitrary positive integer.) When it is their turn, they are allowed to jump1, 2, or 3 feet toward each other. The game starts by First making a move first;the game is over when one player is able to capture (jump on top of) the otherplayer.(a) Which player has a strategy to capture the other player if n= 8?(b) What if the initial distance is n= 21 feet?(c) Generalize the problem for all positive integers n.(d) Generalize the problem further to the case when the initial distance is n feetand the players are allowed to jump any (positive) integer number of feetup to k feet. (Here n and k are arbitrary natural numbers.)arrow_forwardSolve the problem. If all of 48 available apple trees are to be planted in a rectangular array, what are the possible numbers of rows in the array, all rows having the same number of trees? 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 24, and 48 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48 8, 12, 16, 24, and 48 1, 2, 3, 4, and 6arrow_forwardDo all three solution approaches for simultaneous games work independently (not together)? If not, which do notarrow_forward
- Use Gaussian elimination or Gauss-Jordan elimination to solve the problem. A basketball fieldhouse seats 15,000. Courtside seats sell for $8, endzone seats for $7, and balcony for $5. Total for a sellout is $88,000. If half the courtside and balcony and all endzone seats are sold, tickets sales total $51,000. If the first colum represents the number of courtside seats, the second column represents the number of endzone seats, and the third column represents the number of balcony seats, which of the following augmented matrices would give the number of each type of seat there are?arrow_forward2.)A jar contains 2 red, 3 green, and 6 blue marbles. In a game a player closes their eyes, reaches into the jar and randomly chooses two marbles. The player wins the game if at least one of their marbles is red. Suppose it costs $1 to play the game and the winning prize is $3. Mathematically analyze this game and determine if it is in your financial interest to play the game.arrow_forwardThe third term in a geometric row is 5p+1 the fifth term is 4 and the seventh term is 1. Determine the value of parrow_forward
- please send handwritten solution for part darrow_forwardIf ExxonMobil invests in Venezuela's oil fields, it runs the risk that Venezuela will later partially nationalize the assets. The payoffs are represented in the game tree illustrated in the figure to the right Nationalize (24,96) Suppose that the parties could initially agree to a binding contract that Venezuela would pay ExxonMobil x dollars if it nationalizes the oil fields. How large does x have to be for ExxonMobil to invest in Venezuela? Government Venezuela (60,60) Don't nationalize ExxonMobil The value of x would have to be at least equal to $ for ExxonMobil to invest in Venezuela (Enter your response as a whole number) Elsewhere (30,0)arrow_forwardplease send handwritten solution for part carrow_forward
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