Sabrina is on a game show and is presented with a drawer containing 10 red socks, 10 blue socks, 10 green socks, and 10 yellow socks. Sabrina is to take socks out of the drawer and put them in a bag. She will win $1 for every sock she puts in the bag, as long as the bag does not contain 5 or more socks of one color and 5 or more socks of another color. For example, if she takes 5 red, 4 blue, 3 green, and 2 yellow socks, she would win $14. However, if she took 5 red, 5 blue, 3 green, and 2 yellow socks, she would not win anything because there are two colors (red and blue) that have 5 or more socks each. What is the most money that Sabrina can win? Enter your answer as a single integer only (no words, no dollar signs). A/ What is the minimum number n such that if n socks are removed from the drawer and put into a bag, that the bag will necessarily contain at least 5 socks of one color and at least 5 socks of another color? Enter n as a single integer, no words. A
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- Jack and Jill will play a game called Hotter, Colder. Jill chooses a number from 0 to 100, and Jack makes repeated attempts to guess it. For each guess, Jill will respond with: hotter - if the current guess is closer to her number than the previous guess is colder - if the current guess is farther to her number than the previous guess is same - if the current guess is as far (to her number) as the previous guess is For Jack’s first guess, since there is no previous guess yet, Jill will just answer same. Describe an algorithm or a systematic approach that Jack can follow to win the games faster (fewer guesses). Example: Jill chooses number 40. Note: Jack can guess any number from 0 to 100 at any point of the game. Jack guesses 100. Jill responds same (first guess) Jack guesses 60. Jill responds hotter (60 is closer to 40 than previous guess 100) Jack guesses 80. Jill responds colder (80 is farther from 40 than previous guess 60) Jack guesses…Raghu and Sayan both like to eat (a lot) but since they are also looking after their health, they can only eat a limited amount of calories per day. So when Kuldeep invites them to a party, both Raghu and Sayan decide to play a game. The game is simple, both Raghu and Sayan will eat the dishes served at the party till they are full, and the one who eats maximum number of distinct dishes is the winner. However, both of them can only eat a dishes if they can finish it completely i.e. if Raghu can eat only 50 kCal in a day and has already eaten dishes worth 40 kCal, then he can't eat a dish with calorie value greater than 10 kCal.Given that all the dishes served at the party are infinite in number, (Kuldeep doesn't want any of his friends to miss on any dish) represented by their calorie value(in kCal) and the amount of kCal Raghu and Sayan can eat in a day, your job is to find out who'll win, in case of a tie print “Tie” (quotes for clarity). Input:First line contains number of test…A high school has 1000 students and 1000 lockers, one locker for each student. On the first day of school, theprincipal plays the following game: She asks the first student to open all the lockers. She then asks the secondstudent to close all the even-numbered lockers. The third student is asked to check every third locker. If it isopen, the student closes it; if it is closed, the student opens it. The fourth student is asked to check every fourthlocker. If it is open, the student closes it; if it is closed, the student opens it. The remaining students continuethis game. In general, the nth student checks every nth locker. If it is open, the student closes it; if it is closed,the student opens it. After all the students have taken turns, some of the lockers are open and some are closed.The program below, when ran, will prompt the user to enter the number of lockers in the school. After thegame is over, the program will output the number of lockers and the lockers numbers of the lockers…
- 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.Suppose you can buy chocolate bars from a vending machine for $1 each.Inside every chocolate bar is a coupon. You can redeem 7 coupons for 1chocolate bar from the machine.For example, if you have $20, you can initially buy 20 chocolate bars.This gives you 20 coupons. You can redeem 14 coupons for 2 additionalchocolate bars. These 2 chocolate bars have 2 more coupons, so you now have atotal of 8 coupons. This gives you enough to redeem for 1 final chocolate bar.Write a recursive function that would accept the amount of dollars andcoupons as its parameters and output the total number of chocolate bars thatcan be bought (including those redeemed via coupons).Write a test program in C++that would allow the user to enter amount of dollarsand then use the recursive function to compute the number of chocolate barsthe user can buy, and output the number to the screen.Suppose you are a participant in a game show. You have a chance to win a motorbike. You are askedto select one of the 500 doors to open; the motorbike is behind one of the 500 doors; the other remaining doorsare losers and have balloons behind them. Once you select a door, the host of the game show, who knowsexactly what is behind each of the door, randomly opens 480 of the other doors all at once that s/he for sureknows are losing doors and have balloons behind them. Then s/he reoffers you – whether you would like toswitch to the other doors or keep your initial or original selection as before. Now in this case, you are goingto make decision based on probabilistic reasoning. Therefore, whenever you are reoffered by the host to dothe selections among the remaining unopened doors, what is the probability of winning for each of theremaining unopened doors (including your original selection)? Do you want to make a switch based on theprobabilistic reasoning? If you are switching, which…
- The Monty Hall Cash game costs $12 to play. Once you pay, you have a choice of three doors. Behind one door is $20, behind the other two is absolutely nothing (i.e. $0). You pick a door, say number 1, and the host running the game, who knows what’s behind the doors, opens another door, say number 3, which has absolutely nothing. He says to you, “Do you want to switch to door number 2?”. You can decide to switch doors, or stay with your initial choice. You “win” whatever is behind the door you end up choosing. Use a python Jupyter notebook to run simulations of the game to estimate/approximate the expected value of the game if you always switch, and the expected value if you always stay. OR: Prove that the expected value of this game is greatest when you always switch. Include a full mathematical explanation of all probabilities (no “hand waiving”!) and include any references or sources.Suppose a person can buy a chocolate bar from the vending machine for $1 each. Inside every chocolate bar is a coupon. A person can redeem 3 coupons for one chocolate bar from the machine. This means that once a person has started buying chocolate bars from the machine, he/she always has some coupons. A person would like to know how many chocolate bars can be bought, if a person starts with N dollars and always redeem coupons, if he/she has enough for an additional chocolate bar. For example: With 3 dollars a person could buy 4 chocolate bars after purchasing 3 bars giving him/her 3 coupons and then redeeming the 3 coupons for one bar. This would leave him/her with one extra coupon. Thus, will have 4 chocolate bars and still have one coupon leftover. For 11 dollars, a person can have 16 chocolate bars and still have one coupon leftover. For 12 dollars, a person can have 17 chocolate bars and have two coupons leftover. Write a complete Python program that prompts a buyer to input…There are 4 balls in a jar (2 black and 2 white). You randomly choose three balls (one by one with no replacement) and paint them according to one of the following methods (a-c) and replace them in the jar. You ask your friend to pick a ball. What is the probability that this ball is white? a. You paint them all black. b. You paint them all the same color as the first ball that is picked c. You look at the majority color (among the 3 selected ones) and paint them all that color. Write a MATLAB code to simulate each of the above 3 cases in MATLAB for 10,000 times and estimate the probability of getting a white ball in each of those cases
- A local merchant goes to a market to buy apples with 500 UM. They offer two types of apples: green ones at 0.5 UM per kg and red ones at 0.8 UM per kg. We know that he only has space in his van to transport a maximum of 700 kg of apples and that he plans to sell a kilo of green apples for 0.58 UM and red apples for 0.9 UM. Solve the problem with the graphical method.- How many kilograms of apples of each type should you buy to obtain maximum profit?You are given an instance of a problem where you have an n x n grid of squares. Each square can be unpainted or can have a hole, so you cannot go on the square with a hole. The objective is to paint all the squares that do not have a hole. You start in the square (0,0) which is unpainted. The actions you can do are: (1) paint the square you are on if it is not painted; (2) move, either vertically or horizontally, to an adjacent square inside the grid that is not painted and does not have a hole. a. Describe a state-space representation for the problem, specifying the state representation, the initial state, the goal condition, and the actions. b. Is the state space finite? Is it a tree or a graph? c. Propose a heuristic for the problem. Is your heuristics admissible or not? Explain briefly your answerQCC Casino Royale offers its customers a happy way to go home with big bucks playing its “Dice” game. The Dice game is played by asking customers to roll a pair of dice. If customers roll a seven or 11, they win; any other roll and the customer loses. The odds of rolling a seven is 6 to 1 so that if customers bet 1 dollar and win, they receive 7 dollars. The odds of rolling an eleven are 18 to 1 so that if customers bet 1 dollar and win, they receive 19 dollars. Upon entering the casino, customers must be greeted with an appropriate welcoming message. They must be asked to indicate the amount of money that is in their bankroll to play. Customers cannot enter the casino with a bankroll greater than $1,000. Customers must play the game in rounds of 10 plays and the minimum bet for each play is 5 dollars; the maximum bet is 50 dollars. For each try at rolling the dice, customers must be asked how much they want to bet and for each try must be informed of the result and the…