Game of coins alice and bob. If the number of Heads tosses is zero or one, Alice wins.

Game of coins alice and bob. This time, there are three stacks of n coins: A,B,C. A pile of coins is places on a table. You can see evidence that the result is true by looking at the possible sequence of tosses that end the game for Alice versus Bob. Find the sum of elements of the array after the game if both players play optimally. Question: Alice and Bob play a game of guessing number. for the sequence THHHT Alice gets 2 points and Bob gets 1 point. If the player is unable to do so, they lose the game. The parent node of some node is defined as . SOLVED: Alice and Bob are playing a game. Determine the probability that Alice wins. The quarters Question: Suppose Alice flips 3 coins and Bob flips 2 coins. Mar 22, 2024 · Use the Markov Chain to compute a joint distribution of all the states, across all 100 coin flips. They take turns alternately, and Alice makes the first move. In each operation, the player chooses a facing-up coin, removes the coin, and flips the two coins that are adjacent to it. (15) Alice and Bob play a game involving flipping of coins. 8. The problem is he cannot prove it. Alice and Bob play a game where they alternate moves, and Alice starts. There are two players, Alice and Bob, who alternate turns removing one, two or three coins from the pile Alice goes first. Sep 7, 2021 · Alice_ Bob, and Confucius are bored during recess, they decide to play new game. Alice and Bob are playing a game of coins. Assume that both players are very smart and he/she will try his/her best to work out a USING RECURSIONN!!! Mar 2, 2009 · Coin game: Alice and Bob are playing a game using a bunch of coins. Jan 8, 2024 · Bob proposes a game where Alice and Bob are each given a coin. Alice always goes first. Games Homework Rating: 3 Alice is taking Artificial Intelligence from Professor Bob. Initially two stacks of coins areplaced on a table, where the first stack contains 4 coins and the second stack contains 3 coins. Each of them have 2 candies. However, Alice must tell Bob the success probability p 1 p1 they have chosen before Bob decides his Problem #037 - game of coins Alice and Bob sit across each other, ready for their game of coins. Let's first try some experimentation. Two players, who we will call Alice and Bob, take turns removing one of the coins from either end of the remaining Can you solve this real interview question? Stone Game - Alice and Bob play a game with piles of stones. The game begins with Alice and afterwards they alternate the moves. Can you solve this real interview question? Divisor Game - Alice and Bob take turns playing a game, with Alice starting first. Aug 16, 2011 · Alice and Bob play a game as follows. Each second, Alice and Bob simultaneously check one coin. See Question Section 2. During a move, a player can select a node and move one or more coins to . Subsequently, Alice removes some positive number of coins from either one of the two piles, and then Bob does the same. Assign rewards based on whether Alice wins or loses the game. The rule of the new game is quite simple. - There are two piles of coins; the piles contain the same (finite, nonnegative) number of coins. (No funny business allowed — it has Alice and Bob are playing a game on a matrix, consisting of 2 2 rows and m m columns. Question: Alice, Bob, and Confucius are bored during recess, so they decide to play a new game. Being diplomatic, Bob does not accuse Alice of trickery. Sep 24, 2023 · [Bonus question: bonus marks] Alice and Bob play a game. Practice the Game of Coins problem now!Alice and Bob are playing a game. Alice goes first, and can pick up either one or two coins. Find the Winning Player in Coin Game Description You are given two positive integers x and y, denoting the number of coins with values 75 and 10 respectively. Alice and Bob believe that the coins are biased in favor of heads with P (HAlice's model) 0. If k is the picked number, the game is over. (b) Find the probability that X is a multiple of 3. On each player's turn, that player makes a move consisting of: * Choosing any x with 0 < x < n and n % x == 0. If it comes up TT, Alice gives Bob 4dolla. If "TT" appears first, Bob wins. If it comes up HH, Alice gives Bob 6 dollar. They toss 5 fair coins. Question: Consider two players: Alice and Bob. In each turn, a player selects either the first or the last coin from the row, removes it from the row, and receives the value of the coin. Otherwise they repeat, tossing five coins on each round, until the game is decided. If it comes up H H HH, Alice gives Bob $ 6 $6. For example, on Alice's first move she might remove the coin at position 3. See full list on mathspp. Oct 21, 2020 · Alice and Bob are playing a variant of Nim game. Bob flips n + 1 coins and Alice flips the remaining n. When the game starts, Alice and Bob go into separate soundproof rooms — they cannot communicate with each other in any way. - The players, starting with Alice, alternate taking turns. Alice wants to maximize the sum of elements of the array while Bob wants to minimize it. Alice and Bob want to play the following game by alternating turns: They have access to a row of n coins of values v1, , Un, where n is even. They are teammates, so they will win or lose together. Each time a player isallowed to pick 1, 2 or 4 coins, and the player that gets the last coin is Mar 18, 2024 · Flip a fair coin 100 times—it gives a sequence of heads (H) and tails (T). There are an even number of piles arranged in a row, and each pile has a positive integer number of stones piles[i]. Alice starts and then gives the coin to Bob and the cycle repeats until one of them has flipped both a heads and a tails. Each coin is placed head-up (H) or tail-up (T), and cannot be flipped or moved once it has been placed Question: Alice and Bob play a game involving flipping of coins. During their turn, each player removes any number of coins they wish to, all from one pile. At the beginning of the game, they each take out a coin, and end up withcoins labeled 1395 and 504. (b) Compute the probability Math Statistics and Probability Statistics and Probability questions and answers Please help me with this problem. Bob will then flip the coin $2n$ times. In this game, there are n piles of stones. A fair coin (that is, a coin with equal probability of landing heads and tails) is tossed repeatedly until one of the following happens. Alice and Bob play a game using the following arrangement of coins, which are joined by strings and hanging from the ceiling: $\qquad\qquad\qquad\qquad\quad$ The two alternate turns, with Alice going first. If we now consider 100 coin flips, when the walk ends at a number ≥ 1, Alice wins, when the number ends at 0 is a tie, when the number is between 0 and 1 is a tie and when the number is negative Bob wins. When n fair coins are flipped, the Nov 14, 2021 · Bob can apply this general strategy after each of Alice's moves to win the game because it guarantees that it will be Alice's move whenever they land on a number of coins that is a power of 2. Then Bob chooses another sequence of the same length. The Apr 13, 2016 · Define the "game" for Alice as a sequence of coin tosses that terminates in a head followed by a tail. Alice has $15 dollars and Bob has $10 dollars. 4. heads with probability 21 ). Alice obviously wins if there is one coin. In a single move, a player can choose a single pile i \ ( (1 \le i \le N )\) and withdraw any number of coins between 1 and \ (min (A [i],X)\) both inclusive from Math Statistics and Probability Statistics and Probability questions and answers 4. They each flip a coin and note whether it came up Heads or Tails Question: [Bonus question: 4 bonus marks) Alice and Bob play a game. Otherwise, Bob gives Alice $ 5 $5. Here's how the game goes like: Alice and Bob flip a coin. Therefore, when it is Alices turn to remove coins, the number of coins remaining will always be of the form $4m+1$. In this case Alice wins. Probability puzzle - a coin flipping game Alice and Bob are playing a coin flipping game. The player that gets the last coin is the winner. Alice and Bob are playing a game. Alice and Bob play the following coins-on-a-stack game. Let the coins be numbered 1 to 3 from left to right. Alice wins if the coins land all heads or all tails. On each turn, they both flip a fair coin. Alice and Bob both put all the coins they have on a table. 4. Alice, Bob, and Confucius are bored during recess, so they decide to play a new game. Alice spins a coin on a table and waits for it to land on one side. Bob each time guesses a number k. Jul 29, 2021 · 1908. Dec 9, 2019 · Alice and Bob play the following game: There are three fair coins available, a 5p coin, a 10p coin and a 20p coin. Consider the following two player game. Moves Players move in turns. 🏋️ Python / Modern C++ Solutions of All 3093 LeetCode Problems (Weekly Update) - Vijay0292/LeetCode-Solution Alice and Bob are playing a coin-matching game. On a move, a player can remove a square number of coins from either pile; e. Initially, there is a number n on the chalkboard. Oct 20, 2019 · The total way is 1 + 3 + 2 = 6 For input 7, Bob can reach 3 and 6, then Alice just pick 4 or 1 coins to win the game with 2 + 6 = 8 ways to win. Sum the marginal distribution according to whether Alice won, Bob won, or they tied. (a) Find the pmf of X. Then Bob might remove the consecutive pair of coins at positions 8 and 9; but Bob Math Statistics and Probability Statistics and Probability questions and answers U4. I n this project, you are tasked with developing a program that models a coin - tossing game between two players, Alice and Bob. Second, Bob will multiply at most x x elements of the array by −1 − 1. Instead, Bob introduces a small Question: pls RECURSİVE JAVA CODE Coin game: Alice and Bob are playing a game using a bunch of coins. (Another unfair game, 6 points) Alice and Bob play a game with 2n+1 fair coins (i. Alice and Bob are playing a game, defined below: There is an undirected tree graph with nodes that has the following properties: Each node has golden coins. When the game starts, Alice and Bob go into separate soundproof rooms – they cannot communicate with each other in any way. The rules for the game are as follows, Alice and Bob take turnsremoving a coin from the remaining pile, but they may only take a coin that is labeled k ifk = Question: Alice and Bob play a game. Alice owns one of these coins, and Bob owns the other two coins. If both are TAILs, then Alice gives Bob 1 dolloar. Given N, print "Alice" or "Bob" corresponding to who wins Alice and Bob are playing a game of coins. If all tosses are Heads,Bob wins. Dynamic Programming - Coin In a Line Game Problem Objective: In this game, which we will call the coins-in-a-line game, an even number, n, of coins, of various denominations from various countries, are placed in a line. "Coin game: Alice and Bob are playing a game using a bunch of coins. What is the probability that Alice wins this game?. Alice picks a number between 1 and n. “Look”, noted Alice, “one of the ducks left a trail of golden coins on the floor”. There is a box with $n \geq 2$ coins in it. Flip 100 coins, marked 1-100. 1 Alice and Bob play a game where they alternate moves, and Alice starts. Otherwise, Bob gives Alice 5 dollar. Alice believes that the coin is fair and P (heads) = 0:5. Alice and Bob are playing a fun game of tree tag. Bob starts first and he can take any amount of coins from the box and put them on the table, but not all of them. Apr 22, 2019 · Alice, Bob, and Confucius are bored during recess, so they decide to play a new game. Flip a fair coin 100 times—it gives a sequence of heads (H) and tails (T). Determine the condition that Math Statistics and Probability Statistics and Probability questions and answers Problem 5. Prior to placing bets, they tested the coin by tossing it twice and both Jun 8, 2020 · The rain was still falling and Alice and Bob were terribly bored of having to stay inside the caravan, so they decided to play a game. $ The coin lands "tails-tails" (that is, a tails is immediately followed by a tails) for the first time. If the current player can't make any move, they lose the game Alice and Bob have a large bag of coins which they use to play a game called HT-2. Everyday at 12h, prison guard Charles meets Alice and prison guard Daniel meets Bob. Although both players flip a fair coin, Bob has an extra flip, giving him an increased chance of obtaining more heads and thus a higher ** Probability Theory **of winning the game. Each time the piles of Alice and Bob are playing the following game. Aug 4, 2015 · Hi Shivam, lets understand in other way suppose if alice and bob can’t choose two adjacent they are allowed to choose only one coin then what happen alice started game if number of coin are odd then alice will win other wise not because only one coin is allowed to picked up. A valid move is defined as follows: You pick one coin or two adjacent coins and remove them. The cell in the i i -th row in the j j -th column contains ai,j a i j coins in it. The probability of tossing a head is 0. 6, and the probability of a tail is 0. Afterwards, they Jul 23, 2019 · Alice, Bob, and Confucius are bored during recess, so they decide to play a new game. Better than official and forum solutions. Alice and Bob are playing a game using a bunch of coins. The winner is the one with the higher score when Feb 11, 2015 · In the coin-toss game, says Dinur, one might think that after both had flipped and guessed they would have a 25% chance of winning the game, since each had a 50% chance of guessing correctly. Bob proposes a game where Alice and Bob are each given a coin. The game involves N coins and in each turn a player may remove at most M coins. If the result is heads, Alice wins $1 from Bob; if tails, Alice pays $1 to Bob. Alice and Bob believe that the coins are biased in favor of heads with Prior to placing bets, they tested the coin by tossing it twice and both came out to be heads. pls RECURSİVE JAVA CODE Coin game: Alice and Bob are playing a game using a bunch ofcoins. At the start of the game, Alice has two piles of coins in front of her: one pile contains 4 coins and the other pile contains 1 coin. If it is tails then Alice g Question: Suppose that during the playing of the coins-in-a-line game that Alice’s opponent, Bob, makes a choice that is suboptimal for him. Node is root of the tree. The total points remains equal between Bob and Alice for each scenario, as expected. , for the sequence THHHT Alice gets 2 points and Bob gets 1 point. Nov 21, 2023 · To draw a complete game tree for this game, start with a pile of 5 coins. At the beginning of the game, they write down N random positive integers, then they take turns (Alice first) to eith Feb 6, 2014 · 1 Consider this question I found on hackerrank: Coins Problem Alice and Bob were sitting in the sun; drinking orange juice; and watching some migrating ducks fly to Africa. JAVA CODE Coin game: Alice and Bob are playing a game using a bunch of coins. She will just take it and win. Starting with Alice, each player takes turns taking a coin from the top of a stack - they may choose any nonempty stack, but they must only take the top coin in that stack. The game works like this: the experimenter puts Alice in Bob in separate rooms and then explains the rules. Players make moves taking turns and in each move the player removes 1 or 2 coins from one of the stacks (which is not already emptied). e. $1. Description Alice and Bob is playing a game, there N coins in a pile. Engineering Computer Science Computer Science questions and answers Number of ways without recursion is important. Let X be the number of rounds the game lasts. Alice and Bob just invented a new game. Alice and Bob are playing a game of Nim. On their turn, a player must cut a string. They have N coin piles, where the \ (i^ {th}\) coin pile consists of \ (A [i]\) coins initially. In addition, Alice and Bob have also been given some integer X. Question: java recursion Coin game: Alice and Bob are playing a game using a bunch of coins. Alice goes first, she can take away one coin at least, and N-1 coins at most. Now Bob cannot win the game. Alice starts and continues flipping until a tail occurs at which point Bob starts flipping and continues until a tail occurs. Question: pls java code Coin game: Alice and Bob are playing a game using a bunch of coins. 72, and P (H Bob's model) = 0. The game is played on a tree of n n vertices numbered from 1 1 to n n. In each turn a player must remove atleast 1 coin. They will keep repeating the game until one of them has four coins, and the other has none. The objective of the game is to end with the most stones. Alice always places the first coin. Whoever picks up the May 14, 2024 · Who is more likely to win after 100 flips? Alice, who scores for every Heads-Heads, or Bob who scores for every Heads-Tails? An intuitive answer involving a dog on a soccer field is presented. Alice goes in order (1, 2, 3, …); Bob checks the odd coins, then the even (so 1, 3, 5, …, 99, 2, 4, 6, …). There is a circle of 12 coins, and on each move a player can remove either one coin or two coins that were originally adjacent on the circle. Players makemoves taking turns and in each move the player removes 1 or 2 coins from one of the stacks (which is notalready emptied). For each HH in the sequence of flips, Alice gets a point; for each HT, Bob does, so e. Since Alice and Bob can remove coins from either end of the line, an appropriate way to define subproblems is in terms of a range of indices for the coins, assuming they are initially numbered from 1 to n. The rules for the game are as follows, Alice and Bob take turns removing a coin from the remaining pile, but they may only take a coin that is labeled k if k = i + j or k = i − j, where Alice and Bob are playing a game. In second testcase, Alice removes coin numbered 2. If Bob manages Question: [Bonus question: 4 bonus marks) Alice and Bob play a game. Empty moves are not allowed. Alice gets one hundred £1 coins and In-depth solution and explanation for LeetCode 3021. Alice chooses a sequence of 3 coin flips. one can remove 1, 4, 9, ⋯ 1, 4, 9, coins from either pile in one move. For Bob, the game is a sequence of coin tosses that terminates in two consecutive heads. Then, Alice Sep 26, 2019 · If Alice gets $k$ consecutive Heads (H), Bob has to keep tossing until he gets $k$ consecutive H. (a) Compute the expectednumber of coin tosses needed to decide the game. Afterwards, they both flip their coins. If Alice and Bob both get the same number of heads, the game is a draw; otherwise, whoever flips more heads is the winner. If not, Bob gives Alice k coins and Alice tells Bob whether k is too high or too low. Initially, Alice is located at vertex a a, and Bob at vertex b b. Alice and Bob are playing another coin game. Ask him to play according to the optimal strategy, who will Alice and Bob are playing a game where they toss a fair coin. For each HH in the sequence of flips, Alice gets a point; for each HT, Bob does, e. The quarters are fair, and the winner receives a net payment of $2 ($3 - $1 = $2), and the losers Alice and Bob have a large bag of coins which they use to play a game called HT-2. Bob and Alice are playing a game: they are given an array of numbers and they can make a move if two identical numbers are adjacent in the array. for the sequence THHHT Alice gets 2 points and Bob gets… Explanation In first testcase, Alice removes the only coin to win the game. After that, Bob and Alice move away coins in turn, every time he (she) can take away one to twice of previous one. Bob wins if two heads and one tail land. Feb 12, 2024 · Alice and Bob have a large bag of coins which they use to play a game called HT-2. Branch out the game tree as Alice and Bob take turns **picking **up coins. Assume that both players are very smart and he/she will Question: pls RECURSİVE JAVA CODE Coin game: Alice and Bob are playing a game using a bunch of coins. Each player has two moves available: either take the larger pile of coins and give the smaller pile to the other player or pass both piles across the table to the other player. Alice and Bob are playing a game where they place bets on coin tosses. Confucius wins if one head and two tails land. They continue alternately removing coins in this way subject to the rule that the Alice and Bob are playing the following game. While the game sounds fair, Bob suspects the coin may be biased to land on heads more. Bob believes that the coin is biased in favor of heads with P (heads) = 0:6. Assume there are 20 coins, Alice take away 4 coins first, then Bob can take 1 to 8 coins. The game operates under the following rules: * The coin i s tossed n times, and the outcomes are recorded a s a sequence o f Heads (H) and Tails (T). Each is allowed decide the probability of heads for their coin. Each of them puts a dollar in the pot, and each tosses a coin. Prior to placing bets, they tested the coin by tossing it twice and both came out to be heads. For both the infinite-hats problem and the box-problem if the players have a strategy depending on only a finite number of inputs they can't Not my riddle, but wanted to share it. Question:Alice and Bob play the following game. The player unable to move loses. The first player who cannot make a move loses, and the other player wins. We would like to show you a description here but the site won’t allow us. They do not realize that all four coins are biased. Each of them puts dollar in the pot, and each tosses quarter: Alice wins if the coins land all heads or all tails Bob wins if two heads and one tail land, and Confucius wins if one head and two tails land. Find the number of positive integers less than or equal to for which there exists a strategy for Bob that guarantees that Bob will win the game regardless of Alice's play. Solving code challenges on HackerRank is one of the best ways to prepare for programming interviews. To get started, Alice places pile of a coins O the table; and then Bob places a pile of b coins on the table. Return the name of the player who wins the game if both Question: 5. There are n n piles consisting of a, b, c, ⋯ a, b, c, coins respectively. (a) Whose model would you use to place your bet in the next toss? Alice's or Bob's? Why? ( Hint: What is the probability of two 2. Can you solve this real interview question? Stone Game VII - Alice and Bob take turns playing a game, with Alice starting first. Nov 30, 2016 · Alice and Bob are playing a game. 55. Each turn, starting with Alice, the player must pick up coins with a total value 115. (No funny business allowed — it has Question: Alice and Bob are playing a game using a bunch of coins. Who is more likely to see two consecutive heads OR two consecutive tails first? 4. Alice and Bob take turns, with Alice Find the Winning Player in Coin Game - You are given two positive integers x and y, denoting the number of coins with values 75 and 10 respectively. The total number of stones across all the piles is odd, so there are no ties. Oct 16, 2022 · If Alice choses to remove $k$ coins for $k=1,2,3$, then Bob must remove $4-k$ coins. Mar 18, 2024 · Flip a fair coin 100 times—it gives a sequence of heads (H) and tails (T). The player who takes the last coin wins. Recall that a tree on n n vertices is an undirected, connected graph with n − 1 n 1 edges. If the two sides are different, i. For example, "How can Bob send a private message M to Alice in a public-key cryptosystem?" [2] is believed to be easier to describe and understand than if the hypothetical people were simply named A and B as in "How can B send a private In a coin flipping game between Alice and Bob, where each flips a coin n times, Bob wins if he receives more heads than Alice. Alice and Bob believe that the coins are biased with P (HjAlice0s) = 0:7, and P (HjBob0s) = 0:25. Feb 19, 2016 · Bob wins if: 1) Bob and Alice have equal number of heads and Bob tosses his last coin and gets head 2) Bob is ahead after tossing $10$ coins Probability of the first event is $1/2 \cdot 1/2 = 1/4$ As the number of coin flips goes up, both Bob's and Alice's average margin of victory (MoV) improves, but Alice's MoV is consistently higher than Bob's. If the number of heads Alice gets is greater than the number of heads Bob gets, the game continues. The rules for the game are as follows, Alice and Bob take turnsremoving a coin from the remaining pile, but they may only take a coin that is labeled k ifk = Question: Alice and Bob are playing a game. Dec 22, 2023 · This problem is from QuantGuide(namely Tricky Bob 1): Bob proposes a game where Alice and Bob are each given a coin. Bob goes second and can pick on either one or two coins. What I don't understand is that, for input 7, Alice can also reach 5, then Bob just picks 2 to win. What is the expected number of trials for Alice and Bob combined? Oct 18, 2020 · Alice and Bob are going to be incarcerated separately. If all tosses are Heads, Bob wins. They each flip a coin and note whether it came up Heads or Tails. To get started, Alice places a pile of a coins on the table, and then Bob places a pile of b coins on the table. Alice goes first and can pick up either one or two coins. Alice and Bob take turns to play the following game, and Alice goes first. Bob wins if two heads and one tail land, and Confucius wins if one head and two tails land. Alice and Bob play the following game. Dec 26, 2023 · If the coins match (two heads or two tails), Alice gets Bob's coin; if the coins do not match, Bob gets Alice's coin. The game is that Alice chooses a number $x$ in the interval [1 After finding a coin in her farm, Alice proposes the following game to Bob: Alice will flip the coin $n$ times. Before the game starts, they can talk to each other and agree on a strategy. One of them is a special (gold) coin and the rest are ordinary coins. Mar 23, 2019 · 4 Alice and Bob play a coin tossing game. This version of the game is inspired by this tweet. A fair coin has two sides, heads (H) and tails (T), giving each a probability of 0. heads with probability 1 2 ). Subsequently; Alice removes some positive number of coins from either one of the two piles, and then Bob does the same. , one HEAD and one TAIL, then Bob gives Alice 2 dollars. Question: Alice and Bob play a game with 2n + 1 fair coins (i. otherwise bob gives alice $1. if the coin flip is a head, alice gives bob $1. On each player's turn, they can remove either the leftmost stone or the rightmost stone from the row and receive points equal to the sum of the remaining stones' values in the row. In a move, Alice can jump to a vertex with distance at An example of an "Alice and Bob" used in cryptography Alice and Bob are the names of fictional characters used for convenience and to aid comprehension. If the coins match (two heads or two tails), Alice gets Bob's coin; if the coins do not match, Bob gets Alice's coin. In the hopes of making a bit of money, they each sign up to participate in a version of the famous economics lab experiment: the ultimatum game. The player who takes the last coin wins the game. This is a probability question that involves understanding the likelihood of different outcomes when flipping a fair coin multiple times. Otherwise they repeat,tossing five coins on each round, until the game is decided. If Bob takes away 5 coins, then Alice can Question: alice and bob play a coin toss game with a fair coin. For example, if there are 2 coins and Alice is Question 1: Consider a sequential-move game between Alice and Bob. Question: pls java code WITH RECURSION Coin game: Alice and Bob are playing a game using a bunch of coins. The players pick several coins out of the bunch in turn. com Apr 8, 2024 · Today’s puzzle was originally posted by Daniel Litt on Twitter. The game involves N piles of coins of varying sizes. Alice and Bob Playing Flower Game in Python, Java, C++ and more. At the beginning of the game, they each take out a coin, and end up with coins labeled 1395 and 504. Initially two stacks of coins are placed on a table, where the first stack contains 4 coins and the second stack contains 3 coins. They randomly determine who starts, then they take turns flipping a number of coins (N) and adding them to a growing pile. The process repeats until there are no coins left. However, Alice must tell Bob the success probability p1 they have chosen before Bob decides his p2. Alice moves first. Alice and Bob play a game. The rules for the game are as follows, Alice and Bob take turnsremoving a coin from the remaining pile, but they may only take a coin that is labeled k ifk = Jul 18, 2016 · There is no deterministic solution to the Alice-Bob-Box problem since if the adversary knows what box Bob will guess he can make it so that Bob gets it wrong. Alice and Bob are two broke students (neither one knows the other). Otherwise, they repeat, tossing five coins on each round, until the game is decided. 100 coins are stacked one above the other. (b) Compute the probability that Alicewins. Question: Alice and Bob are playing a game. The game is over if anyone is not able to make any valid move, and the other person wins. They will keep repeating the game until one of them has four coins, and the other one has nothing. Each of them puts a dollar in the pot, and each tosses a quarter. Suppose the probability of heads for Alice's coin and Bob's coin is pı and P2, respectively. N coins are placed on the table in a row. Topic description Alice and bob are playing a coin game, Alice first, they turn round coins on a rectangular desktop, ask the coin to not overlap, the coin edge cannot cross the edge of the desktop, the people who can't put down the coins will lose, now You know the diameter of the long-width n, m and coins of the desktop R. The rules for the game are as follows, Alice and Bob take turnsremoving a coin from the remaining pile, but they may only take a coin that is labeled k ifk = Jul 10, 2023 · Alice and Bob are playing a coin-tossing game. “Great!” exclaimed Bob, “let‟s play a game with this line of coins. means analyse it alice always want to make number of coin even because if number of coin will be even then bob choose Dec 4, 2018 · 1. Assume that both players are very smart and he/she will try his/her best to work out a strategy to win the game. * Replacing the number n on the chalkboard with n - x. For example, if there are 2 coins and Alice is Oct 2, 2023 · The game between Alice and Bob is not fair. (a) Compute the expected number of coin tosses needed to decide the game. Intuitions, example walk through, and complexity analysis. Both Alice and Bob aim to maximize their own Alice and Bob are playing a game. If it comes up T T TT, Alice gives Bob $ 4 $4. Who will emerge victorious? Dec 11, 2021 · CS 627 – Artificial Intelligence Games Homework Name: Hetali Chavda (U01758589) Alice is taking Artificial Intelligence from Professor Bob. Each time a player is allowed to pick 1, 2 or 4 coins, and the player that gets the last coin is the winner. On each player’s turn, the player should remove any positive number of stones from a non-empty pile of his or her choice. They each strategically reveal one side of their coins. If it is heads then Bob gives a candy to Alice. For the extra credit portion, the maximum total win for Alice or Bob depends on strategic choices related to the remaining coins and turn order. The first person to flip both a heads and a tails (not necessarily in that order) wins the game. But there is a clever strategy that Bob and Alice can use: If each guesses that the other has flipped exactly the same as their own coin flip, they raise their odds to 50%. If "HT" appears first, Alice wins. There are n stones arranged in a row. Let D be the Consider the following game, played between two players, Alice and Bob. To earn extra credit, Bob offers to play the following game. There are 2024 coins lying on the ground labeled 1 through 2024. Consider two players: Alice and Bob. Who is most likely to win? Option A: Alice Option B: Bob Option C: Equally likely I invite you to pause here for a moment and come up with your own solution The game consists of two steps: First, Alice will remove at most k k elements from the array. The quarters are fair, and the winner receives a net payment of $2 ($3 - $1 = $2), and the losers lose Question: Q7. Bob flips n+1 coins and Alice flips the remaining n. Given n, how many coins does Bob need to finish the game? Write the recurrence and analyze the complexity. Suppose Alice goes first. Alice wins the game if she flips heads two turns in a row, while Bob wins if he flips heads on one turn then tails on the next. Does this require that Alice recompute her table of remaining Mi,j values to plan her optimal strategy from this point on? Dec 7, 2023 · Alice has a winning strategy in the coin game by ensuring that she always leaves 4 coins after her first move. 5 or 50%. They start and continue to toss a fair coin until "HT" or "TT" appears. Jul 31, 2024 · 3222. They will keep repeating the game until one of them has four coins and the other one has nothing. Compute the marginal distribution of each player’s score on the 100th coin flip from the joint distribution. Each player has two moves available: either take the larger pile of coins and give the smaller pile to the other player, or push both piles across the table to the other player Question: Alice and Bob play the following game. If both are HEADs, then Alice gives Bob 3 dollars. Question 6 (16 points) Alice and Bob are playing the following game. Each time a player is allowed to pick 1, 2 or 4 coins. They each have a coin with two sides: HEAD and TAIL. There are 2024 coins lying on the ground labeled 1through 2024. Each prison guard takes his own prison guard coin out of their pocket (a coin with heads and tails, but not necessarily a fair coin) and tosses it, showing the result to the prisoner in front of him. In this game, Alice and Bob take turns placing one coin at a time on the table, each to the right of the previous one; thus they build a row of coins that grows to the right. Suppose the probability of heads for Alice’s coin and Bob’s coin is p1 and p2, respectively. Some asked if there was a computable solution. g. They flip a coin over and over again and a player wins as soon as their sequence appears. The first one to collect their target nu Dynamic Programming - Coin In a Line Game ProblemHard 203. Question: Games HomeworkAlice is taking Artificial Intelligence from Professor Bob. Then Alice starts flipping again and so forth. Also, if a player cannot make a move, they lose the Alice and Bob play the following coins-on-a-stack game. Game of Nim Level Medium Description Alice and Bob take turns playing a game with Alice starting first. If the number of Heads tosses is zero or one, Alice wins. agbnw nekd qpisk imsqvrzmc bmjmj cbjjryrk cbeo nqoahl zvkm npvam