Below is given a board game that Honey and Sunny are playing. They both start from the box showing 'start'. They throw a dice that can show a number from 1 to 6. On the basis of the number that has come on dice, the player who has thrown the dice moves that many steps in the direction as represented by arrows. The boxes on which a player reaches during the game, the numbers on those boxes are added together to get the score of that player. Player reaching box representing 'end' first wins the game. If none of them is able to reach the box representing 'end' in 6 turns, the game results in a draw. Honey has the first turn.If in his first three turns, Honey gets 2, 3 and 6 on the dice, respectively, then what would be his score after three turns?

Alice and Bob are playing a board game.On their turn, a player must roll 𝑁N standard 66-sided dice, and their action will be determined by the sum of values on the top faces of the 𝑁N dice.On a certain turn of Alice, she rolls the dice and obtains the sequence of values 𝐴1,𝐴2,…,𝐴𝑁A 1​ ,A 2​ ,…,A N​ on the top faces.However, Bob isn't paying attention, allowing Alice to cheat a little!Alice can choose a die, and flip it - so the opposite face is upward.Note that these are standard 66-sided dice, so the sum of values on opposite faces is 77. That is:11 is opposite to 66.22 is opposite to 55.33 is opposite to 44.So as to not make Bob suspicious, Alice can perform this flipping operation at most 𝐾K times.What's the maximum score (i.e, sum of values of top faces of the dice) she can obtain?Input FormatThe first line of input will contain a single integer 𝑇T, denoting the number of test cases.Each test case consists of two lines of input.The first line of each test case contains two space-separated integers 𝑁N and 𝐾K — the number of dice and the number of times Alice can flip dice.The second line contains 𝑁N space-separated integers 𝐴1,𝐴2,…,𝐴𝑁A 1​ ,A 2​ ,…,A N​ — the initial values of the dice.Output FormatFor each test case, output on a new line the maximum score Alice can obtain if she flips a die at most 𝐾K times.Constraints1≤𝑇≤1051≤T≤10 5 1≤𝑁≤2⋅1051≤N≤2⋅10 5 1≤𝐾≤𝑁1≤K≤N1≤𝐴𝑖≤61≤A i​ ≤6The sum of 𝑁N over all test cases won't exceed 2⋅1052⋅10 5 .Sample 1:InputOutput42 13 44 23 4 4 55 31 2 3 2 16 26 5 4 3 2 1

A game is played by moving a game piece left or right along a horizontal game board. The board consists of spaces of various colors, as shown. The circle represents the initial location of the game piece.Yellow Black Green Green Red Yellow Black Black Yellow Black                  ● The following algorithm indicates how the game is played. The game continues until the game is either won by landing on the red space or lost when the piece moves off either end of the board.Step 1:Place a game piece on a space that is not red and set a counter to 0.Step 2:If the game piece is on a yellow space, move the game piece 3 positions to the left and go to step 3. Otherwise, if the game piece is on a black space, move the game piece 1 position to the left and go to step 3. Otherwise, if the game piece is on a green space, move the game piece 2 positions to the right and go to step 3.Step 3:Increase the value of the counter by 1.Step 4:If game piece is on the red space or moved off the end of the game board, the game is complete. Otherwise, go back to step 2.If a game is begun by placing the game piece on the rightmost black space for step 1, what will be the value of the counter at the end of the game?Responses2233445

A game is played where two unbiased dice are rolled and the score in the game is thegreater of the two numbers shown. If the two numbers are the same, then the score in thegame is the number shown on one of the dice. A diagram showing the possible outcomes isgiven below.First die1 2 3 4 5 6Second die123456Let T be the random variable “the score in a game”.(a) Complete the table to show the probability distribution of T

if two players A and B are alternatively throwing a coin and a die together. A player who first throws head and 6 wins the game. If A starts the game, then the probability that B wins the game is

In a game show called “Squad Game”, there are n contestants labelled 1 to n, in a circle.Moving clockwise around the circle, starting with contestant 1, each contestant k who has not yet been eliminated nominates a contestant (which may be themselves) for possible elimination. Contestant k then rolls a fair 6-sided die, and if the result is a 6, then the nominated player is eliminated from the game. Play continues in this way until a fixed number L < n of players have been eliminated.(a) Suppose that we watch this game and observe the labels of the L players eliminated in the order in which they were eliminated. Describe a suitable sample space for this experiment.(b) Suppose instead that we watch such a game and observe only the labels of the L players eliminated. Describe a suitable sample space for this experiment.(c) Suppose instead that we watch such a game and observe only whether player 1 is eliminated. Describe a suitable sample space for this experiment.(d) Suppose that each player nominates a uniformly chosen player among those who have not yet been eliminated (i.e. if j < L players have been eliminated then the player whose turn it currently rolls a fair (n − j)-sided die to determine who they will nominate). Find the probability of each sample point in the three experiments (a)-(c) above.