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

There are n pieces arranged in a line, and each piece is colored either by 'A' or by 'B'. You are given a string colors of length n where colors[i] is the color of the ith piece.Alice and Bob are playing a game where they take alternating turns removing pieces from the line. In this game, Alice moves first.Alice is only allowed to remove a piece colored 'A' if both its neighbors are also colored 'A'. She is not allowed to remove pieces that are colored 'B'.Bob is only allowed to remove a piece colored 'B' if both its neighbors are also colored 'B'. He is not allowed to remove pieces that are colored 'A'.Alice and Bob cannot remove pieces from the edge of the line.If a player cannot make a move on their turn, that player loses and the other player wins.Assuming Alice and Bob play optimally, return true if Alice wins, or return false if Bob wins. Example 1:Input: colors = "AAABABB"Output: trueExplanation:AAABABB -> AABABBAlice moves first.She removes the second 'A' from the left since that is the only 'A' whose neighbors are both 'A'.Now it's Bob's turn.Bob cannot make a move on his turn since there are no 'B's whose neighbors are both 'B'.Thus, Alice wins, so return true.Example 2:Input: colors = "AA"Output: falseExplanation:Alice has her turn first.There are only two 'A's and both are on the edge of the line, so she cannot move on her turn.Thus, Bob wins, so return false.Example 3:Input: colors = "ABBBBBBBAAA"Output: falseExplanation:ABBBBBBBAAA -> ABBBBBBBAAAlice moves first.Her only option is to remove the second to last 'A' from the right.ABBBBBBBAA -> ABBBBBBAANext is Bob's turn.He has many options for which 'B' piece to remove. He can pick any.On Alice's second turn, she has no more pieces that she can remove.Thus, Bob wins, so return false.

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?

There is rectangle of size 𝑁×𝑀N×M with opposite corners at (0,0)(0,0) and (𝑁,𝑀)(N,M); and a special point (𝑥+0.5,𝑦+0.5) (0≤𝑥<𝑁,0≤𝑦<𝑀)(x+0.5,y+0.5) (0≤x<N,0≤y<M).Two players play a game on the rectangle where each player takes alternate turns. In his/her turn, the player will choose a line, either 𝑥=𝑘x=k or 𝑦=𝑘y=k, such that:𝑘k is an integer;The chosen line divides the current rectangle into two non-empty parts.The part of rectangle that does not consist of the special point, is discarded for further moves.The player who cannot make a move loses. If both players play optimally, determine the number of special points such that the first player wins.Input FormatThe first line of input will contain a single integer 𝑇T, denoting the number of test cases.Each test case contains two space-separated integers 𝑁N and 𝑀M — the lengths of the sides of the rectangle.Output FormatFor each test case, print the number of special points (𝑥+0.5,𝑦+0.5)(x+0.5,y+0.5) for which the first player wins the game.Note that 0≤𝑥<𝑁0≤x<N and 0≤𝑦<𝑀0≤y<M.Constraints1≤𝑇≤1041≤T≤10 4 1≤𝑁,𝑀≤1061≤N,M≤10 6 The sum of 𝑁N as well as the sum of 𝑀M over all test cases does not exceed 10610 6 .Sample 1:InputOutput42 12 23 51 120100Explanation:Test case 11 : There are 22 possible special points (0.5,0.5)(0.5,0.5) and (1.5,0.5)(1.5,0.5). In both cases, the first player can select the line 𝑥=1x=1 on his first move, and then the second player is left with no moves. Thus, the first player wins for both the special points.Test case 22 : There are 44 possible special points, all of them end up losing for the first player.

General algorithm applied on game tree for making decision of win/lose is

A game can be formally defined as a kind of search problem with the following components.