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Two players are playing a game called 'Pick an alpha'. In this game, there are 2 variables, the first one is 'a', the starting alphabet, and the second one 'n' the maximum range of alphabets starting from 'a'. The game proceeds as follows. One of the players picks an alphabet from the first n alphabets starting from 'a', say 'm', now the second player has to pick an alphabet from the first n alphabets starting from the alphabet just after 'm', and in a similar way, it continues till one player picks the alphabet Z. The player to choose Z loses the game. If at any point during the game, less than n alphabets remain, the player has to choose from these remaining alphabets. Both the players pick alphabets that maximise their chance to win.
Suppose, the value of 'a' is G and the value of n is 3. So, the first player has to pick an alphabet among G, H, I. Suppose he picks I. Then the second player has to pick among J, K and L. It continues in a similar fashion.
Based on the information given above, answer the questions that follow.
Q. If a = A and n = 5, what should the player starting the game choose initially so that he will definitely win the game?
- a)A
- b)B
- c)D
- d)E
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Two players are playing a game called Pick an alpha. In this game, the...
Let us think of it this way. The alphabets from A to Z can be thought of as numbers from 1 to 26 from which the two players pick.
If the player starting the game wants to win, he has to make sure that the other one is left with only one number, i.e the last number 26, in his last chance, which he has to pick necessarily.
Now let us consider a consecutive pair of chances. Whichever number a player picks from the n different choices, the second player can always pick a number such that to adjust it and make a sum of n + 1.
So, suppose, n = 6. If the first player chooses 3, the second player can choose 4 to make the sum 7.
So,
The sum of all numbers should be the total number of characters, that is the alphabet representing 'a' to the alphabet 'Z'. In this case,
26 - ( 3 x 7 + 1) = 4, i.e D.
In this question,
If a = A, this means a = 1.
n = 5.
n + 1 = 6
Total number of alphabets = 26
So, he should choose,
26 - ( 6 x 4 + 1) = 26 - 25 = 1
Hence, A.
Alternate explanation:
Let the player who starts be P1 and the other be P2. We have to figure out which starting positions are definite losing positions.
Z is a losing position. If only Z is left, you have to pick Z and lose.
Y is a winning position as you will pick Y leaving opponent with Z which is a losing position.
Any starting position from U to Y, you pick Y ensuring opponent loses.
Hence U-Y -> winning positions.
T is a losing position as no matter what you pick, opponent's starting position will fall in U-Y which are winning positions.
Similarly, O-S are winning positions as you should always choose S, putting opponent on T.
So we see the pattern that Z, T, N, H, B are losing positions. The corresponding numbers are 26, 20, 14, 8, 2.
As B is definitely losing position, the first player should choose A to put the opponent on B.
Most Upvoted Answer
Two players are playing a game called Pick an alpha. In this game, the...
Understanding the Game
In the game "Pick an alpha," two players alternate picking letters from a specified range, with the goal of avoiding the letter 'Z.' The player who picks 'Z' loses the game. Given the starting letter 'A' and the range of 5, the first player can choose from the letters A, B, C, D, and E.
Game Strategy
- The key to winning lies in controlling the choices available for the opponent.
- By carefully selecting the initial letter, the first player can set up a winning strategy.
Optimal Move Analysis
1. **Choosing 'A'**:
- If the first player picks 'A':
- The second player can choose from B, C, D, E.
- No matter what the second player picks, the first player can always respond in a way that keeps the game going until the second player is forced to pick 'Z'.
2. **Choosing 'B'**:
- If the first player picks 'B':
- The second player picks from C, D, E, F.
- This still allows the second player to have a chance of avoiding 'Z' for longer.
3. **Choosing 'C'**:
- If the first player picks 'C':
- The second player can choose from D, E, F, G.
- The control gradually slips away from the first player.
4. **Choosing 'D'**:
- If 'D' is chosen:
- The second player picks from E, F, G, H.
- The first player is further away from a guaranteed win.
5. **Choosing 'E'**:
- If 'E' is chosen:
- The second player can select F, G, H, I, leading to more opportunities to avoid 'Z'.
Conclusion
Choosing 'A' gives the first player the maximum control and ensures that they can manipulate the game in such a way that the second player is forced to pick 'Z'. Hence, option 'A' is the correct choice to guarantee a win.
In the game "Pick an alpha," two players alternate picking letters from a specified range, with the goal of avoiding the letter 'Z.' The player who picks 'Z' loses the game. Given the starting letter 'A' and the range of 5, the first player can choose from the letters A, B, C, D, and E.
Game Strategy
- The key to winning lies in controlling the choices available for the opponent.
- By carefully selecting the initial letter, the first player can set up a winning strategy.
Optimal Move Analysis
1. **Choosing 'A'**:
- If the first player picks 'A':
- The second player can choose from B, C, D, E.
- No matter what the second player picks, the first player can always respond in a way that keeps the game going until the second player is forced to pick 'Z'.
2. **Choosing 'B'**:
- If the first player picks 'B':
- The second player picks from C, D, E, F.
- This still allows the second player to have a chance of avoiding 'Z' for longer.
3. **Choosing 'C'**:
- If the first player picks 'C':
- The second player can choose from D, E, F, G.
- The control gradually slips away from the first player.
4. **Choosing 'D'**:
- If 'D' is chosen:
- The second player picks from E, F, G, H.
- The first player is further away from a guaranteed win.
5. **Choosing 'E'**:
- If 'E' is chosen:
- The second player can select F, G, H, I, leading to more opportunities to avoid 'Z'.
Conclusion
Choosing 'A' gives the first player the maximum control and ensures that they can manipulate the game in such a way that the second player is forced to pick 'Z'. Hence, option 'A' is the correct choice to guarantee a win.
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Two players are playing a game called Pick an alpha. In this game, there are 2 variables, the first one is a, the starting alphabet, and the second one n the maximum range of alphabets starting from a. The game proceeds as follows. One of the players picks an alphabet from the first n alphabets starting from a, say m, now the second player has to pick an alphabet from the first n alphabets starting from the alphabet just afterm, and in a similar way, it continues till one player picks the alphabet Z. The player to choose Z loses the game. If at any point during the game, less than n alphabets remain, the player has to choose from these remaining alphabets.Both the players pick alphabets that maximise their chance to win.Suppose, the value of a is G and the value of n is 3. So, the first player has to pick an alphabet among G, H, I. Suppose he picks I. Then the second player has to pick among J, K and L. It continues in a similar fashion.Based on the information given above, answer the questions that follow.Q. If a = A and n = 5, what should the player starting the game choose initially so that he will definitely winthe game?a)Ab)Bc)Dd)ECorrect answer is option 'A'. Can you explain this answer?
Question Description
Two players are playing a game called Pick an alpha. In this game, there are 2 variables, the first one is a, the starting alphabet, and the second one n the maximum range of alphabets starting from a. The game proceeds as follows. One of the players picks an alphabet from the first n alphabets starting from a, say m, now the second player has to pick an alphabet from the first n alphabets starting from the alphabet just afterm, and in a similar way, it continues till one player picks the alphabet Z. The player to choose Z loses the game. If at any point during the game, less than n alphabets remain, the player has to choose from these remaining alphabets.Both the players pick alphabets that maximise their chance to win.Suppose, the value of a is G and the value of n is 3. So, the first player has to pick an alphabet among G, H, I. Suppose he picks I. Then the second player has to pick among J, K and L. It continues in a similar fashion.Based on the information given above, answer the questions that follow.Q. If a = A and n = 5, what should the player starting the game choose initially so that he will definitely winthe game?a)Ab)Bc)Dd)ECorrect answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Two players are playing a game called Pick an alpha. In this game, there are 2 variables, the first one is a, the starting alphabet, and the second one n the maximum range of alphabets starting from a. The game proceeds as follows. One of the players picks an alphabet from the first n alphabets starting from a, say m, now the second player has to pick an alphabet from the first n alphabets starting from the alphabet just afterm, and in a similar way, it continues till one player picks the alphabet Z. The player to choose Z loses the game. If at any point during the game, less than n alphabets remain, the player has to choose from these remaining alphabets.Both the players pick alphabets that maximise their chance to win.Suppose, the value of a is G and the value of n is 3. So, the first player has to pick an alphabet among G, H, I. Suppose he picks I. Then the second player has to pick among J, K and L. It continues in a similar fashion.Based on the information given above, answer the questions that follow.Q. If a = A and n = 5, what should the player starting the game choose initially so that he will definitely winthe game?a)Ab)Bc)Dd)ECorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two players are playing a game called Pick an alpha. In this game, there are 2 variables, the first one is a, the starting alphabet, and the second one n the maximum range of alphabets starting from a. The game proceeds as follows. One of the players picks an alphabet from the first n alphabets starting from a, say m, now the second player has to pick an alphabet from the first n alphabets starting from the alphabet just afterm, and in a similar way, it continues till one player picks the alphabet Z. The player to choose Z loses the game. If at any point during the game, less than n alphabets remain, the player has to choose from these remaining alphabets.Both the players pick alphabets that maximise their chance to win.Suppose, the value of a is G and the value of n is 3. So, the first player has to pick an alphabet among G, H, I. Suppose he picks I. Then the second player has to pick among J, K and L. It continues in a similar fashion.Based on the information given above, answer the questions that follow.Q. If a = A and n = 5, what should the player starting the game choose initially so that he will definitely winthe game?a)Ab)Bc)Dd)ECorrect answer is option 'A'. Can you explain this answer?.
Two players are playing a game called Pick an alpha. In this game, there are 2 variables, the first one is a, the starting alphabet, and the second one n the maximum range of alphabets starting from a. The game proceeds as follows. One of the players picks an alphabet from the first n alphabets starting from a, say m, now the second player has to pick an alphabet from the first n alphabets starting from the alphabet just afterm, and in a similar way, it continues till one player picks the alphabet Z. The player to choose Z loses the game. If at any point during the game, less than n alphabets remain, the player has to choose from these remaining alphabets.Both the players pick alphabets that maximise their chance to win.Suppose, the value of a is G and the value of n is 3. So, the first player has to pick an alphabet among G, H, I. Suppose he picks I. Then the second player has to pick among J, K and L. It continues in a similar fashion.Based on the information given above, answer the questions that follow.Q. If a = A and n = 5, what should the player starting the game choose initially so that he will definitely winthe game?a)Ab)Bc)Dd)ECorrect answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Two players are playing a game called Pick an alpha. In this game, there are 2 variables, the first one is a, the starting alphabet, and the second one n the maximum range of alphabets starting from a. The game proceeds as follows. One of the players picks an alphabet from the first n alphabets starting from a, say m, now the second player has to pick an alphabet from the first n alphabets starting from the alphabet just afterm, and in a similar way, it continues till one player picks the alphabet Z. The player to choose Z loses the game. If at any point during the game, less than n alphabets remain, the player has to choose from these remaining alphabets.Both the players pick alphabets that maximise their chance to win.Suppose, the value of a is G and the value of n is 3. So, the first player has to pick an alphabet among G, H, I. Suppose he picks I. Then the second player has to pick among J, K and L. It continues in a similar fashion.Based on the information given above, answer the questions that follow.Q. If a = A and n = 5, what should the player starting the game choose initially so that he will definitely winthe game?a)Ab)Bc)Dd)ECorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two players are playing a game called Pick an alpha. In this game, there are 2 variables, the first one is a, the starting alphabet, and the second one n the maximum range of alphabets starting from a. The game proceeds as follows. One of the players picks an alphabet from the first n alphabets starting from a, say m, now the second player has to pick an alphabet from the first n alphabets starting from the alphabet just afterm, and in a similar way, it continues till one player picks the alphabet Z. The player to choose Z loses the game. If at any point during the game, less than n alphabets remain, the player has to choose from these remaining alphabets.Both the players pick alphabets that maximise their chance to win.Suppose, the value of a is G and the value of n is 3. So, the first player has to pick an alphabet among G, H, I. Suppose he picks I. Then the second player has to pick among J, K and L. It continues in a similar fashion.Based on the information given above, answer the questions that follow.Q. If a = A and n = 5, what should the player starting the game choose initially so that he will definitely winthe game?a)Ab)Bc)Dd)ECorrect answer is option 'A'. Can you explain this answer?.
Solutions for Two players are playing a game called Pick an alpha. In this game, there are 2 variables, the first one is a, the starting alphabet, and the second one n the maximum range of alphabets starting from a. The game proceeds as follows. One of the players picks an alphabet from the first n alphabets starting from a, say m, now the second player has to pick an alphabet from the first n alphabets starting from the alphabet just afterm, and in a similar way, it continues till one player picks the alphabet Z. The player to choose Z loses the game. If at any point during the game, less than n alphabets remain, the player has to choose from these remaining alphabets.Both the players pick alphabets that maximise their chance to win.Suppose, the value of a is G and the value of n is 3. So, the first player has to pick an alphabet among G, H, I. Suppose he picks I. Then the second player has to pick among J, K and L. It continues in a similar fashion.Based on the information given above, answer the questions that follow.Q. If a = A and n = 5, what should the player starting the game choose initially so that he will definitely winthe game?a)Ab)Bc)Dd)ECorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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Here you can find the meaning of Two players are playing a game called Pick an alpha. In this game, there are 2 variables, the first one is a, the starting alphabet, and the second one n the maximum range of alphabets starting from a. The game proceeds as follows. One of the players picks an alphabet from the first n alphabets starting from a, say m, now the second player has to pick an alphabet from the first n alphabets starting from the alphabet just afterm, and in a similar way, it continues till one player picks the alphabet Z. The player to choose Z loses the game. If at any point during the game, less than n alphabets remain, the player has to choose from these remaining alphabets.Both the players pick alphabets that maximise their chance to win.Suppose, the value of a is G and the value of n is 3. So, the first player has to pick an alphabet among G, H, I. Suppose he picks I. Then the second player has to pick among J, K and L. It continues in a similar fashion.Based on the information given above, answer the questions that follow.Q. If a = A and n = 5, what should the player starting the game choose initially so that he will definitely winthe game?a)Ab)Bc)Dd)ECorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Two players are playing a game called Pick an alpha. In this game, there are 2 variables, the first one is a, the starting alphabet, and the second one n the maximum range of alphabets starting from a. The game proceeds as follows. One of the players picks an alphabet from the first n alphabets starting from a, say m, now the second player has to pick an alphabet from the first n alphabets starting from the alphabet just afterm, and in a similar way, it continues till one player picks the alphabet Z. The player to choose Z loses the game. If at any point during the game, less than n alphabets remain, the player has to choose from these remaining alphabets.Both the players pick alphabets that maximise their chance to win.Suppose, the value of a is G and the value of n is 3. So, the first player has to pick an alphabet among G, H, I. Suppose he picks I. Then the second player has to pick among J, K and L. It continues in a similar fashion.Based on the information given above, answer the questions that follow.Q. If a = A and n = 5, what should the player starting the game choose initially so that he will definitely winthe game?a)Ab)Bc)Dd)ECorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Two players are playing a game called Pick an alpha. In this game, there are 2 variables, the first one is a, the starting alphabet, and the second one n the maximum range of alphabets starting from a. The game proceeds as follows. One of the players picks an alphabet from the first n alphabets starting from a, say m, now the second player has to pick an alphabet from the first n alphabets starting from the alphabet just afterm, and in a similar way, it continues till one player picks the alphabet Z. The player to choose Z loses the game. If at any point during the game, less than n alphabets remain, the player has to choose from these remaining alphabets.Both the players pick alphabets that maximise their chance to win.Suppose, the value of a is G and the value of n is 3. So, the first player has to pick an alphabet among G, H, I. Suppose he picks I. Then the second player has to pick among J, K and L. It continues in a similar fashion.Based on the information given above, answer the questions that follow.Q. If a = A and n = 5, what should the player starting the game choose initially so that he will definitely winthe game?a)Ab)Bc)Dd)ECorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Two players are playing a game called Pick an alpha. In this game, there are 2 variables, the first one is a, the starting alphabet, and the second one n the maximum range of alphabets starting from a. The game proceeds as follows. One of the players picks an alphabet from the first n alphabets starting from a, say m, now the second player has to pick an alphabet from the first n alphabets starting from the alphabet just afterm, and in a similar way, it continues till one player picks the alphabet Z. The player to choose Z loses the game. If at any point during the game, less than n alphabets remain, the player has to choose from these remaining alphabets.Both the players pick alphabets that maximise their chance to win.Suppose, the value of a is G and the value of n is 3. So, the first player has to pick an alphabet among G, H, I. Suppose he picks I. Then the second player has to pick among J, K and L. It continues in a similar fashion.Based on the information given above, answer the questions that follow.Q. If a = A and n = 5, what should the player starting the game choose initially so that he will definitely winthe game?a)Ab)Bc)Dd)ECorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Two players are playing a game called Pick an alpha. In this game, there are 2 variables, the first one is a, the starting alphabet, and the second one n the maximum range of alphabets starting from a. The game proceeds as follows. One of the players picks an alphabet from the first n alphabets starting from a, say m, now the second player has to pick an alphabet from the first n alphabets starting from the alphabet just afterm, and in a similar way, it continues till one player picks the alphabet Z. The player to choose Z loses the game. If at any point during the game, less than n alphabets remain, the player has to choose from these remaining alphabets.Both the players pick alphabets that maximise their chance to win.Suppose, the value of a is G and the value of n is 3. So, the first player has to pick an alphabet among G, H, I. Suppose he picks I. Then the second player has to pick among J, K and L. It continues in a similar fashion.Based on the information given above, answer the questions that follow.Q. If a = A and n = 5, what should the player starting the game choose initially so that he will definitely winthe game?a)Ab)Bc)Dd)ECorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice CAT tests.
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