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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 the game is played between Sheldon and Howard and Sheldon gets to start the game, in which of the following games does Sheldon not get to win, no matter which alphabet he picks in the first chance?
  • a)
    a = E, n = 6
  • b)
    a = A, n = 3
  • c)
    a = A, n = 7
  • d)
    a = C, n = 5
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, 
It has been asked when can the player starting the game never win.
Suppose the number of characters is x.
If the player starting the game has to lose, he has to be left with no other choice but Z in his last chance.
Hence, m( n + 1 ) + 1 = x
where m is a natural number.
Option 1: x = 22, n = 6, n + 1 = 7 -> 7 x 3 + 1 = 22, hence this satisfies the equation m( n + 1 ) + 1 = x
Option 2: x = 26, n = 3, n + 1 = 4 -> 4 x 6 + 2 = 26, this does not satisfy the equation m( n + 1 ) + 1 = x
Option 3: x = 26, n = 7, n + 1 = 8 -> 8 x 3 + 2 = 26, this does not satisfy the equation m( n + 1 ) + 1 = x
Option 4: x = 24, n = 5, n + 1 = 6 -> 6 x 3 + 6  = 24, this does not satisfy the equation m( n + 1 ) + 1 = x
Hence, Option 1.
Alternate Solution:
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 the opponent with Z which is a losing position. 
If n=6, any starting position from T to Y, you pick Y ensuring the opponent loses.
Hence T-Y -> winning positions.
S is a losing position as no matter what you pick, the opponent's starting position will fall in T-Y which are winning positions.
Similarly, M-R are winning positions as you should always choose R, putting the opponent on S.
So we see the pattern that Z, S, L, E are losing positions. The corresponding numbers are 26, 19, 12, 5.
As E is definitely losing position for n=6, Sheldon should choose E to definitely lose the game.
Hence, Option(A) is right.
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Most Upvoted Answer
Two players are playing a game called Pick an alpha. In this game, the...
Understanding the Game Dynamics
In the game "Pick an Alpha," players aim to avoid selecting the letter 'Z'. The game mechanics dictate that a player can only choose from a limited range of alphabets, starting from a specified letter. The challenge lies in maximizing one's chance of winning while minimizing the opponent's options.
Analysis of Each Game Scenario
1. Game A: a = E, n = 6
- Starting from 'E', the available letters are E, F, G, H, I, J.
- If Sheldon picks E, Howard can then pick from F, G, H, I, J, K.
- Regardless of Sheldon’s first choice, Howard can always navigate to force Sheldon into a position where he eventually has to pick 'Z'.
- Conclusion: Sheldon cannot win.
2. Game B: a = A, n = 3
- Starting from 'A', the letters are A, B, C.
- If Sheldon picks A, Howard picks from B, C, D, and so forth.
- Sheldon can strategically choose letters to avoid losing.
- Conclusion: Sheldon has winning strategies.
3. Game C: a = A, n = 7
- Starting from 'A', the letters extend to A, B, C, D, E, F, G.
- Sheldon can always avoid picking 'Z' by choosing wisely.
- Conclusion: Sheldon can win.
4. Game D: a = C, n = 5
- Starting from 'C', the letters are C, D, E, F, G.
- Similar to the previous games, Sheldon has options to avoid 'Z'.
- Conclusion: Sheldon can win.
Final Conclusion
The only scenario where Sheldon cannot secure a win is Game A (a = E, n = 6). No matter what choice he makes, Howard can always maneuver the game towards a win.
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Community 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, 
It has been asked when can the player starting the game never win.
Suppose the number of characters is x.
If the player starting the game has to lose, he has to be left with no other choice but Z in his last chance.
Hence, m( n + 1 ) + 1 = x
where m is a natural number.
Option 1: x = 22, n = 6, n + 1 = 7 -> 7 x 3 + 1 = 22, hence this satisfies the equation m( n + 1 ) + 1 = x
Option 2: x = 26, n = 3, n + 1 = 4 -> 4 x 6 + 2 = 26, this does not satisfy the equation m( n + 1 ) + 1 = x
Option 3: x = 26, n = 7, n + 1 = 8 -> 8 x 3 + 2 = 26, this does not satisfy the equation m( n + 1 ) + 1 = x
Option 4: x = 24, n = 5, n + 1 = 6 -> 6 x 3 + 6  = 24, this does not satisfy the equation m( n + 1 ) + 1 = x
Hence, Option 1.
Alternate Solution:
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 the opponent with Z which is a losing position. 
If n=6, any starting position from T to Y, you pick Y ensuring the opponent loses.
Hence T-Y -> winning positions.
S is a losing position as no matter what you pick, the opponent's starting position will fall in T-Y which are winning positions.
Similarly, M-R are winning positions as you should always choose R, putting the opponent on S.
So we see the pattern that Z, S, L, E are losing positions. The corresponding numbers are 26, 19, 12, 5.
As E is definitely losing position for n=6, Sheldon should choose E to definitely lose the game.
Hence, Option(A) is right.
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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 the game is being played between Simon and Billy, and Simon gets the first chance, what should he pick in the first chance so that he wins the game definitely? a = D, n = 8.

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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 the game is played between Sheldon and Howard and Sheldon gets to start the game, in which of the following games does Sheldon not get to win, no matter which alphabet he picks in the first chance?a)a = E, n = 6b)a = A, n = 3c)a = A, n = 7d)a = C, n = 5Correct answer is option 'A'. Can you explain this answer?
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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 the game is played between Sheldon and Howard and Sheldon gets to start the game, in which of the following games does Sheldon not get to win, no matter which alphabet he picks in the first chance?a)a = E, n = 6b)a = A, n = 3c)a = A, n = 7d)a = C, n = 5Correct 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 the game is played between Sheldon and Howard and Sheldon gets to start the game, in which of the following games does Sheldon not get to win, no matter which alphabet he picks in the first chance?a)a = E, n = 6b)a = A, n = 3c)a = A, n = 7d)a = C, n = 5Correct 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 the game is played between Sheldon and Howard and Sheldon gets to start the game, in which of the following games does Sheldon not get to win, no matter which alphabet he picks in the first chance?a)a = E, n = 6b)a = A, n = 3c)a = A, n = 7d)a = C, n = 5Correct 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 the game is played between Sheldon and Howard and Sheldon gets to start the game, in which of the following games does Sheldon not get to win, no matter which alphabet he picks in the first chance?a)a = E, n = 6b)a = A, n = 3c)a = A, n = 7d)a = C, n = 5Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
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 the game is played between Sheldon and Howard and Sheldon gets to start the game, in which of the following games does Sheldon not get to win, no matter which alphabet he picks in the first chance?a)a = E, n = 6b)a = A, n = 3c)a = A, n = 7d)a = C, n = 5Correct 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 the game is played between Sheldon and Howard and Sheldon gets to start the game, in which of the following games does Sheldon not get to win, no matter which alphabet he picks in the first chance?a)a = E, n = 6b)a = A, n = 3c)a = A, n = 7d)a = C, n = 5Correct 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 the game is played between Sheldon and Howard and Sheldon gets to start the game, in which of the following games does Sheldon not get to win, no matter which alphabet he picks in the first chance?a)a = E, n = 6b)a = A, n = 3c)a = A, n = 7d)a = C, n = 5Correct 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 the game is played between Sheldon and Howard and Sheldon gets to start the game, in which of the following games does Sheldon not get to win, no matter which alphabet he picks in the first chance?a)a = E, n = 6b)a = A, n = 3c)a = A, n = 7d)a = C, n = 5Correct 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 the game is played between Sheldon and Howard and Sheldon gets to start the game, in which of the following games does Sheldon not get to win, no matter which alphabet he picks in the first chance?a)a = E, n = 6b)a = A, n = 3c)a = A, n = 7d)a = C, n = 5Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice CAT tests.
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