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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 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.
  • a)
    E
  • b)
    F
  • c)
    G
  • d)
    H
Correct answer is option 'C'. 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 = D, this means a = 4.
n = 8.
n + 1 = 9
Total number of alphabets = 26 - 4 + 1 = 23
So, he should choose,
23 - ( 9 x 2 + 1) = 23 - 19 = 4
Hence, D + 4 - 1 = G.
Alternate explanation:
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.
Any starting position from R to Y, you pick Y ensuring the opponent loses.
Hence R-Y -> winning positions.
Q is a losing position as no matter what you pick, the opponent's starting position will fall in R-Y which are winning positions.
Similarly, I-P are winning positions as you should always choose P, putting the opponent on Q.
So we see the pattern that Z, Q, H are losing positions. The corresponding numbers are 26, 17, 8.
As H is definitely losing position, the first player should choose G to put the opponent on H. 
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Most Upvoted 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 = D, this means a = 4.
n = 8.
n + 1 = 9
Total number of alphabets = 26 - 4 + 1 = 23
So, he should choose,
23 - ( 9 x 2 + 1) = 23 - 19 = 4
Hence, D + 4 - 1 = G.
Alternate explanation:
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.
Any starting position from R to Y, you pick Y ensuring the opponent loses.
Hence R-Y -> winning positions.
Q is a losing position as no matter what you pick, the opponent's starting position will fall in R-Y which are winning positions.
Similarly, I-P are winning positions as you should always choose P, putting the opponent on Q.
So we see the pattern that Z, Q, H are losing positions. The corresponding numbers are 26, 17, 8.
As H is definitely losing position, the first player should choose G to put the opponent on H. 
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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?

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. Suppose the rules of the game are changed such that the one who picks Z wins. What should the player who is starting the game pick in his first chance so that he definitely wins? a = A, n = 4.

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?

The chief scientist of a major vaccine producing company has the responsibility to keep the formula of the vaccine confidential. He stores the formula in his e-device with 3 consecutive locks, all of which need to be unlocked to access the formula. The first of the 3 locks is a pattern lock, the second one is a numeric lock and the third and final one is an alphanumeric lock. The pattern lock is in the form of a regular hexagon with 6 distinct vertices A1, A2, A3, A4, A5, A6, in that order. One needs to connect all the 6 vertices one after the another in any random order connecting each vertex only once and only one order of connecting the 6 vertices exists which will unlock the first lock. The numeric lock has a code of ABC, where A, B and C are single digit natural numbers. A is a multiple of 2. B is a multiple of 3, C is a multiple of 4 but not equal to A.The alphanumeric lock has a code MNPQRS, where M and N are alphabets and P, Q, R and S are digits. M and N have to be consecutive vowels or consecutive consonants, not necessarily in order. Two alphabets are said to be consecutive vowels if both of them are vowels and they are consecutive when all the 5 vowels are written in alphabetical order. For example, E and I are consecutive vowels, but A and O are not. Two alphabets are said to be consecutive consonants if both of them are consonants and they are consecutive when all the 21 consonants are written in alphabetical order. For example, D and F are consecutive consonants but D and V are not. For example, M and N can be A and E respectively or E and A respectively. P is equal to Base-Ten-Index of M. Q is equal to the Base-Ten-Index of N. R and S can only take binary values, that is, 0 or 1.Base-Ten-Index of an alphabet = Index of alphabet % 10, where Index of an alphabet is its position when all alphabets from A to Z are arranged alphabetically and a%b is the remainder when a is divided by b.For example, Base-Ten-Index of J = 10 = 0 , Base-Ten-Index of M = 13 = 3.The chief scientist can only set passwords/patterns which follow all of the conditions mentioned above.Based on the information given above, answer the questions that follow.Q.How many alphanumeric codes for the third lock are possible which necessarily have an A as one of the alphabets in the code?

The chief scientist of a major vaccine producing company has the responsibility to keep the formula of the vaccine confidential. He stores the formula in his e-device with 3 consecutive locks, all of which need to be unlocked to access the formula. The first of the 3 locks is a pattern lock, the second one is a numeric lock and the third and final one is an alphanumeric lock. The pattern lock is in the form of a regular hexagon with 6 distinct vertices A1, A2, A3, A4, A5, A6, in that order. One needs to connect all the 6 vertices one after the another in any random order connecting each vertex only once and only one order of connecting the 6 vertices exists which will unlock the first lock. The numeric lock has a code of ABC, where A, B and C are single digit natural numbers. A is a multiple of 2. B is a multiple of 3, C is a multiple of 4 but not equal to A.The alphanumeric lock has a code MNPQRS, where M and N are alphabets and P, Q, R and S are digits. M and N have to be consecutive vowels or consecutive consonants, not necessarily in order. Two alphabets are said to be consecutive vowels if both of them are vowels and they are consecutive when all the 5 vowels are written in alphabetical order. For example, E and I are consecutive vowels, but A and O are not. Two alphabets are said to be consecutive consonants if both of them are consonants and they are consecutive when all the 21 consonants are written in alphabetical order. For example, D and F are consecutive consonants but D and V are not. For example, M and N can be A and E respectively or E and A respectively. P is equal to Base-Ten-Index of M. Q is equal to the Base-Ten-Index of N. R and S can only take binary values, that is, 0 or 1.Base-Ten-Index of an alphabet = Index of alphabet % 10, where Index of an alphabet is its position when all alphabets from A to Z are arranged alphabetically and a%b is the remainder when a is divided by b.For example, Base-Ten-Index of J = 10 = 0 , Base-Ten-Index of M = 13 = 3.The chief scientist can only set passwords/patterns which follow all of the conditions mentioned above.Based on the information given above, answer the questions that follow.Q.Given below is a list of patterns/passwords, some of which are in accordance with the rules mentioned and some are not. The chief scientist can use any combination of valid patterns/passwords from the following to lock the e-device. What is the total number of ways in which he can do so?Pattern:(1) A1 A2 A5 A6 A5 A2 A4 (2) A1 A2 A3 A4 A5 A6 (3) A6 A5 A4 A3 A2 A1 (4) A1 A6 A5 A2 A4Numeric password:(1) 234 (2) 434 (3) 298 (4) 634 (5) 894 (6) 230 (7) 638Alphanumeric password:(1) AE1500 (2) CD3410 (3) HJ8000 (4)QP7600 (5) AB1211 (6) YZ4600 Correct answer is '40'. 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 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.a)Eb)Fc)Gd)HCorrect answer is option 'C'. 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 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.a)Eb)Fc)Gd)HCorrect answer is option 'C'. 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 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.a)Eb)Fc)Gd)HCorrect answer is option 'C'. 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 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.a)Eb)Fc)Gd)HCorrect answer is option 'C'. 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 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.a)Eb)Fc)Gd)HCorrect answer is option 'C'. 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 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.a)Eb)Fc)Gd)HCorrect answer is option 'C'. 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 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.a)Eb)Fc)Gd)HCorrect answer is option 'C'. 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 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.a)Eb)Fc)Gd)HCorrect answer is option 'C'. 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 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.a)Eb)Fc)Gd)HCorrect answer is option 'C'. 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 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.a)Eb)Fc)Gd)HCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice CAT tests.
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