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Direction: Akshat and Akanksha were given some toffees and a bar of chocolate. They could divide the toffees among themselves equally, but each wanted the complete bar of chocolate for themselves. So they decided to play a game.
Akshat took 12 toffees and arranged them in two columns as shown.
The rules of the game are as follows:
1. Each person will get a turn alternately. During a turn, a person has to pick up at least 1 toffee. A person can pick up any number of toffees during their turn as long as they all belong to the same column.
For example, the first person to play can pick up 7 toffees, but not 8 as the eighth would belong to the other column.
2. The last person to pick up a toffee will win. He/She will be given the chocolate bar as well as half of the remaining toffees, which were not used in the game. The loser of the game will get the remaining half of the unused toffees. A person is allowed to keep the toffees he/she picked up during the game.
Each person plays logically and to win.
Q. Akshat went first and picked up some toffees which ensured that he wins. What is the total number of toffees that Akanksha picks up during the game?
Correct answer is '5'. Can you explain this answer?
Most Upvoted Answer
Direction: Akshat and Akanksha were given some toffees and a bar of c...
In these types of games, one has to rely on backward induction.
Let (a,b) denote that there are 'a' and 'b' toffees in the two columns.
Since there is no constraint on how many toffees a person can pick up from a single column, the number of toffees left in a single column does not matter if the second column is empty. Hence to win, a player should never pick up all the toffees from a column. Since the players are playing logically and to win, they will never do this.
Hence on the second last turn, at least 1 toffee is left in each column.
But if a person wants to win, and leaves 1 toffee in one column and 2 or more toffees in the other, then the other player will just pick up one toffee from the column which has 2 toffees. Because of this, the first player will be forced to pick a toffee and a toffee will be left in the other column.
Hence if (1,1) toffees are left, the person whose turn it is next will lose.
But if he leaves 2 toffees two toffees in each column after his/her turn, then no matter how many toffees are picked up next, he/she will always win.
If the second person picks 1, the first has to pick 1 from the other column, leaving (1,1) toffees, which is a winning situation for the first.
The second player cannot pick up 2, as explained earlier that a logical player will not empty a column, as it means immediate defeat.
Hence if (2,2) toffees are left, the person whose turn it is next will lose.
Hence we can see the pattern that a person has to leave an equal number of toffees in each column after their turn to ensure winning. Hence a person must pick up the number of toffees which makes the toffees equal in both the columns.
Initially, the number of toffees were (7,5). So Akshat will pick up 2 toffees to make it (5,5).
After this, If Akanksha picks up 1 toffee, Akshat will also pick up 1 toffee, making it (4,4). The same will go on till (1,1) toffees are left. So after the first turn, Akshat will ensure that both of them pick up the same number of toffees. Hence Akshat will have picked up (2+5)=7 toffees and Akanksha will have picked up 5 toffees by the time the game ends.
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Direction: Akshat and Akanksha were given some toffees and a bar of chocolate. They could divide the toffees among themselves equally, but each wanted the complete bar of chocolate for themselves. So they decided to play a game.Akshat took 12 toffees and arranged them in two columns as shown.The rules of the game are as follows:1. Each person will get a turn alternately. During a turn, a person has to pick up at least 1 toffee. A person can pick up any number of toffees during their turn as long as they all belong to the same column.For example, the first person to play can pick up 7 toffees, but not 8 as the eighth would belong to the other column.2. The last person to pick up a toffee will win. He/She will be given the chocolate bar as well as half of the remaining toffees, which were not used in the game. The loser of the game will get the remaining half of the unused toffees. A person is allowed to keep the toffees he/she picked up during the game.Each person plays logically and to win.Q. Akshat went first and picked up some toffees which ensured that he wins. What is the total number of toffees that Akanksha picks up during the game?Correct answer is '5'. Can you explain this answer?
Question Description
Direction: Akshat and Akanksha were given some toffees and a bar of chocolate. They could divide the toffees among themselves equally, but each wanted the complete bar of chocolate for themselves. So they decided to play a game.Akshat took 12 toffees and arranged them in two columns as shown.The rules of the game are as follows:1. Each person will get a turn alternately. During a turn, a person has to pick up at least 1 toffee. A person can pick up any number of toffees during their turn as long as they all belong to the same column.For example, the first person to play can pick up 7 toffees, but not 8 as the eighth would belong to the other column.2. The last person to pick up a toffee will win. He/She will be given the chocolate bar as well as half of the remaining toffees, which were not used in the game. The loser of the game will get the remaining half of the unused toffees. A person is allowed to keep the toffees he/she picked up during the game.Each person plays logically and to win.Q. Akshat went first and picked up some toffees which ensured that he wins. What is the total number of toffees that Akanksha picks up during the game?Correct answer is '5'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Direction: Akshat and Akanksha were given some toffees and a bar of chocolate. They could divide the toffees among themselves equally, but each wanted the complete bar of chocolate for themselves. So they decided to play a game.Akshat took 12 toffees and arranged them in two columns as shown.The rules of the game are as follows:1. Each person will get a turn alternately. During a turn, a person has to pick up at least 1 toffee. A person can pick up any number of toffees during their turn as long as they all belong to the same column.For example, the first person to play can pick up 7 toffees, but not 8 as the eighth would belong to the other column.2. The last person to pick up a toffee will win. He/She will be given the chocolate bar as well as half of the remaining toffees, which were not used in the game. The loser of the game will get the remaining half of the unused toffees. A person is allowed to keep the toffees he/she picked up during the game.Each person plays logically and to win.Q. Akshat went first and picked up some toffees which ensured that he wins. What is the total number of toffees that Akanksha picks up during the game?Correct answer is '5'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: Akshat and Akanksha were given some toffees and a bar of chocolate. They could divide the toffees among themselves equally, but each wanted the complete bar of chocolate for themselves. So they decided to play a game.Akshat took 12 toffees and arranged them in two columns as shown.The rules of the game are as follows:1. Each person will get a turn alternately. During a turn, a person has to pick up at least 1 toffee. A person can pick up any number of toffees during their turn as long as they all belong to the same column.For example, the first person to play can pick up 7 toffees, but not 8 as the eighth would belong to the other column.2. The last person to pick up a toffee will win. He/She will be given the chocolate bar as well as half of the remaining toffees, which were not used in the game. The loser of the game will get the remaining half of the unused toffees. A person is allowed to keep the toffees he/she picked up during the game.Each person plays logically and to win.Q. Akshat went first and picked up some toffees which ensured that he wins. What is the total number of toffees that Akanksha picks up during the game?Correct answer is '5'. Can you explain this answer?.
Direction: Akshat and Akanksha were given some toffees and a bar of chocolate. They could divide the toffees among themselves equally, but each wanted the complete bar of chocolate for themselves. So they decided to play a game.Akshat took 12 toffees and arranged them in two columns as shown.The rules of the game are as follows:1. Each person will get a turn alternately. During a turn, a person has to pick up at least 1 toffee. A person can pick up any number of toffees during their turn as long as they all belong to the same column.For example, the first person to play can pick up 7 toffees, but not 8 as the eighth would belong to the other column.2. The last person to pick up a toffee will win. He/She will be given the chocolate bar as well as half of the remaining toffees, which were not used in the game. The loser of the game will get the remaining half of the unused toffees. A person is allowed to keep the toffees he/she picked up during the game.Each person plays logically and to win.Q. Akshat went first and picked up some toffees which ensured that he wins. What is the total number of toffees that Akanksha picks up during the game?Correct answer is '5'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Direction: Akshat and Akanksha were given some toffees and a bar of chocolate. They could divide the toffees among themselves equally, but each wanted the complete bar of chocolate for themselves. So they decided to play a game.Akshat took 12 toffees and arranged them in two columns as shown.The rules of the game are as follows:1. Each person will get a turn alternately. During a turn, a person has to pick up at least 1 toffee. A person can pick up any number of toffees during their turn as long as they all belong to the same column.For example, the first person to play can pick up 7 toffees, but not 8 as the eighth would belong to the other column.2. The last person to pick up a toffee will win. He/She will be given the chocolate bar as well as half of the remaining toffees, which were not used in the game. The loser of the game will get the remaining half of the unused toffees. A person is allowed to keep the toffees he/she picked up during the game.Each person plays logically and to win.Q. Akshat went first and picked up some toffees which ensured that he wins. What is the total number of toffees that Akanksha picks up during the game?Correct answer is '5'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: Akshat and Akanksha were given some toffees and a bar of chocolate. They could divide the toffees among themselves equally, but each wanted the complete bar of chocolate for themselves. So they decided to play a game.Akshat took 12 toffees and arranged them in two columns as shown.The rules of the game are as follows:1. Each person will get a turn alternately. During a turn, a person has to pick up at least 1 toffee. A person can pick up any number of toffees during their turn as long as they all belong to the same column.For example, the first person to play can pick up 7 toffees, but not 8 as the eighth would belong to the other column.2. The last person to pick up a toffee will win. He/She will be given the chocolate bar as well as half of the remaining toffees, which were not used in the game. The loser of the game will get the remaining half of the unused toffees. A person is allowed to keep the toffees he/she picked up during the game.Each person plays logically and to win.Q. Akshat went first and picked up some toffees which ensured that he wins. What is the total number of toffees that Akanksha picks up during the game?Correct answer is '5'. Can you explain this answer?.
Solutions for Direction: Akshat and Akanksha were given some toffees and a bar of chocolate. They could divide the toffees among themselves equally, but each wanted the complete bar of chocolate for themselves. So they decided to play a game.Akshat took 12 toffees and arranged them in two columns as shown.The rules of the game are as follows:1. Each person will get a turn alternately. During a turn, a person has to pick up at least 1 toffee. A person can pick up any number of toffees during their turn as long as they all belong to the same column.For example, the first person to play can pick up 7 toffees, but not 8 as the eighth would belong to the other column.2. The last person to pick up a toffee will win. He/She will be given the chocolate bar as well as half of the remaining toffees, which were not used in the game. The loser of the game will get the remaining half of the unused toffees. A person is allowed to keep the toffees he/she picked up during the game.Each person plays logically and to win.Q. Akshat went first and picked up some toffees which ensured that he wins. What is the total number of toffees that Akanksha picks up during the game?Correct answer is '5'. 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 Direction: Akshat and Akanksha were given some toffees and a bar of chocolate. They could divide the toffees among themselves equally, but each wanted the complete bar of chocolate for themselves. So they decided to play a game.Akshat took 12 toffees and arranged them in two columns as shown.The rules of the game are as follows:1. Each person will get a turn alternately. During a turn, a person has to pick up at least 1 toffee. A person can pick up any number of toffees during their turn as long as they all belong to the same column.For example, the first person to play can pick up 7 toffees, but not 8 as the eighth would belong to the other column.2. The last person to pick up a toffee will win. He/She will be given the chocolate bar as well as half of the remaining toffees, which were not used in the game. The loser of the game will get the remaining half of the unused toffees. A person is allowed to keep the toffees he/she picked up during the game.Each person plays logically and to win.Q. Akshat went first and picked up some toffees which ensured that he wins. What is the total number of toffees that Akanksha picks up during the game?Correct answer is '5'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Direction: Akshat and Akanksha were given some toffees and a bar of chocolate. They could divide the toffees among themselves equally, but each wanted the complete bar of chocolate for themselves. So they decided to play a game.Akshat took 12 toffees and arranged them in two columns as shown.The rules of the game are as follows:1. Each person will get a turn alternately. During a turn, a person has to pick up at least 1 toffee. A person can pick up any number of toffees during their turn as long as they all belong to the same column.For example, the first person to play can pick up 7 toffees, but not 8 as the eighth would belong to the other column.2. The last person to pick up a toffee will win. He/She will be given the chocolate bar as well as half of the remaining toffees, which were not used in the game. The loser of the game will get the remaining half of the unused toffees. A person is allowed to keep the toffees he/she picked up during the game.Each person plays logically and to win.Q. Akshat went first and picked up some toffees which ensured that he wins. What is the total number of toffees that Akanksha picks up during the game?Correct answer is '5'. Can you explain this answer?, a detailed solution for Direction: Akshat and Akanksha were given some toffees and a bar of chocolate. They could divide the toffees among themselves equally, but each wanted the complete bar of chocolate for themselves. So they decided to play a game.Akshat took 12 toffees and arranged them in two columns as shown.The rules of the game are as follows:1. Each person will get a turn alternately. During a turn, a person has to pick up at least 1 toffee. A person can pick up any number of toffees during their turn as long as they all belong to the same column.For example, the first person to play can pick up 7 toffees, but not 8 as the eighth would belong to the other column.2. The last person to pick up a toffee will win. He/She will be given the chocolate bar as well as half of the remaining toffees, which were not used in the game. The loser of the game will get the remaining half of the unused toffees. A person is allowed to keep the toffees he/she picked up during the game.Each person plays logically and to win.Q. Akshat went first and picked up some toffees which ensured that he wins. What is the total number of toffees that Akanksha picks up during the game?Correct answer is '5'. Can you explain this answer? has been provided alongside types of Direction: Akshat and Akanksha were given some toffees and a bar of chocolate. They could divide the toffees among themselves equally, but each wanted the complete bar of chocolate for themselves. So they decided to play a game.Akshat took 12 toffees and arranged them in two columns as shown.The rules of the game are as follows:1. Each person will get a turn alternately. During a turn, a person has to pick up at least 1 toffee. A person can pick up any number of toffees during their turn as long as they all belong to the same column.For example, the first person to play can pick up 7 toffees, but not 8 as the eighth would belong to the other column.2. The last person to pick up a toffee will win. He/She will be given the chocolate bar as well as half of the remaining toffees, which were not used in the game. The loser of the game will get the remaining half of the unused toffees. A person is allowed to keep the toffees he/she picked up during the game.Each person plays logically and to win.Q. Akshat went first and picked up some toffees which ensured that he wins. What is the total number of toffees that Akanksha picks up during the game?Correct answer is '5'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Direction: Akshat and Akanksha were given some toffees and a bar of chocolate. They could divide the toffees among themselves equally, but each wanted the complete bar of chocolate for themselves. So they decided to play a game.Akshat took 12 toffees and arranged them in two columns as shown.The rules of the game are as follows:1. Each person will get a turn alternately. During a turn, a person has to pick up at least 1 toffee. A person can pick up any number of toffees during their turn as long as they all belong to the same column.For example, the first person to play can pick up 7 toffees, but not 8 as the eighth would belong to the other column.2. The last person to pick up a toffee will win. He/She will be given the chocolate bar as well as half of the remaining toffees, which were not used in the game. The loser of the game will get the remaining half of the unused toffees. A person is allowed to keep the toffees he/she picked up during the game.Each person plays logically and to win.Q. Akshat went first and picked up some toffees which ensured that he wins. What is the total number of toffees that Akanksha picks up during the game?Correct answer is '5'. Can you explain this answer? tests, examples and also practice CAT tests.
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