Three CAT exam problems: digit game, silver coins, and inequality

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1. Aswin and Vivek relax after breakfast with a simple number game. Alternately Aswin chooses a digit and Vivek substitutes it for one of the stars in the difference “**** - **** “. Aswin is trying to maximize the difference and Vivek is trying to minimize it. What difference will be arrived at with the best play?

2. n2 coins, of which exactly n are silver, are arranged at random in n rows, each containing n coins. What is the chance that at least one row occurs in which there is no silver coin?

3. Given positive real numbers a, b, and c such that a + b + c = 1, show that a^a*b^b*c^c + a^b*b^c*c^a + a^c*b^a*c^b <=1.

please anyone solve these problems or suggest me any books dealing with these problems


Thanks u!
 

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msg_1989 said:
1. Aswin and Vivek relax after breakfast with a simple number game. Alternately Aswin chooses a digit and Vivek substitutes it for one of the stars in the difference “**** - **** “. Aswin is trying to maximize the difference and Vivek is trying to minimize it. What difference will be arrived at with the best play?

2. n2 coins, of which exactly n are silver, are arranged at random in n rows, each containing n coins. What is the chance that at least one row occurs in which there is no silver coin?

3. Given positive real numbers a, b, and c such that a + b + c = 1, show that a^a*b^b*c^c + a^b*b^c*c^a + a^c*b^a*c^b <=1.

please anyone solve these problems or suggest me any books dealing with these problems


Thanks u!

Welcome to PF :smile:

Before you can receive help, you need to show us an attempt at solving the problem and what equations or formulas you think are relevant to solving it. It's just the rules of this forum.

Also, in the future it is best to ask each question as a separate post.