Please solve these CAT problems

[msg_1989]

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!

 

[_mariyan_]

are we allowed to use 1 digit more than once?

 

[Redbelly98]

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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