Question #21425

In the following problems, Θ = 20 + units digit of your day of birth. For example, if you

were born on April 1st, then Θ = 20 + 1 = 21. If you were born on March 30th, then Θ = 20

+ 0 = 20.

1. Alok and Bhanu play the following game on arithmetic expressions. Given the

expression

N = (Θ + A)/B + (Θ + C + D)/E

where A, B, C, D and E are variables representing digits (0 to 9), Alok would like to

maximize N while Bhanu would like to minimize it. Towards this end, they take turns in

instantiating the variables. Alok starts and, at each move, proposes a value (digit 0-9)

and Bhanu substitutes the value for a variable of her choice. Assuming both play to their

optimal strategies, what is the value of N at the end of the game? Also find a sequence

of moves (digits by Alok and variables by Bhanu) that would yield this value.

Note: Moves that lead to a divide-by-zero condition are disallowed. A non-optimal

sequence of moves is (5 → B, 6 → C , 3 → D, 2 → E, 0 → A) and the expression

evaluates to Θ/5 + (Θ+9)/2.

were born on April 1st, then Θ = 20 + 1 = 21. If you were born on March 30th, then Θ = 20

+ 0 = 20.

1. Alok and Bhanu play the following game on arithmetic expressions. Given the

expression

N = (Θ + A)/B + (Θ + C + D)/E

where A, B, C, D and E are variables representing digits (0 to 9), Alok would like to

maximize N while Bhanu would like to minimize it. Towards this end, they take turns in

instantiating the variables. Alok starts and, at each move, proposes a value (digit 0-9)

and Bhanu substitutes the value for a variable of her choice. Assuming both play to their

optimal strategies, what is the value of N at the end of the game? Also find a sequence

of moves (digits by Alok and variables by Bhanu) that would yield this value.

Note: Moves that lead to a divide-by-zero condition are disallowed. A non-optimal

sequence of moves is (5 → B, 6 → C , 3 → D, 2 → E, 0 → A) and the expression

evaluates to Θ/5 + (Θ+9)/2.

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