April 2, 2015

Homework Help: Maths

Posted by Rashmi Krishna on Sunday, May 27, 2012 at 7:32am.

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.

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