# Answer to Question #21425 in Algebra for Minaketan Das

Question #21425
In the following problems, &Theta; = 20 + units digit of your day of birth. For example, if you
were born on April 1st, then &Theta; = 20 + 1 = 21. If you were born on March 30th, then &Theta; = 20
+ 0 = 20.

1. Alok and Bhanu play the following game on arithmetic expressions. Given the
expression
N = (&Theta; + A)/B + (&Theta; + 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 &rarr; B, 6 &rarr; C , 3 &rarr; D, 2 &rarr; E, 0 &rarr; A) and the expression
evaluates to &Theta;/5 + (&Theta;+9)/2.
0

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