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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.

  • Maths -

    There are a few things I do not quite get about this "game". It looks to me it's just a question of maximizing or minimizing N(n,A,B,C,D,E) for a specific n (birthdate) by varying the parameters A to E.

    "proposes a value (digit 0-9)"
    proposes a value of what?
    The date, one of the values of A,B,C,D,E or all of them?

    Why is it called a "move" when all the variables are initialized at every "move", meaning that there is no continuity in the "game"?

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