Q.19 Alok and Bhanu play the following min-max game. Given
the expression N=9+X+Y–Z where X, Y and Z are variables
representing single digits (0 to 9), Alok would like to
maximize N while Bhanu would like to minimize it. Towards
this end, Alok chooses a single digit number and Bhanu
substitutes this for a variable of her choice (X, Y or Z).
Alok then chooses the next value and Bhanu, the variable to
substitute the value. Finally Alok proposes the value for
the remaining variable. Assuming both play to their optimal
strategies, the value of N at the end of the game would be
27
18
20
Answer is: 20
can someone plzzzzzzzzz tell me how this answer is
calculeted???
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Answer / Shyama Pathak
To calculate the final value of N in this min-max game, both Alok and Bhanu should make optimal moves to minimize and maximize the expression. Here's one possible sequence of moves:
1. Alok chooses a number '3' for variable Z.
2. Bhanu chooses variable X and replaces it with the minimum value '0'.
3. N becomes 9 + 0 + Y – 3 = 6 – 3 = 3.
4. Now, Alok chooses a number '7' for variable Y.
5. Bhanu chooses variable Z and replaces it with the maximum value '9'.
6. N becomes 9 + 0 + 7 – 9 = 2.
7. Finally, Alok chooses a number '2' for variable X.
8. The final expression is N = 9 + 2 + 7 – 9 = 18, but since Bhanu wanted to minimize the expression, her actual move was choosing Z as '0' and accepting the value of N as 3. However, this game can have multiple optimal solutions depending on the players' strategies.
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