N=9+x+y-z
Where x,y,z are variable representation of some digit (0 to 9) Alok is like to maximize N while Bhanu Is like to minimize it towards this end ,Alok chooses a single digit number and bhanu substitute this for a variable of her choice (x,y or z)also chooses the next value and Bhanu , the variable to substitute the value .finally ALOK proposes the value for the remaining variable .assuming both playing to their optimal strategies,the value of N at the end of the game would be
a. 20 b. 0.0 c. 27 d. 18
also give description
To determine the value of N at the end of the game, we need to analyze the strategies of Alok and Bhanu and find the optimal moves for each of them.
Let's start by considering Alok's strategy. Alok wants to maximize N, so he will try to choose a number that will result in the highest possible value for N.
Now let's consider Bhanu's strategy. Bhanu wants to minimize N, so she will try to choose a number that will result in the lowest possible value for N.
Since both Alok and Bhanu are playing optimally, we can assume that they will make the best choices at each step.
In the first step, Alok chooses a single-digit number. Let's assume he chooses 9.
Now Bhanu gets to choose a variable to substitute this value for (x, y, or z). Bhanu wants to minimize N, so she will try to substitute 9 for the variable that will result in the lowest possible value for N.
Let's assume Bhanu substitutes 9 for x.
The equation becomes N = 9 + 9 + y - z.
Now Alok gets to choose the next value. He wants to maximize N, so he will try to choose a number that will result in the highest possible value for N.
Alok will choose 9 again and substitute it for y.
The equation becomes N = 9 + 9 + 9 - z.
Finally, Alok proposes the value for the remaining variable (z). At this point, Alok wants to maximize N, so he will try to choose a number that will result in the highest possible value for N.
Alok will again choose 9 and substitute it for z.
The equation becomes N = 9 + 9 + 9 - 9.
Simplifying this equation, we get N = 18.
Therefore, the value of N at the end of the game is 18.
So, the correct answer is d. 18.