Alok and Bhanu play the following min-max game. Given the
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
Question Submitted By :: Electronics-Communications
the ans is 20
since alok and banu play a optimal game
alok in first chance do not tell 9,7,8 since banu substitute
for z and he also did not tell values like 0,1,2,3,4 since
banu subsitute it for x or y and minimize the maximum profit
of Alok. so alok in first move choose a value of 6 0r 5.
If he choses 5 banu subsstitute for z.similarly both of them
work and finally for X+Y-Z the value obtained is 11. so the
solution is 11+9=20
similarly for N=c+x(y-z) the value of X(Y-Z) the value is 18
and add the constant value so the final ans is c+18
the ans is 20
since banu will try to reduce number (N) so in first turn if
alok say 9,8,7,6 banu will substitute for Z also if alok
says 1,2,3,4 banu will substitute for X or Y ..........
therefore in first turn alok will choose 5 0r 6....
consider alok says 6 then banu will substitute for Z....
then alok knows only positive (X,Y) variable available so he
will say as 9(the max value now)then banu can substitute for
either X or Y.....at last alok will substitute 8(the max
value mow)for Xor Y.....so 9+9+8-6=20;