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
a) 0 b) 27 c) 18 d) 20

The Q's concept is same but the equation of N's is changing.

• 9+11=20
  x+y-z=11
• 13 years agoHelpfull: Yes(36) No(11)
• 9+9=18
• 13 years agoHelpfull: Yes(13) No(24)
• 20 ans is write
• 13 years agoHelpfull: Yes(7) No(7)
• pls explain it in clearly manner.
• 13 years agoHelpfull: Yes(6) No(5)
• x+y-z=11
  so 9+x+y-z=11+9=20
• 12 years agoHelpfull: Yes(5) No(7)
• Answer is c)18
• 9 years agoHelpfull: Yes(1) No(1)
• please anyone explain it clearly.
  
• 8 years agoHelpfull: Yes(1) No(0)
• Alok has to maximize the value of N this means that he has to maximize the value of X and Y and minimize the value of Z, since N = X + Y - Z
  Now, the values Alok can assign range from 0 to 9 but to which variable the value is assigned is decided by Bhanu only. The best possible combination for X, Y and Z that Alok can choose so as to achieve the highest possible value of N is 9, 9 and 9 resp. This is because if he would take any number less than 9, then Bhanu would substitute that smaller value for X or Y because he has to minimize the value of N.
  Thus, N would be 9 + X + Y - Z = 9 + 9 + 9 - 9 = 18.
  
  9
  
  X
  
  Y
  
  Z
  
  Total
  
  
  
  9
  
  9(third)
  
  9(second)
  
  9(first)
  
  18
  
  If Alok choses 9 as first no. then Bhanu will definitely put it at Z.
  
  9
  
  9
  
  9
  
  8
  
  19
  
  If Alok choses 8 as first no. then Bhanu can put it at Z or at X. If Bhanu put it at Z then definitely Alok will chose 9 for X and Y. If Bhanu put it at X then Alok will chose next no as 4 and 0, because for any other no he will get smaller number. If Bhanu put second no. ie 4 at Z then Alok can chose 9 as third no. and in this case total will be 22.
  
  9
  
  8
  
  4
  
  0
  
  21
  
  9
  
  9
  
  9
  
  7
  
  20
  
  If Alok choses 7 as first no. then Bhanu can put it at Z or at X. If Bhanu put it at Z then definitely Alok will chose 9 for X and Y. If Bhanu put it at X then Alok will chose next no as 4 and 0, because for any other no he will get smaller number. If Bhanu put second no. ie 4 at Z then Alok can chose 9 as third no. and in this case total will be 21.
  
  9
  
  7
  
  4
  
  0
  
  20
  
  9
  
  9
  
  9
  
  6
  
  21
  
  If Alok choses 6 as first no. then Bhanu can put it at Z or at X. If Bhanu put it at Z then definitely Alok will chose 9 for X and Y. If Bhanu put it at X then Alok will chose next no as 4 and 0, or 5 and 9 because for any other no he will get smaller number. If Bhanu put second no. ie 4 at Z then Alok can chose 9 as third no. and in this case total will be 20. If Bhanu put second no. ie 5 at Y then Alok can chose 0 as third no. and in this case total will be 20.
  
  9
  
  6
  
  4
  
  0
  
  19
  
  9
  
  6
  
  9
  
  5
  
  19
  
  
  Similarly we can check for other numbers as well but the highest possible value will be 20.
  
  Note: If Alok choses first no as 8 then Bhanu will definitely put that no at Z to get the minimum possible value of N.
  
  If Alok choses first no as 6 then Bhanu will definitely put that no at X to get the minimum possible value of N.
  
  So Alok will chose 7 as first number.
• 5 years agoHelpfull: Yes(1) No(0)
• X+Y+Z;
  now Alok:x=9, bhanu: either (y=0 or z=8) ie. x+y+z = 9-z or 1+y
  Alok: z=0 or y=7
  So for x+y+z to be minimum bhanu will select z=8 in first choice
  So 1+y=8 (alok:y=7 no choice)
  Thus 8 and 9+8 =17
• 9 years agoHelpfull: Yes(0) No(1)