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Alok and Bhanu play the following min-max game. Given the
expression
N = 38 + 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?
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Answer Posted / Vibhut Narayan Pandey
Assuming optimal strategies are being employed, let's examine possible moves: 1. Alok chooses a large number (e.g., 9) as X. Bhanu selects Z to minimize N. If Z is less than 1, then N will be maximized by selecting Y as close to 9 as possible. If Z >= 1, then Bhanu should select Y=0 and Z=9, resulting in N = 57 - 9*9 = -104, which does not make sense in this context. Therefore, Bhanu would choose a small number (e.g., 0) as Z, and Alok would select Y as close to 9 as possible. In the end, with optimal strategies, Alok chooses X=9, Bhanu chooses Z=0, and Alok chooses Y=8 or 9 (depending on whether 9-0 is already greater than 38). The final N value would be either 47 or 56.
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