Let N denote the number that turns up when a fair die is rolled. If the probability that the system of equations $x + y + z = 1$ $2x + \mathrm{N}y + 2z = 2$ $3x + 3y + \mathrm{N}z = 3$ has unique solution is ${k \over 6}$, then the sum of value of k and all possible values of N is :

Question

Let N denote the number that turns up when a fair die is rolled. If the probability that the system of equations

$x + y + z = 1$

$2x + \mathrm{N}y + 2z = 2$

$3x + 3y + \mathrm{N}z = 3$

has unique solution is ${k \over 6}$, then the sum of value of k and all possible values of N is :

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