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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 2 x + Ny + 2 z = 2 3 x + 3 y + Nz = 3 has unique solution is 6 k then the sum of value of k and all possible values of N is

1. 18
2. 20
3. 21
4. 19

Correct answer: 20

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