Extended project: project 1: [x (2/3)] n

Item 2: n [x (2/3)] (n-1) (1/x)

Item 3: n (n-1)/2 [x (2/3)] (n-2) (1/x)?

Index of the third item X: 2(n-2)/3-2.

2(n-2)/3-2=2 according to the meaning of the question.

The solution is n=8.