Suppose that *n = {n - 2, n + 2, 2n, n/2}. for example, *6 = {3,4,8,12}. for how many distinct integers n does *n have exactly three distinct elements?

*n wil have three distinct elements when exactly two of the elements (n-2, n+2, 2n, n/2) are the same.

If n-2=n+2:


If n-2=2n:


If n-2=n/2:


If n+2=2n:


If n+2=n/2:


If 2n=n/2:


*n have exactly three distinct elements for 5 distinct integers n.
*(-4)={-8, -6, -2}
*(-2)={-4, -2, -1}
*0={-2, 0, 2}
*2={0, 1, 4}
*4={2, 6, 8}