# X numbers that when subtracted will produce the same absolute value

Let's say I have X unique numbers and I choose one number y out of this set. Is it possible to create these X numbers such that the absolute difference between y and any other number in X will always be the same? This should work for every value of y in X.

This is trivial for X = 2 ...

Numbers: -1, 1
|(-1) - 1| = 1
|1 - (-1)| = 1


But with X > 2 this seems more complicated (or impossible?). What are your thoughts?

Is it possible to accomplish this with X > 2 so the difference is at least almost the same?

• With real numbers, $X\gt 2$ implies that there are duplicated numbers in the set. With complex numbers, there can be as many numbers in your set as you wish... Of course, even with the complex numbers there is still a limitation where there are only certain $y$ such that the count of other numbers in the set which are equidistant from $y$ is greater than a certain amount... – abiessu Dec 5 '14 at 3:18
• Or, if you choose an open disk in the complex plane as your set $X$ then every $y$ has an infinite number of values around it which are equidistant from it... – abiessu Dec 5 '14 at 3:26