IBM Ponder This #042 · October 2001

This month's puzzle comes from Laszi Ladanyi, who heard it in college.

Find a function f from R (that is, the set of real numbers) to R
such that for all open intervals I=(u,v) ,we have that f maps (u,v) onto R.
The function f is independent of u,v.

(That is, given any target real number t, and any interval
I=(u,v) with u<v, there is x with u<x<v and f(x)=t.)

Solution

Best opened after a real attempt

To be added.