I received this interesting question from my friend.
Suppose we have 3 random number generators, each generates value from the uniform distribution on the interval $[a, b]$. Can we construct random number generator that generate uniform distribution on $[0,1]$ given that $a$ and $b$ is unknown?
Yes. The generators produce three numbers; order them as $x\ge y\ge z $ and define $$t=\frac{x-y}{x-z}$$ The quantity $t$ is uniformly distributed on $[0,1]$.
Sketch of proof. The probability density of the triple $(x,y,z)$ is $6$ times the Lebesgue measure restricted to the tetrahedron with vertices $(0,0,0)$, $(1,0,0)$, $(1,1,0)$, $(1,1,1)$. The probability that $t$ lies in the interval $(\alpha,\beta)$ is $6$ times the volume of the tetrahedron with vertices $(0,0,0)$, $(1,\alpha, 0)$, $(1,\beta,0)$, $(1,1,1)$. The volume of the latter tetrahedron is $$\frac16\begin{vmatrix} 1 & \alpha & 0 \\ 1 & \beta & 0 \\ 1 & 1 & 1 \end{vmatrix} =\frac{\beta-\alpha}6 $$
