The maximum uniform circular velocity, is limited by the static frictional force of the tires on the pavement.
So, Newton's 2nd law gives us $$∑F = f = m a_{\text{rad}}=\frac{m v^2}{R}$$
The maximum friction for available is fmax = usm g.
So, you need to consider the radial acceleration...
You'll want to use conservation of energy to solve this, as it's the easiest approach.
U1 + K1 + W = U2 + K2.
The initial energy is just that of the height of the center of mass (2R), m g h = (.3)(9.8)(2*.2) = 1.176J.
The ending energy is the rotational KE of the hoop about the axis, or (.5) I...
There are 9*9*8 = 648 integers which do not have a repeating digit.
(1 - 9) * (0 - 9 -1) * (0 - 9 - 2)
So, you must pick 649 to insure you have an integer with a repeating digit.