Three uniform round rigid cylindrical logs of the same size and weight are placed on a horizontal plane. The two at the bottom are touching each other, the third one is placed on the top as shown in the picture. The coefficient of friction between any two logs is $\mu_1$, the coefficient of friction between any log and the floor is $\mu_2$. For some asymptotic values of $\mu_{1}$ and $\mu_{2}$ one can immediately conclude about existence or non-existence of equilibrium. For example if both $\mu_{1}$ and $\mu_{2}$ are zero then obviously there is no equilibrium. Further, one can argue that if either $\mu_1$ or $\mu_2$ is zero than there is no equilibrium no matter what the other coefficient is. In general, for what values of $\mu_1$ and $\mu_2$ would this system be in equilibrium?
P.S. The problem is currently closed for some obscure reasons; but if you like it please vote to reopen it (the link is below), and then perhaps we can discuss the solution.
