If God can do anything, can He make a mountain which is too heavy for Him to lift?

If God could make a mountain which he couldn’t lift, there is something that he cannot do. Likewise, if God cannot make a mountain which he couldn’t lift, then there is something which he cannot do. What does this say about the limits of an omnipotent being? Is even God subjected to the rules of logic? Or perhaps nonsense statements remain nonsense statements, even when you append ‘God’ to it.