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That said.

Imagine you have a container of water in excess. You have a mass M of ice floating on top of the water. Tied to the ice is a mass T that is more dense than water. Therefore T is submerged and under the surface of the liquid. Assume the string is massless.

What information would you need to be able to figure out the minimum mass of ice (M) you need to make the system (M+T) float? T can be submerged, but it should not pull M down below the surface of the water.

If you have that information, how would you solve it to figure out the mass of M?

Similarly. Is it possible to have a mass of ice (M) such that the system would be in equilibrium, but the ice is completely under the water, but T is not touching the bottom of the container of water? I think this phenomenon is called Natural or Neutral Buoyancy.

Thanks again.