AS Challenge question

There's a question from the 2007 AS Physics Challenge paper that I don't understand how they got the answer.

"A piece of ice floats in a glass filled with water. The ice contains a small stone, so that when the ice has all melted, the stone sinks to the bottom of the glass. What will happen to the level of water in the class, firstly as the ice melts, and secondly as the stone is released from the ice and sinks to the bottom?"

The answer is "The water level will remain the same and then fall", but I don't understand that.

Ice is less dense than water, so I would have thought that as the ice melts, the water level will drop. The density of the stone remains the same so when it falls to the bottom, there shouldn't be a change in water level. I'd have thought it would be "The water level will fall and then remain the same", so why is this wrong?

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The water from the melted ice will have the same volume as the water it was displacing although the ice is less dense - remember about 10% of the volume of the ice will be above the level of water to begin with.

However, the stone is denser than the water (as it sinks) and therefore ice, so the ice cube was having to displace more water than if the ice didn't have a stone in it to have the required upthrust to float. When the ice melts to the stone, the water level will then drop as there is no more ice to melt to replace the volume of water displaced to provide the extra upthrust needed for the stone.

Those are my immediate thoughts at least. Someone else will probably have a better answer.

I don't understand, how do you know this?