Solution to: Eureka!
The upward force, needed to keep a block of ice floating, is equal to the weight of the ice. According to Archimedes, the weight of the ice therefore equals the weight of the displaced water. When the ice has melted, the weight of the resulting water still equals the original weight of the ice. Therefore, the amount of water from the melted ice equals the amount of displaced water.
Conclusion: the water level stays the same.