Answer:
Unmeltedd ice = 308.109 g
Explanation:
Gibbs Free energy: 
A systems Gibbs Free Energy is defined as the free energy of the product of the absolute temperature and the entropy change less than the enthalpy change.
Therefore, G = ΔH-TΔS
where G is Gibbs Free Energy
           ΔH is enthalpy change
           T is absolute temperature
           ΔS is entropy change
Here since there is a phase change, therefore G will be 0.
∴ΔH = TΔS
Given: Temperature, T = 0°C = 273 K
            Entropy change,ΔS = 600 J/K
            Latent heat of fusion of water = 333 J/g
 ∴ΔH = TΔS
   ∴ΔH = 273 x 600
            = 163800 J
So this is the amount of enthalpy that will be used into melting of ice.
   ∴ΔH = mass of ice melted x latent heat of fusion of water
     Mass of ice melted = ΔH / latent heat of fusion of water
                                      = 163800 / 333
                                      = 491.891 g
This is the mass of ice melted.
And initial amount of ice is 800 g
 Amount of ice left after melting = Initial amount of ice - amount of ice melted
                                                    = 800-491.891
                                                   = 308.109 g
Amount of ice remained after melting = 308.109 g