To develop this problem it is necessary to apply the concepts related to the force of gravity, and the force expressed in terms of density and volume, by definition we know that,

Where,
Density
V = Volume
In addition we also know that by Newton's second law the weight can be defined as

For balance to exist, the Bouyancy force is equal to the weight, therefore



We know that the total weight is conditioned at 5.59 Kg plus the number of objects in Kilograms, that is

We know that the Volume is the equivalent of
plus the volume of each weight of
, so,

Replacing with our values we have that




Therefore the minimum number of weights is 8.