You will need a minimum of 119 grams of ice.
There are three events occurring here, and each has its own energy factor:
The ice must warm to 0°C. We will call the energy for this change
The ice must melt at 0°C (without further change in temperature). We will call the energy for this change
The water must cool from 10°C to 0°C. We will call the energy for this change
The first two of these will require an absorption of energy. The third (which is occurring simultaneously with the other two) will supply all this energy.
Conservation of energy requires that
For the two effects that involve temperature changes, the equation is
Finally, to find
Putting it all together, remembering that