Cause Granny has 10 grandchildren and all of them have a different ages so 

I call the ages of ten children are \(x_1,x_2,....,x_{10}\)

Cause Alice is the eldest 

We have \(x_1+x_2+....+x_{10}=180\)

=> \(10x_{10}\ge180\)       

<=>  \(x_{10}\ge18\)

So , at least , the age of alice is 10