Running the code
listoflists = []
list = []
for i in range(0,10):
list.append(i)
if len(list)>3:
list.remove(list[0])
listoflists.
The list variable (which I would recommend to rename to something more sensible) is a reference to a list object, which can be changed.
On the line
listoflists.append((list, list[0]))
You actually are only adding a reference to the object reference by the list variable. You've got multiple possibilities to create a copy of the list, so listoflists contains the values as you seem to expect:
Use the copy library
import copy
listoflists.append((copy.copy(list), list[0]))
use the slice notation
listoflists.append((list[:], list[0]))