The integers −1, 2, −3, 4, −5, 6 are written on a blackboard. At each move, we erase two numbers a and b, then we re-write 2a+b and 2b+a. How many of the sextuples (0,0,0,3,−9,9), (0,1,1,3,6,−6), (0,0,0,3,−6,9), (0,1,1,−3,6,−9), (0,0,2,5,5,6) can be gotten?<spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 3<spanclass=′latex−bold′>(D)</span> 4<spanclass=′latex−bold′>(E)</span> 5 invariantinequalitiesabsolute valuecombinatorics proposedcombinatorics