The following solution in eleven manipulations shows the contents of every vessel at the start and after every manipulation:--
10-quart. 10-quart. 5-quart. 4-quart.
10 .. 10 .. 0 .. 0 5 .. 10 .. 5 .. 0 5 .. 10 .. 1 .. 4 9 .. 10 .. 1 .. 0 9 .. 6 .. 1 .. 4 9 .. 7 .. 0 .. 4 9 .. 7 .. 4 .. 0 9 .. 3 .. 4 .. 4 9 .. 3 .. 5 .. 3 9 .. 8 .. 0 .. 3 4 .. 8 .. 5 .. 3 4 .. 10 .. 3 .. 3
