  Veech groups are discrete subgroups of SL(2, R) which play an important role
in the theory of translation surfaces. For a special class of translation
surfaces called origamis or square-tiled surfaces their Veech groups are
subgroups of finite index of SL(2, Z). We show that each stratum of the space
of translation surfaces contains infinitely many origamis whose Veech group is
a totally non congruence group, i.e. it surjects to SL(2, Z/nZ) for any n.
