I will use these--and although the groups are not necessary, they make it clearer to me what I am doing.
^([0]+)\s([0]+)\s([0]+)$
^(0*[1-9]\d*)\s([0]+)\s([0]+)$
^(0*[1-9]\d*)\s(0*[1-9]\d*)\s([0]+)$
^(0*[1-9]\d*)\s(0*[1-9]\d*)\s(0*[1-9]\d*)$
Thank you, @sln