Aqui está o meu e funciona (não me pergunte sobre detalhes, no entanto ... Eu o tenho há anos em máquinas diferentes e simplesmente copio e colo). O usuário precisa estar no grupo "sudo".
#
# This file MUST be edited with the 'visudo' command as root.
#
# Please consider adding local content in /etc/sudoers.d/ instead of
# directly modifying this file.
#
# See the man page for details on how to write a sudoers file.
#
Defaults env_reset
Defaults mail_badpass
Defaults secure_path="/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin"
# Host alias specification
# User alias specification
# Cmnd alias specification
# User privilege specification
root ALL=(ALL:ALL) ALL
# Members of the admin group may gain root privileges
%admin ALL=(ALL) ALL
# Allow members of group sudo to execute any command
%sudo ALL=(ALL:ALL) ALL
# See sudoers(5) for more information on "#include" directives:
# members of the sudo group don't have to enter the pass
%sudo ALL=NOPASSWD: ALL
#includedir /etc/sudoers.d