The following is tested with Ubuntu 13.04 and system's Python, using Gtk bindings (PyGobject).

Here is one way a bit dirty though and it needs more investigation:

Summary

• Add a .desktop file at /usr/share/xsessions we will name it custom




• Add an .xsession file at the user in question (your kids) we will name their user as kid




• Create the Python GUI application for the math puzzle and run it from .xsession, we will name it as puzzle.py

Details

• sudo vi /usr/share/xsessions/custom.desktop

Add the following in the file:

[Desktop Entry]

Name=Custom

Comment=This session logs you into your managed desktop environment

Exec=/etc/X11/Xsession

X-Ubuntu-Gettext-Domain=gnome-session-3.0

• vi /home/kid/.xsession

Add the following in the file:

#!/bin/bash

lightdm &

exec /home/kid/puzzle.py

• vi /home/kid/puzzle.py

Add the following in the file:

#!/usr/bin/python

# -*- coding: utf-8 -*-

import subprocess

import random

from gi.repository import Gtk





#----------------------------------------------------------------------

class PuzzleWindow(Gtk.Window):



    def __init__(self):

        Gtk.Window.__init__(self, title="Math Puzzle", resizable=False)



        super(PuzzleWindow, self).set_position(Gtk.WindowPosition.CENTER)

        super(PuzzleWindow, self).maximize()



        self.a_number = random.randint(1, 5)

        self.b_number = random.randint(1, 5)

        self.result = self.a_number + self.b_number



        self.vbox = Gtk.Box(orientation=Gtk.Orientation.VERTICAL, spacing=5)



        self.label = Gtk.Label("What is the sum of the numbers bellow?")

        self.number_label = Gtk.Label("{num_a} + {num_b}".format(

            num_a=self.a_number, num_b=self.b_number))



        self.entry = Gtk.Entry()

        self.button = Gtk.Button(label="Check answer!")

        self.button.connect("clicked", self.on_button_clicked)



        self.vbox.pack_start(self.label, True, True, 0)

        self.vbox.pack_start(self.number_label, True, True, 0)

        self.vbox.pack_start(self.entry, True, True, 0)

        self.vbox.pack_start(self.button, True, True, 0)

        self.add(self.vbox)



    def on_button_clicked(self, widget):



        if int(self.entry.get_text()) == self.result:

            subprocess.call("unity &", shell=True)

        else:

            self.label.set_text("Wrong answer, try again.")

#----------------------------------------------------------------------

def main():

    """Application's entry point"""

    win = PuzzleWindow()

    win.connect("delete-event", Gtk.main_quit)

    win.show_all()

    Gtk.main()



if __name__ == "__main__":

    main()

Results:

• If you logout, at the login screen you will see a new session named Custom.


• By choosing the custom session and after successful login you will presented by a small PyGtk (using pygobject) window asking for a math puzzle. There will be no top bar, launcher and the rest of the default desktop widgets:

• If you answer correctly, Unity will load...

It needs further research though but i hope that it helps as a starting point.