A certain clock marks every hour by st riking a number of t imes equal
to the hour, and the t ime requi red for a st roke i s exact ly equal to the
t ime interval between st rokes. At 6:00 the t ime lapse between the
beginning of the fi rst st roke and the end of the last st roke i s 22
seconds. At 12:00, how many seconds elapse between the beginning
of the fi rst st roke and the end of the last st roke?