Question 3
A forest ranger unit wants to prepare a patrol schedule for the whole year 2006 satisfying:
(i) The number of patrol days exceeds half the number of days in the year.
(ii) No two patrol days are exactly one week apart.
1. Prove that such a schedule exists, knowing that 2006 has $365$ days.
2. How many such patrol schedules are there?
(i) The number of patrol days exceeds half the number of days in the year.
(ii) No two patrol days are exactly one week apart.
1. Prove that such a schedule exists, knowing that 2006 has $365$ days.
2. How many such patrol schedules are there?