Suppose you are flying Northeast Airlines, a well-loved airline with a wildly permissive boarding procedure. There are 180 passenger seats on a Northeast Airlines plane, and they are arranged in rows of 6, with a group of 3 on either side of the aisle (thus, there are 30 rows total). Passengers are assigned a boarding number between 1 and 180 with their ticket. Passengers board the plane in the order given by their boarding numbers, and may sit in any empty seat. For example, the passenger with boarding number 1 may sit wherever they wish; the passenger with boarding number 2 may sit anywhere except where passenger 1 is sitting; and so on. You may assume that all of the 180 passengers are present, nobody swaps seats, and nobody is beaten and forcibly removed from the aircraft. a. You and your business partner Rhonda are taking a trip to recruit more employees for your triangular-shaped business venture. Suppose your boarding number is n, and Rhonda's is n+1. What is the maximum boarding number n you can have in order to still guarantee that you and Rhonda can sit in adjacent seats in the same row, not separated by the aisle?---b. What is the maximum boarding number you can have in order to guarantee you can get an aisle seat?---It's the holidays and lots of people are traveling. Things are getting out of control at baggage claim. Suppose everybody has exactly one bag, tagged with their first and last initial, which are both uppercase letters from the English alphabet. c. What is the minimum number of people needed to guarantee that at least 3 luggage tags have the same 2 initials (in the same order) on them?