Miscellaneous Problems, HWK 14
2 points total, 10 subpoints total
1. (2 points) Dr. Ritter has a dinner party, and there are N seats around a round table, where N has values of 2, 3, 4, 5, and 6 (depending on how far the table is expanded).
(a) (1/2) How many ways can he sit his guests when all the chairs are full in each case, and assuming that the seat nearest the kitchen makes the seats all different?
(b) (1) Assuming that he has the same people come back twice, what is the probability that a pair of people will sit next to each other at two consecutive dinners?
(c) (1/2) At what size table would being set next to each other on two separate occasions be a rare occasion if seating is random? Define rare and show why it would be rare for that sized table.
2. (2 points) section 10.2, grammars
(a) p. 335#2; write an language to accept (b) natural numbers, (c) integers, and (d) decimal numbers.
3. (2 points) Finite state machines p. 347#4,8,10,14
Prove that if you transpose two digits in a number (e.g., 334 -> 343), that the difference between the original number and the resulting number is divisible by 9.
5. (2 points) Metareview
In several cases this course has covered a concept in several ways, repeating it but using a different formalism or method for examining it. What is one of the most important concepts that this has been done for, why is it one of ate most important concepts, and what are the ways that it has been covered?