Question

In: Advanced Math

Logic/ Game theoryLet f(n) count the different perfect covers of a 2-by-n chessboard by dominoes. Evaluate...

Logic/ Game theoryLet f(n) count the different perfect covers of a 2-by-n chessboard by dominoes. Evaluate f(1),f(2),f(3),f(4), and f(5). Try and find (and verify) a simple relation that the counting function f satisfies. Compute f(12) using the relation.


Here is a solution it is titled exercise 4a.) in the packet on page 3:
http://jade-cheng.com/uh/coursework/math-475/homework-01.pdf  
Not sure on how to follow the logic.

Solutions

Expert Solution


Related Solutions

A special chessboard is 2 squares wide and n squares long. Using n dominoes that are...
A special chessboard is 2 squares wide and n squares long. Using n dominoes that are 1 square by 2 squares, there are many ways to completely cover this chessboard with no overlap. How many are there? Prove your answer.
2. The Fibonacci sequence is defined as f(n) = f(n - 1) + f(n - 2)...
2. The Fibonacci sequence is defined as f(n) = f(n - 1) + f(n - 2) with f(0) = 0 and f(1) = 1. Find f(54) by a program or maually. Note that this number must be positive and f(53) = 53.......73 (starting with 53 and ending with 73). I must admit that my three machines including a desktop are unable to find f(54) and they quit during computation. The answer is f(54) = 86267571272 */ The Java code: public...
a) write a program to compute and print n, n(f), f(f(n)), f(f(f(n))).........for 1<=n<=100, where f(n)=n/2 if...
a) write a program to compute and print n, n(f), f(f(n)), f(f(f(n))).........for 1<=n<=100, where f(n)=n/2 if n is even and f(n)=3n+1 if n is odd b) make a conjecture based on part a. use java
Suppose f : N→N satisestherecurrencerelation f(n + 1) (f(n) 2 if f(n)iseven 3f(n)+ 1 if f(n)isodd...
Suppose f : N→N satisestherecurrencerelation f(n + 1) (f(n) 2 if f(n)iseven 3f(n)+ 1 if f(n)isodd . Notethatwiththeinitialcondition f(0) 1,thevaluesofthefunction are: f(1) 4, f(2) 2, f(3) 1, f(4) 4, and so on, the images cyclingthroughthosethreenumbers. Thus f isNOTinjective(andalso certainlynotsurjective). Mightitbeunderotherinitialconditions?3 (a) If f satisestheinitialcondition f(0) 5,is f injective? Explain whyorgiveaspecicexampleoftwoelementsfromthedomain withthesameimage. (b) If f satisestheinitialcondition f(0) 3,is f injective? Explain whyorgiveaspecicexampleoftwoelementsfromthedomain withthesameimage. (c) If f satisestheinitialcondition f(0) 27,thenitturnsoutthat f(105) 10 and no two numbers less than 105 have the same...
2) This question is about providing game logic for the game of craps we developed its...
2) This question is about providing game logic for the game of craps we developed its shell in class. THe cpp of the class is attached to this project. At the end of the game, you should ask user if wants to play another game, if so, make it happen. Otherwise quit. Here is the attached cpp file for que2:- /*** This is an implementation of the famous 'Game of Chance' called 'craps'. It is a dice game. A player...
Fibonacci Sequence: F(0) = 1, F(1) = 2, F(n) = F(n − 1) + F(n −...
Fibonacci Sequence: F(0) = 1, F(1) = 2, F(n) = F(n − 1) + F(n − 2) for n ≥ 2 (a) Use strong induction to show that F(n) ≤ 2^n for all n ≥ 0. (b) The answer for (a) shows that F(n) is O(2^n). If we could also show that F(n) is Ω(2^n), that would mean that F(n) is Θ(2^n), and our order of growth would be F(n). This doesn’t turn out to be the case because F(n)...
If f(n) = 3n+2 and g(n) = n, then Prove that f(n) = O (g(n))
If f(n) = 3n+2 and g(n) = n, then Prove that f(n) = O (g(n))
Fibonacci Sequence in JAVA f(0) = 0, f(1) = 1, f(n) = f(n-1) + f(n-2) Part...
Fibonacci Sequence in JAVA f(0) = 0, f(1) = 1, f(n) = f(n-1) + f(n-2) Part of a code public class FS { public static void main(String[] args){ IntSequence seq = new FibonacciSequence(); for(int i=0; i<20; i++) { if(seq.hasNext() == false) break; System.out.print(seq.next()+" "); } System.out.println(" "); } } ///Fill in the rest of the code! Output 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 You should define...
How to prove f(n)=O(n) for any integer ⩾1, if f(1)=1 and f(n)=2f(⌊n/2⌋)+1 for n⩾2? Do you...
How to prove f(n)=O(n) for any integer ⩾1, if f(1)=1 and f(n)=2f(⌊n/2⌋)+1 for n⩾2? Do you need induction? If so, how do you do it?
Find f(1), f(2), f(3) and f(4) if f(n) is defined recursively by f(0)=4f(0)=4 and for n=0,1,2,…n=0,1,2,…...
Find f(1), f(2), f(3) and f(4) if f(n) is defined recursively by f(0)=4f(0)=4 and for n=0,1,2,…n=0,1,2,… by: (a) f(n+1)=−2f(n) f(1)= f(2)= f(3)= f(4)= (b) f(n+1)=4f(n)+5 f(1)= f(2)= f(3)= f(4)= (b) f(n+1)=f(n)2−4f(n)−2 f(1)= f(2)= f(3)= f(4)=
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT