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.

Expert Solution

Colby Messinger answered 2 years ago

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...

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...

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...

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))

Evaluate, if = 0.4502 , = 0.4185 , n 1 = 800 , n 2 = 750, ...

Evaluate, if = 0.4502 , = 0.4185 , n 1 = 800 , n 2 = 750, Round the result to four digits after the point. Evaluate, if = 15.3 , = 10.2 , µ1 - µ2 = 0 , s 1= 2.1 , s 2= 2.0 , n 1 = 50, n 2 = 40 Round the result to four digits after the point. Evaluate, if = 0.4307 , = 0.4502 , = 0.4185 , n 1= 900 , n 2= 800. Round the...

The production function is f(K,N) = N/2 + √ K, where N is the amount of...

The production function is f(K,N) = N/2 + √ K, where N is the amount of labor used and K the amount of capital used. (a) What is returns to scale of this production function? What is the marginal product of labor? (b) In the short run, K¯ = 4. Labor is variable. On the graph, draw output as a function of labor input in the short run in blue. Draw the marginal product of labor as a function of...

Define the following function f(n) = 5(2^n)-(2^(n-1)), n ≥ 1. Write a recursive definition for the...

Define the following function f(n) = 5(2^n)-(2^(n-1)), n ≥ 1. Write a recursive definition for the function f(n)? Consider the following recurrence: an= 2an-1 + 3 (where a1 = 1). Compute the values of an for n ≤ 5. Find a solution for the recurrence definition and validate its correctness. Consider the following recurrence: an=2an-1 +an-1an-2 (where a1 = 1). Compute the values of an for n ≤ 5.

1)For the function f(x)=6x^2−2x, evaluate and simplify. f(x+h)−f(x)/h 2)Evaluate the limit: limx→−6 if x^2+5x−6/x+6 3)A bacteria...

1)For the function f(x)=6x^2−2x, evaluate and simplify. f(x+h)−f(x)/h 2)Evaluate the limit: limx→−6 if x^2+5x−6/x+6 3)A bacteria culture starts with 820820 bacteria and grows at a rate proportional to its size. After 22 hours there will be 16401640 bacteria. (a) Express the population PP after tt hours as a function of tt. Be sure to keep at least 4 significant figures on the growth rate. P(t)P(t)= (b) What will be the population after 8 hours? bacteria (c) How long will it...

Question