Suppose there are 1 x 1 tiles of the same color, and 1 x 2 tiles in 12 different colors. Write the recurrence relation with initial conditions for the number of ways to pave a path of the size 1 × n. Next provide the solution.
are trying to tile a 1 x n walkway with 5 different types of tiles: a 6. (15 points) Suppose you tile, a blue 2 × 1-tile, a white 1 x 1 tile, and a black 1 × 1 tile red 2 × 1 tile, a white 2 x 1 a. (5pts) Set up and explain a recurrence relation for n a recurrence relation for the number of different tilings for a sidewalk of length n. Include initial conditions. b....
A 2 × n checkerboard is to be tiled using three types of tiles. The first tile is a white 1 × 1 square tile. The second tile is a red 2 × 2 tile and the third one is a black 2 × 2 tile. Let t(n) denote the number of tilings of the 2 × n checkerboard using white, red and black tiles. (a) Find a recursive formula for t(n) and use it to determine t(7). (b) Let...
please solve only part(a) and part(b) Problem 7. A 2 × n clockerboard is to be tiled using three types of tiles. The first tile is a white 1 x 1 square tile. The second tile is a red 2 × 2 tile and the third one is a black 2 x 2 tile. Let t(n) denote the number of tilings of the 2 × n checkerboard using white red and black tiles. (a) Find a recursive formula for t(n)...
ind a solution to the following recurrence relation and initial condition.< n-1 40 .a. Suppose the number of bacteria in a colony quadruples every hour. Set up a recurrence relation for the number of bacteria in the colony at the end of n hours. 3.b. Find an explicit formula for the number of bacteria remaining in the colony after n hours.< 3.c. If 80 bacteria form a new colony, how many will be in the colony after three hours?d 4....
3. (4 points) Let Nm(G) be the the number of ways to properly color the vertices of a graph G with m colors. Pn and Cn are the path and circuit (or cycle) Show that on n vertices, respectively. Nm(P N(C= (m - 1) (-1)"-1 (m 1)"-2) 3. (4 points) Let Nm(G) be the the number of ways to properly color the vertices of a graph G with m colors. Pn and Cn are the path and circuit (or cycle)...
Discrete Math 1: Please explain and prove each step with clear handwriting, and write every detail so that I can understand for future problems. This is discrete math one so please do not make it very complicated. PLEASE MAKE THE HANDWRITING AND THE STEPS CLEAR AND ORGANIZED Problem 2 (4 pts.): Solve the following recurrence relations together with the initial conditions. (a): an-2an-l + 3an-2 with ao = 2 and al = 4. (b): bn =-bn-l + 12bn-2 with bo...
Suppose that an initial bank deposit was $2.000 At the end of each year it is increased by 5% and an additional $500 is deposited amount of the deposit after the nth year. Write the recurrence relation with initial condition for the amount deposited after nth year. Next provide the solution.
Suppose a vending machine accepts $1 bills and $1 gold coins, as well as $3 bills, $3 silver coins and $3 gold coins. a. Write a recurrence for the number of ways to deposit n dollars into the machine, where the order in which the coins and bills are deposited matters. b. What are the initial conditions? c. How many ways are there to deposit $5 into the machine?
15to25 15.How many ways are there to seat ten people around a circular table where two seatings are considered the same when every one has the same immediate left and immediate right neighbor? 16.In how many ways can a photographer at a wedding arrange six people in a row, including the bride and groom, if a) the bride must be next to the groom? b) the bride is not next to the groom? 17.How many bit strings of length seven...
Problem 5. Let t, denote the number of wayş to tile a 2 x n rectangle using1×1 tiles and L-tiles. L tiles are 2 x 2 tiles with one of the squares missing. Figure 1 shows the L tiles in all possible rotations. 1. Find a recursive formula for tn, including the appropriate initial conditions. Hint: there are 7 cases you need to consider to reduce a 2 x n rectangle to a smaller rectangle, and 3 initial conditions. 2....