The Mathematical Forest is grown in a two-dimensional plane, where trees can only grow on points...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
The Mathematical Forest is grown in a two-dimensional plane, where trees can only grow on points with integer coordinates. To start with, there are no trees at all. The foresters plant the first tree at (0,0). Each year, they carry out tree planting according to the following rule. If there is a tree on the point (m, n) but there are no trees on the points (m+1, n) and (m, n + 1), then they can choose to remove the tree on (m, n) and plant new trees on the points (m, n + 1) and (m + 1,n). For an integer k > 1, the kth diagonal consists of all points (m,n) with m +n = k – 1. Is it possible for the foresters to arrange their planting so that eventually there are no trees on the first 2 diagonals? What about the first 3 diagonals? 4 diagonals? Can you generalize? The Mathematical Forest is grown in a two-dimensional plane, where trees can only grow on points with integer coordinates. To start with, there are no trees at all. The foresters plant the first tree at (0,0). Each year, they carry out tree planting according to the following rule. If there is a tree on the point (m, n) but there are no trees on the points (m+1, n) and (m, n + 1), then they can choose to remove the tree on (m, n) and plant new trees on the points (m, n + 1) and (m + 1,n). For an integer k > 1, the kth diagonal consists of all points (m,n) with m +n = k – 1. Is it possible for the foresters to arrange their planting so that eventually there are no trees on the first 2 diagonals? What about the first 3 diagonals? 4 diagonals? Can you generalize?
Expert Answer:
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
A rotating cylinder placed in a two dimensional incompressible uniform flow has two stagnation points on its lower section. When the angular velocity of the cylinder is increased to 3/2 times its...
-
How many points with integer coordinates lie in the feasible region defined by 3x + 4y 12, x 0 and y 1?
-
Two points in a plane have polar coordinates (2.50 m, 30.0) and (3.80 m, 120.0). Determine (a) the Cartesian coordinates of these points and (b) the distance between them.
-
A double-ended queue or deque (pronounced "deck") is a collection that is a combination of a stack and a queue. Write a class Deque that uses a linked list to implement the following API: public...
-
What are the relative advantages of fixed and adjustable rate loans?
-
The accompanying data file shows the average price of gas (Price in $ per gallon) for the 50 states during January 2019. a. Construct a boxplot for the Price variable. Does the boxplot suggest that...
-
Electric motors generate heat in their rotor. What is the average time for a loaded motor to reach stable temperature?
-
In New York City, 2406-12 Amsterdam Associates LLC brought an action in a New York state court against Alianza Dominicana and Alianza LLC to recover unpaid rent. The plaintiff asserted cause to...
-
Consider the following FIRE-INSURANCE PROBLEM where fire partially destroys a $500 house. EVENT FIRE PROBABILITY 0.02 OUTCOME $100 NO FIRE 0.98 $500 INSURANCE PAYOUT PREMIUM $400 0 ?? ?? (a) What do...
-
A number of cities are arranged on a graph that has been divided up like an ordinary Cartesian plane. Each city is located at an integral (x, y) coordinate intersection. City names and locations are...
-
The @ 6.5A a first line of 18.8 A 25.399 95-3 n the Balmer series -
-
Data for the Bidwell Company are as follows: Required: a. Based on the preceding data, calculate break-even sales in units. b. If Bidwell Company is subject to an effective income tax rate of 40...
-
Do you use decompositional analyses to understand what behavioral aspects (e.g., frequency, order size) are most strongly associated with these differences?
-
As you perform customer-base audits on an ongoing basis, how do they change as you gain more experience and perspective? Are they simpler or more complex?
-
Before contemplating a full audit, what kinds of basic analyses do you perform with this integrated dataset? What are the first crossover (product customer) questions you seek to answer?
-
Do you seek to know which products tend to be disproportionately favored by high-value customers?
-
5. Option pricing - Single-period binomial approach Aa The value of an option can be calculated by using a step-by-step approach in the case of single periods or by using sophisticated formulas that...
-
Do the three planes x + 2x + x 3 = 4, X X 3 = 1, and x + 3x = 0 have at least one common point of intersection? Explain.
-
If $4000 is saved in an account offering a return of 4% compounded continuously, the future value, S, after t years is given by S = 4000e 0.04t (1) Calculate the value of S when (a) t = 5 (b) t =...
-
Find, if possible, the minimum value of the objective function 3x 4y subject to the constraints, 2x + y 12, x y 2, x 0 and y 0
-
The demand function of a good is given by P = 80/3Q (a) Show that the price elasticity of demand is a constant. (b) Sketch a graph of the demand curve. (c) Shade the area which gives the consumers...
-
Donna Corporation manufactures custom cabinets for kitchens. It uses a normalcosting system with two direct-cost categoriesdirect materials and direct manufacturing laborand one indirect-cost pool,...
-
Donna Corporation manufactures custom cabinets for kitchens. It uses a normalcosting system with two direct-cost categoriesdirect materials and direct manufacturing laborand one indirect-cost pool,...
-
Donna Corporation manufactures custom cabinets for kitchens. It uses a normalcosting system with two direct-cost categoriesdirect materials and direct manufacturing laborand one indirect-cost pool,...
Study smarter with the SolutionInn App