Stars, Bars & Linear Systems This assignment is about exploring the validity of the solution to this question: "How many integer solutions are there to the equation

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
How would I approach this?
**Stars, Bars & Linear Systems**

This assignment is about exploring the validity of the solution to this question:

“How many integer solutions are there to the equation x+y+z=10 for which x, y and z are greater or equal than -3?”

In class and in the book, we found out that the answer to this problem is equivalent to adding 9 stars, 3 for each variable. Thus, C(21,2)=C(21,19)=210.

Some of you were puzzled by this approach because you correctly noticed that the worst-case scenario is x=-3, y=-3 and z=16. This would suggest that we only need to add 6 stars and not 9.

Your goal is to investigate these two claims and find a final answer by doing the following:

- Write a program in your preferred programming language that finds all possible solutions of the above problem and writes them into a comma delimited file with one solution per line (e.g., 0,0,10)
- Count the lines in the output file and discuss your findings.
- Submit the code, your conclusions, and the file in MOER.
Transcribed Image Text:**Stars, Bars & Linear Systems** This assignment is about exploring the validity of the solution to this question: “How many integer solutions are there to the equation x+y+z=10 for which x, y and z are greater or equal than -3?” In class and in the book, we found out that the answer to this problem is equivalent to adding 9 stars, 3 for each variable. Thus, C(21,2)=C(21,19)=210. Some of you were puzzled by this approach because you correctly noticed that the worst-case scenario is x=-3, y=-3 and z=16. This would suggest that we only need to add 6 stars and not 9. Your goal is to investigate these two claims and find a final answer by doing the following: - Write a program in your preferred programming language that finds all possible solutions of the above problem and writes them into a comma delimited file with one solution per line (e.g., 0,0,10) - Count the lines in the output file and discuss your findings. - Submit the code, your conclusions, and the file in MOER.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,