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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

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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 МOER
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 МOER
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