Alper is the owner of Cube-XYZ, a perfect cube-shaped planet, and builds a mansion on one vertex of the cube, and distinct houses on the seven other vertices. Houses are considered next door if they are connected by an edge of the cube. He is to host an intergalactic tea party for his friends; Wes, Ethan, Henry, Alan, James, Vincent, and Tom. They are to be accommodated in separate houses. As host, Alper has conditions on how the guests must be placed on his planet: i. His best friend Ethan must live next door to him ii. Henry and James must not live next door to each other iii. Alan and Vincent must live next door to each other iv. Wes should be as many edges away from Alper as possible v. Alper lives in the Mansion vi. Tom lives (strictly) closer in distance to Wes than Alper i. Given all conditions are met, how many combinations of living arrangements are there?
Alper is the owner of Cube-XYZ, a perfect cube-shaped planet, and builds a mansion on one vertex of the cube, and distinct houses on the seven other vertices. Houses are considered next door if they are connected by an edge of the cube. He is to host an intergalactic tea party for his friends; Wes, Ethan, Henry, Alan, James, Vincent, and Tom. They are to be accommodated in separate houses. As host, Alper has conditions on how the guests must be placed on his planet: i. His best friend Ethan must live next door to him ii. Henry and James must not live next door to each other iii. Alan and Vincent must live next door to each other iv. Wes should be as many edges away from Alper as possible v. Alper lives in the Mansion vi. Tom lives (strictly) closer in distance to Wes than Alper i. Given all conditions are met, how many combinations of living arrangements are there?
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
Alper is the owner of Cube-XYZ, a perfect cube-shaped planet, and builds a mansion on one vertex of the cube, and distinct houses on the seven other vertices. Houses are considered next door if they are connected by an edge of the cube. He is to host an intergalactic tea party for his friends; Wes, Ethan, Henry, Alan, James, Vincent, and Tom. They are to be accommodated in separate houses. As host, Alper has conditions on how the guests must be placed on his planet:
i. His best friend Ethan must live next door to him
ii. Henry and James must not live next door to each other
iii. Alan and Vincent must live next door to each other
iv. Wes should be as many edges away from Alper as possible
v. Alper lives in the Mansion
vi. Tom lives (strictly) closer in distance to Wes than Alper
i. Given all conditions are met, how many combinations of living arrangements are there?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 7 steps with 6 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education