MHB Q&A: Understanding Part C of a Round Trip Problem

  • Thread starter Thread starter find_the_fun
  • Start date Start date
AI Thread Summary
The discussion centers on the confusion regarding the calculation of return routes in part c of a round trip problem. The answer key indicates there are 14 ways to reach point C, but the user believes the return options vary based on the road taken. They argue that if certain roads are used to reach C, it limits the return routes differently depending on which roads are restricted. The user concludes that if R1R5 is used to get to C, the only restricted return trip is R5R1, allowing for other routes back. The core issue is the misunderstanding of how the restrictions on return trips affect the total number of valid routes.
find_the_fun
Messages
147
Reaction score
0
I don't understand the answer for part c of the following question

View attachment 1615

The answer key gives 14x13 as the solution to part c. I understand there are 14 ways to get to point C but depending on which road can no longer be used, there is anywhere between 10 and 13 ways to return home. For example, say R8 was taken to get to C. Then there are 14-1 ways to make the return trip (just don't use R8). However, if R1R5 is used then we can't use either R1 (so now there are 3x3+2=11 ways to make the trip) or R5 (so now there are 2x4+2=10 ways to make the trip). What is wrong with my reasoning?
 

Attachments

  • question.png
    question.png
    50.9 KB · Views: 83
Physics news on Phys.org
As I understand the problem statement in c), if Linda takes R1R5 to get from A to C, there is a single trip she is not allowed to take back: R5R1. All other trips are allowed.
 

Thread 'Deductive proof in logic formal systems'

I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
View full post »

Similar threads

I Understanding Spacetime simultaneity in twin paradox scenarios
Replies
35
Views
3K
I A Sequence T based on the Rule of Three
Replies
15
Views
2K
Solve Thevenin Problem: A & B for R1 Circuit
Replies
1
Views
2K
Finding the Magnitude and Direction of the Displacement Vector for a Ship's Trip
Replies
2
Views
5K
I Einstein brother-in-law elevator
Replies
11
Views
2K
Counting problem - how many ways....
Replies
4
Views
3K
I One Way Twin Revisited: Understanding Tim & Tom's Watches on Home & Northbound
Replies
37
Views
3K
Solution of basic special relativity problem
Replies
4
Views
1K
Engineering Solve Delta-Wye Circuit: Find R3, R12 & R13
Replies
7
Views
4K
Auto/Motor Honda NT700V Deauville motorcycle maintenence: Drive shaft
Replies
27
Views
4K

Hot Threads

Recent Insights

Back
Top