Skip to main content

Timeline for answer to All (red and blue) roads lead to Rome by Pranay

Current License: CC BY-SA 4.0

Post Revisions

12 events
when toggle format what by license comment
yesterday comment added Pranay @NuclearHoagie. Exactly, I need not have used so many symbols but that's essentially the argument.
yesterday comment added Nuclear Hoagie Nice, I wondered how to prove it was minimal. To rephrase the proof: Rome itself must use an out-and-back route, or else go all the way around and use more than 10 steps. Any out-and-back route consists of an even number of steps, therefore the optimal plan has an even number of steps. But the only way to use an even number of steps starting from only 1 step away is to go 10 steps around the other way - we can't do better than 10 steps.
yesterday vote accept Misha Lavrov
yesterday comment added Misha Lavrov Correct - well done!
2 days ago history edited Pranay CC BY-SA 4.0
Removed mathjax and streamlined the proof of minimality a bit
2 days ago comment added Pranay I have improved the answer since I posted the above comment. Instead of reveal spoilerk+1 R’s, we need only k R’s.
2 days ago history edited Pranay CC BY-SA 4.0
Improved the solution
2 days ago history rollback Pranay
Rollback to Revision 2
2 days ago history edited Pranay CC BY-SA 4.0
added 292 characters in body
2 days ago history edited Pranay CC BY-SA 4.0
added 292 characters in body
2 days ago comment added Pranay To anyone wondering how I came up with this colouring, I tried doing this for 3 cities, then 5 cities, and noticed that reveal spoilerfor n = 2k+1 cities, k+1 R's followed by k B's always seemed to work, and when you start from Rome, you go all the way around. This fixes all the colours of the edges.
2 days ago history answered Pranay CC BY-SA 4.0