Problem of the Week
for Friday, November 19

You are an unscrupulous cab driver taking innocent new Saint Ann's teachers to their first day of school.
What is the longest (most expensive) possible route from the train station to Saint Ann's?
You cannot drive on the same street twice (they will get suspicious)
but you can go through an intersection more than once (and of course you have to stay on the map!)

Explain WHY no path could be longer than yours.

Nicholas' Solution:
The most number of streets the taxi driver can drive is 25. This is because there are 10 intersections (which have been circled) that have 3 streets and none of these intersections are at the starting or ending point. So, you have to go in and out of these intersections, this will use 2 of the 3 streets in these intersections, but the last one can't be used. Also, you go out of the starting point and into the ending point once, so these 2 intersections, which have 2 streets, will have one street that isn't used. So there are 12 intersections that need to leave out a street. Because these intersections share streets, you only need to leave out half as many streets as intersections.



Congratulations to Roy and Louis for their solutions too!


 

Animated Solution (click on cab to start - school to reset):

email answers to rmann@saintannsny.org