[Aaryan]

This is pretty easy, just need confirmation for my bro. My brother (thingamajigi) won't believe me, so I need you guys to confirm it.

Assume you are on a boardwalk. Your hotel is x feet from one end (point A). The total length of the boardwalk (end to end) is 4 mi. If you want to walk, from your hotel, to point B (the opposite end of A), then go ALL the way to point A, then back to your hotel. The debate is, does to location of x make a difference in the distance of your route?

[Guest]

No. Did you show him the math? Or a draw it on paper? It should be 8 miles regardless of where x is.

A and B are endpoints. Hotel is at x. For the route: Distance to B is B-x. From B to A is B-A. Then to x is A-x. All distance are absolute values. The distance from x to A plus from x to B combine to be the distance from B to A. So you walk twice the distance from B to A.

[Guest]

What you are trying to do is as good as moving in a circle. Mathematically speaking if A to hotel is x fee and hotel to B is y feet then first you move y feet, then x+y feet and then x feet. Hence the total distance is going to remain 2(x+y) irrespective of the values of x and y. I hope this answers your query.

[Auramyna]

Point x is inbetween Point A and Point b. If Point x is, e.g, 1 mile from Point A and 9 miles from Point B, then it does make a difference where x is situated.

I think you need to draw it on paper for him so you are both on the same page as to where the Point A, B and x are situated.

[Guest]

Point x is inbetween Point A and Point b. If Point x is, e.g, 1 mile from Point A and 9 miles from Point B, then it does make a difference where x is situated.

I think you need to draw it on paper for him so you are both on the same page as to where the Point A, B and x are situated.

Rightly pointed out. There are now two cases (where i would like to correct your statement too as the variable "x" is not a point but the distance from point A to hotel).

1) When the hotel is on the broad walk

2) when the hotel is outside broad walk

However, the question asks me to assume that i'm ON THE BROAD WALK initially and I can only be on the broad walk AND start from the hotel if and only if the hotel is on the broad walk (the necessary and sufficient condition).

With this under consideration, i think what nana7 and i have written is correct.

Edited May 28, 2011 by Silver Surfer

[Aaryan]

Thank you, guys. Nana and Silver, and Aura. I have drawn it and he gets it.

[Akriti]

Darn, I am late again for this riddle