I stopped at a street corner and asked for directions to Burger Jack. Unfortunately, the person I wasked was Larry Longway, whose directions are guaranteed to be too complicated. He said,"You are now facing north:
Go straight for two blocks.
$\ \ \ $Turn left. Go straight for one block.
$\ \ \ $Turn right. Go stright for three blocks.
$\ \ \ $Turn right. Go straight for five blocks.
$\ \ \ $Turn right. Go straight for three blocks.
$\ \ \ $Turn left. Go straight for one block.
$\ \ \ $Turn right. Go straight for four blocks.
$\ \ \ $Turn left. Go straight for two blocks.
$\ \ \ $Turn left. Go straight for one block.
$\ \ \ $Turn left. Go straight for five blocks, and you are there.
By the time I arrived I was out of breath and Burger Jack was closed. Please give me the directions for the shortest path from my original spot to Burger Jack (assume no street have dead ends.)
Below I included a picture of my work as a rough sketch. Here is the points I have labeled on my graph:
(0,0) as the starting point
(-1,2)
(4,5)
(4,2)
(5,2)
(5,-2)
(7,-2)
(7,-1)
(2,-1) Ending point
So, he is two blocks east and one block south from his original point. I am looking for a confirmation on this answer if anyone else has time to work the problem, it would be greatly appreciated.
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Best Answer
I combined the "turn and go straight..." commands to just
(Cardinal direction: N/S/E/W):(# of blocks)
N:2
W:1
N:3
E:5
S:3
E:1
S:4
E:2
N:1
W:5
Now clearly many of these "cancel" with others (e.g. E:5 cancels with W:5, N:3 cancels with S:3). We are left with a net change of E:2 and S:1, corresponding to the point $(2, -1)$ on the plane if you started from the origin.