Surveillance Camera puzzle
Imagine a city layout, as in the diagram with a bird's eye view of a city map, with the gray lines representing streets.
A group wants to place the least number of surveillance cameras necessary to have a video log of every person and vehicle that travels these streets.
Suppose buildings or obstructions are between the streets so a clear view is only possible by looking up and down the streets.
Where could the least number of cameras be placed so all streets can be monitored?
Hint: Guess and check or trial and error. Only two cameras are needed.
Place a camera and imagine what it will view and what it will not view.
Reason, from where you placed the camera, if that placement will view more or if another placement will view more.
Reason if a placement at an intersection or along a street will generally view more.
Reason if the placement of a camera at an intersection of four streets is better than at two streets.
Imagine what a camera placed at the red dot would view.
Can draw sight lines from a camera down the streets that can be viewed.
Are there streets that can't be viewed?
Use symmetry for the placement of a second camera.
Are there streets that still can't be viewed?
Do sight lines cover all streets?
Is there a better placement?
What conclusion can be made about camera placement and intersections and non intersections.