The map.
Below is a map of Alpeno, which shows all the horizontal, vertical, and diagonal streets of the city. The local government is planning to place CCTV cameras around the streets to fight the increase in crime, but they are on a tight budget.
What is the minimum number of security cameras that need to be placed to get a full view of all the streets?
Assumptions and Hints:
- These cameras can turn around 360 degrees.
- You can put them anywhere on the streets, but it would be best to choose from the 25 colored dots.
The answer is 7.
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1 solution
There are seven streets going diagonally from the lower-left to the upper-right, and each camera can monitor at most one of these streets, so there need to be at least seven cameras. The diagram below shows that seven cameras suffice, so this is the answer.