# Math riddle help needed for findin a general rule through an equation!

Every block of a neighborhood is 100 meters long by 100 meters wide. Every policeman can see 100 meters. How many policemen do you need to patrol the area?
For a 3x3 rectangular area you need 8 policemen.
Find the rule/rules which give the number of policemen needed for any size of rectangular district.

I have the rule for the even number of squares (2x2, 4x4, 6x6, 8x8 etc). but I am having trouble finding a rule for the odd numbers of squares (1x1, 3x3,5x5 etc). I've been sitting and trying to work this out for ages and I have come so close, yet cannot find it exactly. I would really appreciate it if someone could lead me in the right direction:). thanx for your help!!

Even number of squares rule is Number of policemen = (N/2) ^2 + (N/2 + 1) ^2

Basically, the complete overview of the 'neighborhood'is made up of separate squares each 100m length by 100m breadth which make the total NxN 'neighborhood' rectangular number (hope this isn't confusing).
it is N + 1