# 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).