FantasiaLimav
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- Nov 27, 2010
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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!!
Rule for even number is Number of policemen = (N/2) ^2 + (N/2 + 1) ^2.
Basically, the complete picture of the total overview is made up of separate squares each with 100m length and 100m breadth which make up the NxN 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!!Rule for even number is Number of policemen = (N/2) ^2 + (N/2 + 1) ^2.
Basically, the complete picture of the total overview is made up of separate squares each with 100m length and 100m breadth which make up the NxN area