Is there a way to work out the minimum number
of policeman needed to 'watch' a block x block area. (Each policeman
can see for 1 block in all directions)i.e. A 2 block x 2 block area
would need 4 policeman to watch all ways. What if it was say, 5
blocks x 4 blocks? How do i find out the least number of policeman
needed to cover all streets and avenues?
Find the perimiter then divide by the distance
required between policemen. So in your 5x4 block example 5+5+4+4
= a perimiter of 18 - a policeman can see 1 block in 1 direction
and 1 block in the other direction so 18/2 = 9 policemen. ON your
2 x 2 block you have a perimiter of 2+2+2+2 = 8 divide by 2 and
you get 4 policemen.
Greg
Many thanks for your help. It's easy when you know
how! Ha! Ha!
That answer will cover the perimeter of your set
of blocks but what about the middle where crime is rife because
those policemen around the edge cannot see deep into the city? It
took me a while to figure this out but the answer is almost as simple
as Greg's. Start by imagining a policeman at every intersection
and the edges of your blocks. After a few drawings you can quickly
see that the number of policeman equals the number of blocks in
your street plus one multiplied by the number of blocks in the avenue
plus one. So in a five by four set you will need six by five policeman
which is 30 cops. Greg was right when he said that the actual number
of policemen is "every other one" - so you divide by two. When the
answer is, for example, 7 and a half (try a four by two) then the
right answer is seven since half a policeman is no good to anybody.
The mathematical answer is INT((S+1)*(A+1)/2) where S is the number
of blocks in a street and A is the number of blocks in an avenue.
The INT bit removes any halves that might come from the division
by two.
Brian
Thank you very much for your efforts. It is much
appreciated.
Patrick
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