Math Is Fun Forum

guitfiddler83

Member

Registered: 2012-04-28

Posts: 3

how many possible variations for security guard patrols?

I hope this is the right forum
> Long story short I am trying to calculate the number of possibilities to reach a desired sum using only whole numbers zero and grater.
Example would be there are 0 possibilities to reach 0
> 1 possibility to reach 1 (1+1)
> 3 possibilities to reach 2 (1+1) (2+0)
> 4 possibilities to reach 3 (1+1+1) (1+2) (2+1)
> I work as a security supervisor and I am trying to introduce my guys on how many possible ways they can vary their rounds. Just to be more complex I want to give a number of possible ways to do their rounds if they only patrol once an hour going clockwise or counter clockwise around the site. Shifts are not always the Same amount of hours so I need a formula to figure it out myself. > If possible would I also be able to get a way to calculate this and include a varying number of starting locations? > example > Guard works an 8 hour shift and has 4 different possible starting locations. The guard also randomly changes direction
eexample
(3 clockwise patrols at point a, one clockwise patrol starting at point b, one counter clockwise patrol a point c, 1 clockwise patrol at point d, 2 clockwise patrols at point b)

Thank you guys...any help is appreciated!!!!

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: how many possible variations for security guard patrols?

Hi

Welcome to the forum!

The formula for the first one is given by something called Bell's numbers. Look it up on the internet.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: how many possible variations for security guard patrols?

Hi;

Welcome to the forum. The first part of your problem is called a partition. They are calculated by using generating functions.

The second part will require a bit more explanation and a complete example.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

guitfiddler83

Member

Registered: 2012-04-28

Posts: 3

Re: how many possible variations for security guard patrols?

Ok...so a complete example...
8 hour shift.
4 possible locations to start a patrol from (lets call them a b c and d)
One patrol each hour that can start at any point...so 8 possible ways to start each patrol.
Side note : our company uses proxi chips placed on different places on sites like shopping centers. A proxi ready is carried by the guard. Each time the reader hit a button it logs chip id. And satellite time stamp. Thus why a certain number can be chosen for how many starting points and why possible number of variations per shift need to be identified.
How many total different ways can a guard patrol for the entire shift (repetition possible ie..point a clockwise twice in a row).
In other words...how many different patterns are possible for an 8 hour shift with four starting point. What about 9 hours with 5 starting points? 4 hours with 16 starting points? .

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: how many possible variations for security guard patrols?

He must cover a,b,c,d in his shift? 1 different checkpoint per hour?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.