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#1 2006-10-27 07:45:34

Toast
Real Member
Registered: 2006-10-08
Posts: 1,321

How many possibilities?

I hate those stupid questions that say:
How many ways can you arrange a $10, $20, $50, and $100 note so that the total adds up to $500 etcetc.
They always appear on those yearly competition tests and stuff...>_<
How are these questions actually done? Is it possible to use simple algebra to explain them or must they be all done in incomprehensible calculus/algorithmic talk?

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#2 2006-10-28 08:35:12

All_Is_Number
Member
Registered: 2006-07-10
Posts: 258

Re: How many possibilities?

Toast wrote:

I hate those stupid questions that say:
How many ways can you arrange a $10, $20, $50, and $100 note so that the total adds up to $500 etcetc.
They always appear on those yearly competition tests and stuff...>_<
How are these questions actually done? Is it possible to use simple algebra to explain them or must they be all done in incomprehensible calculus/algorithmic talk?

The number of possibilities can be expressed:

Where x is the total amount, h is the number of $100 bills, f is the number of $50 bills, and t is the number of $20 bills.
(Notice the floor operation in the upper limit of the inner most series.)

Substituting 500 for x yields:

So there are 341 different ways that $100, $50, $20 and $10 bills can be combined to obtain a total of $500.






Suppose we wanted to allow the use of $5 and $1 bills, also. Our expression then changes to:

Where n is the number of $10 bills and v is the number of $5 bills.

Substituting 500 for x yields:


I hope this helps.

Last edited by All_Is_Number (2006-10-28 10:46:24)


You can shear a sheep many times but skin him only once.

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#3 2006-10-28 17:01:11

Toast
Real Member
Registered: 2006-10-08
Posts: 1,321

Re: How many possibilities?

oh dear dunno, thanks for your help anyway

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