Denominations Combinations
June 20th, 2011 at 2:06:07 PM
permalink
I know this is a fairly common problem, But, I am interested if anyone knows some form of linear algebra solution? I have a suspicion that one exists... Unfortunately my linear algebra skills are far from decent. I have been trying to come up with something but no luck. No, this isn't a homework assignment.
Problem:
Given denominations of {.01, .1, .25, 1.0} how many different combinations exist for deriving the value 1.11 (or any value) using any combination of denominations.
You may use denominations more than once.
Comments:
I am aware of the iterative solutions. But, I am interested if it is possible without an iterative solution? Using some fashion of binomial coefficients and linear algebra, perhaps? I have no clue...just been bothering me for awhile....
Problem:
Given denominations of {.01, .1, .25, 1.0} how many different combinations exist for deriving the value 1.11 (or any value) using any combination of denominations.
You may use denominations more than once.
Comments:
I am aware of the iterative solutions. But, I am interested if it is possible without an iterative solution? Using some fashion of binomial coefficients and linear algebra, perhaps? I have no clue...just been bothering me for awhile....
