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 Apr 26 comment Which Denominations to use for payroll with no returned change @lulu, thank you very much, I will check on this some more and let you know if I come with a counter example... Apr 26 comment Which Denominations to use for payroll with no returned change @lulu, actually I was wondering how to provide (any) solution. Some algorithms, of course you know this, provide a 'next' solution as one iterates but this is not necessary. Again, I am curious about the problem. As for solving each one individually, I still think that we can't 'always' get a solution unless we have 'enough' number of each denomination required. I could try to come up with an example. Apr 26 revised Which Denominations to use for payroll with no returned change edited title Apr 26 comment Which Denominations to use for payroll with no returned change @lulu, thank you for your comments and for the links. Of course it would be fancier to add constraints, but I thought this would make it harder. As for the generating function approach, it is elegant. However, I guess it works for a single amount (employee in this case) only. I also think that trying to satisfy each individual separately, could lead to the situation where one runs out of 1 or more denominations suddenly, and would have to start over again. Apr 26 asked Which Denominations to use for payroll with no returned change Apr 17 comment find the rate of change $f(x) = 4\sin^3 x$ when $x = \frac{5\pi}{6}$ You need to know Trigonometry. Many sources exist, for example:sites.csn.edu/istewart/mathweb/math127/any_angles/any_angle.htm Apr 17 comment Sum of integer squares with zero sum for k=4: 1,-2,-3,4 Apr 16 comment How can we prove that a quadratic equation has at most 2 roots? if there were more than 2 roots, you would get $f(x)=(x-r1)(x-r2)(x-r3)$, this when expanded results in a polynomial of 3rd degree if the value r3 is different from r2 and r1. Apr 16 answered How to come up with Gauss arithmetic progression solution in this sum Apr 15 comment Real analysis for a non-mathematician. For someone with Engineering background, you probably would not benefit from Real Analysis. I suggest you consider Applied Mathematics, Numerical Methods, and such. Apr 14 comment Unique solution for circuits in Linear Algebra @Omnomnomnom, you are correct. My statement was incomplete. Corrected now to state: If a system of equations has the same number of variables as equations, and the equations are independent and consistent and a determinant exists, then the solution will be unique. Apr 14 revised Prove if $(x+1/x)$ is an integer then $(x^n+1/x^n)$ is an integer LaTex on header Apr 14 revised get data to draw a gauss curve Add tag Apr 14 comment Issue with optimization problem It is OK, this is not the reason for my comment. To better explain my point try to change the length of triangles in the link below, you will see that when you drag a point, the other lines and angles all change. In you case, there is no relationship (constraint) to force a similar change. See: mathopenref.com/coordtriangleareabox.html Apr 14 comment Issue with optimization problem I assume that your representation of L is not forcing the three lines to be connected at the intersection point for the lines l1 and l2, so the result is independent of the shape they are embedded in. You need some constraints to force the 3 lines to be tightly coupled so that a change in one results corresponding change in the other(s) - Somewhat like a rubber/elastic construct if you know what I mean. Apr 14 revised Calculation of Covariance fixed tags Apr 14 comment Using points on a line to find the number of segments I suggest you list the question exactly as it appears in your text. Apr 13 comment Fitting a curve of the form Y = ae^(-b) using Least Squares Estimators Apr 13 comment Elementary Algebra problem about calculation of profit Thank you for all your help. I had to reward the bonus to Justin because he brought a critical point (although it was not already in the question text to be honest). Apr 13 comment Elementary Algebra problem about calculation of profit Thank you for your explanation.