You would also want an additional constraint: n >= 0. Such problems form the class of so called Integer Programming problems. These problems are NP-hard in general, but there are good software (including open-source) available to solve such problems. e.g. https://projects.coin-or.org/Cbc
The above solver, Cbc, is available as an optional package for sage. See: http://www.sagemath.org/packages/optional/ I haven't used it myself though. Hope this helps. -- regards Ashutosh Mahajan http://coral.ie.lehigh.edu/~asm4 On Wed, Feb 17, 2010 at 07:21:01PM -0600, Oscar Gerardo Lazo Arjona wrote: > A friend of mine proposed me the following problem: > > A reporter asks a military officer how many soldiers are at a certain > military base. The officer, not wanting to reveal such sensitive > information, but also not wanting to seem overly secretive, gives an > indirect answer: > > When my soldiers form 2 collumns there is 1 soldier left. > When my soldiers form 3 collumns there are 2 soldier left. > When my soldiers form 4 collumns there are 3 soldier left. > When my soldiers form 5 collumns there are 4 soldier left. > When my soldiers form 6 collumns there are 5 soldier left. > When my soldiers form 7 collumns there are 0 soldier left. > > How many soldiers are there? > > I formed the following equations system and put it on a notebook cell: > > var('x1 x2 x3 x4 x5 x6 n') > eq1=7*x1 ==n > eq2=6*x2 +5 ==n > eq3=5*x3 +4 ==n > eq4=4*x4 +3 ==n > eq5=3*x5 +2 ==n > eq6=2*x6 +1 ==n > equations=(eq1,eq2,eq3,eq4,eq5,eq6) > solve(equations,x2,x3,x4,x5,x6,n) > > And got: > > [[ > x2 == 7/6*x1 - 5/6, > x3 == 7/5*x1 - 4/5, > x4 == 7/4*x1 - 3/4, > x5 ==7/3*x1 - 2/3, > x6 == 7/2*x1 - 1/2, > n == 7*x1]] > > Which is correct as far as I can see, but it only produces a valid n > when all of x1,x2,x3,x4,x5,x6 are integer. > > I know I could find the answer by examining succesive values of x1 > untill all the x are integer, but is there some way to tell sage that we > are dealing with integer variables? I have the feeling that this is a > more profound problem than it appears (finding integer solutions). > > thanks! > > Oscar > > > -- > To post to this group, send email to sage-support@googlegroups.com > To unsubscribe from this group, send email to > sage-support+unsubscr...@googlegroups.com > For more options, visit this group at > http://groups.google.com/group/sage-support > URL: http://www.sagemath.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
