Re: Solving equations and inequalities with Reduce - how?
- To: mathgroup at smc.vnet.net
- Subject: [mg87723] Re: [mg87655] Solving equations and inequalities with Reduce - how?
- From: Daniel Lichtblau <danl at wolfram.com>
- Date: Wed, 16 Apr 2008 05:02:59 -0400 (EDT)
- References: <200804150950.FAA24909@smc.vnet.net>
Marc Heusser wrote: > I tried to solve equations with Reduce and somehow did not quite > formulate it right, so Reduce complains with > "Reduce::ivar: 1 is not a valid variable". > > This is what I tried: > > Wanted: A six digit number satisfying the following conditions: > The first digit is not zero. > If you take the first two digits and move them to the end of the number, > the resulting number must be twice the original number. > > In[23]:=Reduce[200000a +20000 b +2000 c+200 d+20 e + 2 f > \[Equal]100000c +10000 d +1000 e+100 f+10 a + b , {a,b,c,d,e,f}, > Modulus\[Rule]9] > > I did solve the problem through exhaustive search: > > In[14]:=Timing[Select[Range[10^6], FractionalPart[#/10000] 1000000 + > IntegerPart[#/10000]\[Equal] 2 #&]] > Out[14]={34.2848 Second,{142857,285714,428571}} > > but would like to understand how to use Reduce (or another function) to > solve such a set of equations. > > TIA > > Marc > I realize this has been answered by now, but you might want to have a look at problem 1 in the notebook at http://library.wolfram.com/infocenter/Conferences/6530/ Among other things, I'll note that you really need to enforce "one digitedness" by inequalities, not with a Modulus setting. Along the lines of that notebook, here is some code for your particular problem. In[26]:= Reduce[{2*n==100*m+k, n==m+10^4*k, Element[{n,m,k},Integers], 10^4>m>=10^3, 0<=k<=99, n>=10^5}, {n,m,k}] Out[26]= (n == 142857 && m == 2857 && k == 14) || (n == 285714 && m == 5714 && k == 28) || (n == 428571 && m == 8571 && k == 42) Daniel Lichtblau Wolfram Research
- References:
- Solving equations and inequalities with Reduce - how?
- From: Marc Heusser <marc.heusser@byeheusser.commercialspammers.invalid>
- Solving equations and inequalities with Reduce - how?