Re: Solving equations and inequalities with Reduce - how?

*To*: mathgroup at smc.vnet.net*Subject*: [mg87699] Re: [mg87655] Solving equations and inequalities with Reduce - how?*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Wed, 16 Apr 2008 04:58:28 -0400 (EDT)*References*: <200804150950.FAA24909@smc.vnet.net>

On 15 Apr 2008, at 18:50, 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 > > -- > remove bye and from mercial to get valid e-mail > <http://www.heusser.com> Reduce[200000*a + 20000*b + 2000*c + 200*d + 20*e + 2*f == 100000*c + 10000*d + 1000*e + 100*f + 10*a + b && Inequality[1, Less, a, LessEqual, 9] && 0 <= b <= 9 && 0 <= c <= 9 && 0 <= d <= 9 && 0 <= e <= 9 && 0 <= f <= 9, {a, b, c, d, e, f}, Integers] (a == 2 && b == 8 && c == 5 && d == 7 && e == 1 && f == 4) || (a == 4 && b == 2 && c == 8 && d == 5 && e == 7 && f == 1) Andrzej Kozlowski

**References**:**Solving equations and inequalities with Reduce - how?***From:*Marc Heusser <marc.heusser@byeheusser.commercialspammers.invalid>