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Re: Solving equations and inequalities with Reduce - how?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg87710] Re: [mg87655] Solving equations and inequalities with Reduce - how?
*From*: "W_Craig Carter" <ccarter at mit.edu>
*Date*: Wed, 16 Apr 2008 05:00:33 -0400 (EDT)
*References*: <200804150950.FAA24909@smc.vnet.net>
Hello Marc,
Your initial example worked fine for me:
Reduce[200000 a + 20000 b + 2000 c + 200 d + 20 e + 2 f ==
100000 c + 10000 d + 1000 e + 100 f + 10 a + b, {a, b, c, d, e, f},
Modulus -> 9]
resulted in
a == C[1] && b == C[2] && c == C[3] && d == C[4] && e == C[5] &&
f == 8 C[1] + 8 C[2] + 8 C[3] + 8 C[4] + 8 C[5]
Perhaps you had a typo? In your original post you had 20000a
and not
20000 a
Craig
On Tue, Apr 15, 2008 at 5:50 AM, Marc Heusser
<marc.heusser at byeheusser.commercialspammers.invalid> 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>
>
>
--
W. Craig Carter
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