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Re: Solve - takes very long time

• To: mathgroup at smc.vnet.net
• Subject: [mg121824] Re: Solve - takes very long time
• From: "Dr. Wolfgang Hintze" <weh at snafu.de>
• Date: Tue, 4 Oct 2011 01:31:04 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j6bris$8m4$1@smc.vnet.net>

"Fredob" <fredrik.doberl at gmail.com> schrieb im Newsbeitrag 
news:j6bris$8m4$1 at smc.vnet.net...
> Hi,
>
> I tried the following on Mathematica 8 and it doesn't seem to stop
> running (waited 40 minutes on a 2.6 Ghz processor w 6 GB of primary
> memory).
>
> Solve[
> {100*Subscript[x, 2] + 10*Subscript[x, 1] + Subscript[x, 0] +
>    100*Subscript[y, 2] + 10*Subscript[y, 1] + Subscript[y, 0] ==
>   100*Subscript[z, 2] + 10*Subscript[z, 1] + Subscript[z, 0],
>   Subscript[x, 0] > 0, Subscript[y, 0] > 0, Subscript[z, 0] > 0,
>  Subscript[x, 1] > 0, Subscript[y, 1] > 0, Subscript[z, 1] > 0,
>  Subscript[x, 2] > 0, Subscript[y, 2] > 0, Subscript[z, 2] > 0,
>  Subscript[x, 0] <= 9, Subscript[y, 0] <= 9, Subscript[z, 0] <= 9,
>  Subscript[x, 1] <= 9, Subscript[y, 1] <= 9, Subscript[z, 1] <= 9,
>  Subscript[x, 2] <= 9, Subscript[y, 2] <= 9, Subscript[z, 2] <= 9,
>  Subscript[x, 0] != Subscript[y, 0] != Subscript[z, 0] != Subscript[
>   x, 1] != Subscript[y, 1] != Subscript[z, 1] != Subscript[x, 2] !=
>   Subscript[y, 2] != Subscript[z, 2]},
> {Subscript[x, 2], Subscript[y, 2], Subscript[z, 2], Subscript[x, 1],
>  Subscript[y, 1], Subscript[z, 1], Subscript[x, 0], Subscript[y, 0],
>  Subscript[z, 0] },
> Integers]
>
> The problem was a homework for my daugther where you are supposed to
> use all digits to build - but only once - 2 three digit numbers and
> addition.
>
>
Even the simplest operation of the type Reduce[eq, x>0] takes very long 
time also on my PC.
It might be better to look for a different approach to the problem.

I understand you are looking for three numbers
A={a,b,c},B={d,e,f},C={g,h,i} such that
(1)     A+B = C and
(2)    {a,b, ...,i} = Permutation {1,2, ...,9}

There are 168 different solutions (i.e. with A<B),
These are the 4 with the smallest C (=459)
{186, 273, 459}, {183, 276, 459}, {176, 283, 459}, {173, 286, 459}

these are the 8 with the largest C (=981)

{357, 624, 981}, {354, 627, 981}, {327, 654, 981}, {324, 657, 981},
{246, 735, 981}, {245, 736, 981}, {236, 745, 981}, {235, 746, 981}

The code I used for finding all solutions is

p=FromDigits/@(Partition[#, 3] & /@ Permutations[Range[9]]); (* form 
all possible sets of three 3-digit numbers *)
sp = Select[p, #[[1]] + #[[2]] == #[[3]] &]; (* the equation *)
sp1 = Select[sp, #[[1]] < #[[2]] &]; (* no repetition *)
Reverse /@ Sort[Reverse /@ sp1] (* sort according to sum *)

Wolfgang