Re: Solve - takes very long time
- To: mathgroup at smc.vnet.net
- Subject: [mg121856] Re: Solve - takes very long time
- From: Ray Koopman <koopman at sfu.ca>
- Date: Wed, 5 Oct 2011 04:00:34 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
The basic condition can be written as
100*(x2 + y2) + 10*(x1 + y1) + (x0 + y0) = 100*z2 + 10*z1 + z0,
in which form it is clear that we can always swap corresponding xi and
yi, and that solutions therefore come is sets of 8. Requiring xi < yi
for all i is just a way of picking a "canonical" member of each set.
----- DrMajorBob <btreat1 at austin.rr.com> wrote:
> The conditions #[[2]] < #[[5]] and #[[3]] < #[[6]] do not belong, however.
>
> Bobby
>
> On Tue, 04 Oct 2011 00:30:53 -0500, Ray Koopman <koopman at sfu.ca> wrote:
>
>> On Oct 3, 1:26 am, Fredob <fredrik.dob... at gmail.com> wrote:
>>> 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.
>>
>> For each of the 42 solutions found by the brute force search given
>> below there are seven other solutions that may be obtained by
>> interchanging x0,y0 and/or x1,y1 and/or x2,y2.
>>
>> FromDigits/@Partition[#,3]& /@ Select[Permutations@Range@9,
>> #[[1]] < #[[4]] && #[[2]] < #[[5]] && #[[3]] < #[[6]] &&
>> #.{100,10,1,100,10,1,-100,-10,-1} == 0 &]
>>
>> {{124,659,783}, {125,739,864}, {127,359,486},
>> {127,368,495}, {128,439,567}, {134,658,792},
>> {142,596,738}, {142,695,837}, {143,586,729},
>> {152,487,639}, {152,784,936}, {162,387,549},
>> {162,783,945}, {173,286,459}, {173,295,468},
>> {182,394,576}, {182,493,675}, {214,569,783},
>> {214,659,873}, {215,478,693}, {215,748,963},
>> {216,378,594}, {216,738,954}, {218,349,567},
>> {218,439,657}, {234,657,891}, {235,746,981},
>> {241,596,837}, {243,576,819}, {243,675,918},
>> {251,397,648}, {271,593,864}, {271,683,954},
>> {281,394,675}, {314,658,972}, {317,529,846},
>> {317,628,945}, {324,567,891}, {324,657,981},
>> {341,586,927}, {342,576,918}, {352,467,819}}