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Math problem

Math problem :

x1 = 33
x2 = 66
x3 = 2
x4 = 17
x5 = 25
-----------------
x1+x2+x3+x4+x5=x6=143
33+66+2+17+25=143
-----------------
x1*x2*x3*x4*x5=x7=1851300
33*66*2*17*25=1851300
-----------------
x1/x2/x3/x4/x5=x8=5.8823529411764705882352941176471e-4
33/66/2/17/25=5.8823529411764705882352941176471e-4
-----------------

How to know x1, x2, x3 ,x4 ,x5 if we know x6, x7, x8 ?

Thank You.
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ghjlk
Asked:
ghjlk
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1 Solution
 
mikelittlewoodCommented:
I could be wrong, but if you have 5 missing variables, do you not need 5 working solutions to get each value.
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ghjlkAuthor Commented:
Yes. I have to get x1,x2,x3,x4,x5 from x6,x7,x8 results.

Thank You.
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ghjlkAuthor Commented:
Or to use some other results to get x1, x2, x3, x4, x5.

Thank You.
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mikelittlewoodCommented:
I think you misunderstand me.
What I meant to say is, if my old maths is correct, is that you cannot get values for x1, x2, x3, x4, x5 if you only have 3 solutions x6, x7, x8.
You need at least 2 more calculations to make x9 and x10 before you can get x1, x2, x3, x4, x5
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ghjlkAuthor Commented:
Please mikelittlewood, if You can make more calculations x9 and x10, because I don't know how to perform correctly results x6, x7 and x8 to get x1, x2, x3, x4 and x5 values.

Thank You.
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TNameCommented:
My faint memories seem to suggest that Mike is right ;)

Try this brute force approach (put a memo and a button on a form):

procedure TForm1.Button1Click(Sender: TObject);
var
x1,x2,x3,x4,x5:Integer;
SL:TStringList;
c,tc:Integer;
cal:Double;
begin
  SL:=TStringList.Create;
  Memo1.Clear;
  tc:=GetTickCount;
  c:=0;
  cal:=33/66/2/17/25;
  //for x1:=1 to 139 do begin
  x1:=33;     //x1 will always be 33. To test, delete "x1:=33;"
                 // and uncomment  "for x1:=1 to 139 do begin" and the additional
                // "end;"  towards the end (above this line: "Memo1.Lines:=SL;")
   for x2:=1 to 139 do begin
     for x3:=1 to 139 do begin
        for x4:=1 to 139 do begin
          for x5:=1 to 139 do begin
             if ((x1+x2+x3+x4+x5=143)  and
                 (x1*x2*x3*x4*x5=1851300) and
                  ((x1/x2/x3/x4/x5>cal-0.000000000000000001) and //To compensate for rounding errors
                  (x1/x2/x3/x4/x5<cal+0.000000000000000001)))then begin

                  SL.Add('x1='+IntToStr(x1)+', '+
                         'x2='+IntToStr(x2)+', '+
                         'x3='+IntToStr(x3)+', '+
                         'x4='+IntToStr(x4)+', '+
                         'x5='+IntToStr(x5));
             end;
             c:=c+1;
          end;
        end;
        Application.ProcessMessages;
      end;
    end;
  //end;
  Memo1.Lines:=SL;
  Memo1.Lines.Add('Milliseconds: '+IntToStr(GetTickCount-tc));
  Memo1.Lines.Add('Loops: '+IntToStr(c));
  beep;
end;
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TNameCommented:
ghjlk,
this is the list of possible solutions I get when I run the above code:

x1=33, x2=2, x3=17, x4=25, x5=66
x1=33, x2=2, x3=17, x4=66, x5=25
x1=33, x2=2, x3=25, x4=17, x5=66
x1=33, x2=2, x3=25, x4=66, x5=17
x1=33, x2=2, x3=66, x4=17, x5=25
x1=33, x2=2, x3=66, x4=25, x5=17
x1=33, x2=5, x3=5, x4=34, x5=66
x1=33, x2=5, x3=5, x4=66, x5=34
x1=33, x2=5, x3=34, x4=5, x5=66
x1=33, x2=5, x3=34, x4=66, x5=5
x1=33, x2=5, x3=66, x4=5, x5=34
x1=33, x2=5, x3=66, x4=34, x5=5
x1=33, x2=17, x3=2, x4=25, x5=66
x1=33, x2=17, x3=2, x4=66, x5=25
x1=33, x2=17, x3=25, x4=2, x5=66
x1=33, x2=17, x3=25, x4=66, x5=2
x1=33, x2=17, x3=66, x4=2, x5=25
x1=33, x2=17, x3=66, x4=25, x5=2
x1=33, x2=25, x3=2, x4=17, x5=66
x1=33, x2=25, x3=2, x4=66, x5=17
x1=33, x2=25, x3=17, x4=2, x5=66
x1=33, x2=25, x3=17, x4=66, x5=2
x1=33, x2=25, x3=66, x4=2, x5=17
x1=33, x2=25, x3=66, x4=17, x5=2
x1=33, x2=34, x3=5, x4=5, x5=66
x1=33, x2=34, x3=5, x4=66, x5=5
x1=33, x2=34, x3=66, x4=5, x5=5
x1=33, x2=66, x3=2, x4=17, x5=25
x1=33, x2=66, x3=2, x4=25, x5=17
x1=33, x2=66, x3=5, x4=5, x5=34
x1=33, x2=66, x3=5, x4=34, x5=5
x1=33, x2=66, x3=17, x4=2, x5=25
x1=33, x2=66, x3=17, x4=25, x5=2
x1=33, x2=66, x3=25, x4=2, x5=17
x1=33, x2=66, x3=25, x4=17, x5=2
x1=33, x2=66, x3=34, x4=5, x5=5

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