``````
unit U_SquaresCubes5;
{Whew!  This could be a tough one.  }
{Find two  integers with the following properties:
The square of the first equals the cube of the
second and together they contain all of the
digits 0 to 9 exactly once.}
{Since there are 10 digits in the results, there
must be 4 in the nbr to be cubed and 6 in the  nbr
to be squared.  4 digit numbers range from 10^3 to 10^4
so cubes values wil range from 10^9 to 10^12, 10 to 13
digits.  6 digit numbers(10^5 to 10^6) squared will
range from 11 to 13 digits
Nbr digits  Min Val  Max val  Cubed       Nbr Digits
Min   Max   Min Max
3        10^2     10^3     10^6  10^9    7  10
4        10^3     10^4     10^9  10^12  10  13
5        10^4     10^5     10^12 10^15  13  16

Squared    Nbr Digits
Min Max     Min  Max
5        10^4     10^5     10^8  10^10  9   11
6        10^5     10^6     10^10 10^12 11   13
7        10^6     10^7     10^12 10^14 13   15
}

interface

uses
Windows, Messages, SysUtils, Classes, Graphics, Controls, Forms, Dialogs,
StdCtrls;

type
TForm1 = class(TForm)
SolveBtn: TButton;
Memo1: TMemo;
procedure SolveBtnClick(Sender: TObject);
private
{ Private declarations }
public
{ Public declarations }
end;

var
Form1: TForm1;

implementation

{\$R *.DFM}

Uses Combo, math;

type
TDigits=array[0..9] of char;
var
chars:TDigits=('0','1','2','3','4','5','6','7','8','9');

procedure TForm1.SolveBtnClick(Sender: TObject);
var
n,n2,n3:int64;
solved:boolean;
i:int64 ;
j:integer;
combo:TComboset;
s:string;
c:string;
begin
{Find 2 numbers m and n such that m^2 = n^3 and together m and n
contain all of 10 digits 0..9.}
combo:=TComboset.create;
i:=1233;   {start at smallest 4 digit # with 4 different digits}
screen.cursor:=crHourGlass;
solved:=false;
{stop at match with 4 different digits}
while (i < 9876) and (not solved) and (tag=0) do
begin
inc(i);
{check to see if i has 4 different digits}
s:=inttostr(i);
c:='0123456789';
{make an array of the unused digits}
for j:= 1 to length(s) do c[ord(s[j])-ord(pred('0'))]:='_';
{delete used numbers - from back to front to preserve valid indexing}
for j:= 10 downto 1 do if c[j]='_' then delete(c,j,1);
if length(c)=6 then {we deleted 4 different digits, keep checking}
begin
n3:=i*i*i;
{init combo to get all 6 of 6 permutations}
combo.init(6,6,false{uniqueflag false= get permutations});
while combo.getnext do
begin
n:=0;
for j:=1 to 6 do n:=n*10+ord(c[combo.selected[j]])-ord('0');
n2:=n*n;
if n2=n3 then
begin
showmessage (format('Found!  %4.0n squared = %6.0n cubed = %10.0n',
[0.0+n, 0.0+i, 0.0+n2]));
{note: adding 0.0 above forces conversion to floating pt for formatting}
solved:=true;
break;
end
{since we generate values in order, if n2 gets
too big, we can stop checking}
else if n2>n3 then break;
end;
end;
end;
screen.cursor:=crDefault;
end;

end.

``````