program Statistics_Module_4;
//**************************************************
//all 4 examples discuss a combination lock (Zahlenschloss)
//loc's = 198, ex. 212_ , adapt from _92
//...we discuss the 4 types of stat with a combination lock (zahlenschloss):

{1. Permutation = n!
 2. Permutation(Variation without repeating) = nPr = n!/(n-k)!
 3. Combination (binominal coefficient)= nCr = nPr / k!
 4. Variation(repeating) = n^k

where,
      n,k are non negative integers and k<=n.
      k is the size of each permutation.
      n is the size of a set from which elements are permuted.
      ! is the factorial operator.
  
1 Anordnungen (Permutationen)
2 Auswählen mit Beachtung der Reihenfolge (Variationen)
    * 2.1 Variation ohne Zurücklegen
    * 4.1 Variation mit Zurücklegen
3 Auswählen ohne Beachtung der Reihenfolge (Kombinationen)

------------------------------------------------------------------------------
{1. ex. lock of 4 numbers [0..3] permuatation, ex. [0123], 4! = 24 results 
 2. ex. 4 lock with 10 numbers [0..9] permutation, ex. [3579],  
                                                    nPr(10,4) = 5040 results  
 3. ex. 21 lock with 4 possibilities, ex. [000010000100010100000]
                                                    nCr(20,4) = 4845 results
 4. ex. 4 lock with 10 numbers (norm case), ex. [1122], 10^4  = 10000 results
 -----------------------------------------------------------------------------}      

const 
  DIM = 660;
  PI2 = 6.28318530717958647692528676655901;
  E = 2.718281828459;
  SEP = '----------------------------------------------------';
  BODY = 23;
  EMOTION = 28;
  SPIRIT = 33;
 
type TBIOVector = array[0..DIM] of TPoint; 
     Tperm = array[1..4] of byte;
     TCube = array[1..6] of byte;

var
   hnd: THandle;
   mname, mdes: string;
   mfilel: TStringList;
   st_string: shortstring;
   time1, time2, diff: TDateTime;

// 1. Permutation n!
//--------------------------------------------------------------
Procedure One_Permutation_4;
var
  i,k,l,m: byte;
  count: integer;
begin
 count:= 0;
 for i:= 0 to 3 do 
   for k:= 0 to 3 do 
     for l:= 0 to 3 do 
       for m:= 0 to 3 do begin
         if (i<>k) and (i<>l) and (i<>m) and (k<>l) and (k<>m) and (l<>m)   
         then begin
           inc(count);
           Writeln(Format('Case: %d - %d%d%d%d',[count,i,k,l,m]))
           //inc(i); inc(k);
         end;
       end;
  Writeln(IntToStr(count)+' Permutations')
  Writeln('All Permutations of 0..3: '+intToStr(round(Fact(4))))
  Writeln(SEP)
end;


// 2. Permutation(Variation without repeating) = nPr = n!/(n-k)!
//--------------------------------------------------------------
Procedure Two_Permutation_4_of_10;
var
  i,k,l,m: byte;
  count: integer;
begin
 count:= 0;
 for i:= 0 to 9 do 
   for k:= 0 to 9 do 
     for l:= 0 to 9 do 
       for m:= 0 to 9 do begin
         if (i<>k) and (i<>l) and (i<>m) and (k<>l) and (k<>m) and (l<>m)   
         then begin
           inc(count);
           Writeln(Format('Case: %d - %d%d%d%d',[count,i,k,l,m]))
           //inc(i); inc(k);
         end;
       end;
  Writeln(intToStr(count)+' Permutations')
  Writeln('All Permutations 4 of 10: '+intToStr(round(Fact(10)/Fact(10-4))))
  Writeln(SEP)
end;


// 3. Combination (binominal coefficient)= nCr = nPr / k!
//-------------------------------------------------------
procedure Three_Combination_without_Order_4_of_20;
//binominal coefficient)= nCr = nPr / k!
//4 of 20 = 4845 = NCR(20,4) on a calculator or a lotto 4 of 20
var  
  i,k,l,m,n,o,p,q,r,s,t,u,v,w,q1,r1,s1,t1,u1,v1: byte;
  count: integer;
begin
  i:=1; k:=1; l:=1; m:=1; n:=1; o:= 1; p:=1;
  q:=1; r:=1; s:=1; t:=1; u:=1; v:= 1; w:=1;
  q1:=1; r1:=1; s1:=1; t1:=1; u1:=1; v1:= 1; 
  count:= 0;
  for i:= 0 to 1 do 
    for k:= 0 to 1 do 
      for l:= 0 to 1 do 
        for m:= 0 to 1 do 
          for n:= 0 to 1 do 
            for o:= 0 to 1 do 
              for p:= 0 to 1 do 
              for q:= 0 to 1 do 
              for r:= 0 to 1 do 
              for s:= 0 to 1 do 
              for t:= 0 to 1 do 
              for u:= 0 to 1 do 
              for v:= 0 to 1 do 
              for w:= 0 to 1 do 
              for q1:= 0 to 1 do 
              for r1:= 0 to 1 do 
              for s1:= 0 to 1 do 
              for t1:= 0 to 1 do 
              for u1:= 0 to 1 do 
              for v1:= 0 to 1 do 
  if i+k+l+m+n+o+p+q+r+s+t+u+v+w+q1+r1+s1+t1+u1+v1 = 4 then begin 
    inc(count);
    Writeln(Format('Case: %d - %d%d%d%d%d%d%d%d%d%d%d%d%d%d%d%d%d%d%d%d',
            [count,i,k,l,m,n,o,p,q,r,s,t,u,v,w,q1,r1,s1,t1,u1,v1]));                 
  end;  
  Writeln(inttostr(count)+' All combinations in a Set')
  Writeln(SEP)
end;


// 4. Variation (repeating) = n^k
//------------------------------------
procedure Four_Variation_Lock_4;
//solution is n^k  = 10^4 = 10000
var  
  i,k,l,m: byte;
  count: integer;
begin
  i:=1; k:=1; l:=1; m:=1;
  count:= 0;
  for i:= 0 to 9 do 
    for k:= 0 to 9 do 
      for l:= 0 to 9 do 
        for m:= 0 to 9 do begin
          inc(count);        
          writeln(Format('Case: %d - %d%d%d%d',[count, i,k,l,m]))
        end;  
  Writeln(inttostr(count)+' All Variations of a Lock')
  Writeln(SEP)
end;


// main calc & plot
begin
  //Sudoku_permutation_1;
  maxForm1.ShellStyle1Click(self);
  st_String:= 'STATISTIC MODULE 4';
  Writeln(st_String)
  time1:= time;
  
  //Showmessage(' First a 4 of 4 permutation')
    One_Permutation_4;
  //Showmessage(' Second a 4 of 10 permutation')
    Two_Permutation_4_of_10;
  //Showmessage(' Third a 20 of 4 combination')
    Three_Combination_without_Order_4_of_20;
  //Showmessage(' Fourth a 4 of 10 variation')
    Four_Variation_Lock_4;
  
  time2:= time;
  Diff:= time2 - time1; 
  writeln(FormatDateTime('" Statistic Module run time is:" nn:ss:zzz',Diff));
  Writeln(st_String)
  //maxForm1.SaveOutput1Click(self);
  writeln('maXbox V: '+GetVersionString('maxbox3.exe'))
  //hnd:= ExecuteFile('maxbox3.exe','',ExePath,1)
  //writeln(inttostr(hnd))
  getAssociatedProgram('.pdf',mname, mdes)
  writeln(mname + mdes)
  mfilel:= TStringlist.create;
  //FilesFromWildcard(Exepath, '21*.txt',mfilel, true, true, true)
  //Writeln(mfilel.text)
  mfilel.Free;
end.

just maXbox
         ____    ___   _      ____    _   _   _
        |  _ \  |  _| | |    |  _ \  | | | | | |
        | | . | | |_  | |    | |_| | | |_| | | |
        | | | | |  _| | |    |  __/  |  _  | | |          
        | |_. | | |_  | |__  | |     | | | | | |                      
        |____/  |___| |____| |_|     |_| |_| |_|