unit Unit1;

{$mode objfpc}{$H+}

interface

uses
  Classes, SysUtils, FileUtil, Forms, Controls, Graphics, Dialogs, StdCtrls;

type

  { TForm1 }

  TForm1 = class(TForm)
      Memo1 : TMemo;
  private
    { private declarations }
  public
    { public declarations }
  end;

var
  Form1 : TForm1;

implementation

{$R *.lfm}

const
    A = 3;
    B = 3;
    N = 7;

var
    Checkboard : array [1..A] of array [1..B] of Integer;
    Visited: array [1..A] of array [1..B] of Boolean;
    X, Y, Sum, Count : Integer;

function IsNeighbour(X1, Y1, X2, Y2 : Integer) : Boolean;
begin
    Result := False;
    // valid index
    if (X2 >= 1) and (X2 <= A) and (Y2 >= 1) and (Y2 <= B) then
    begin
        // to left
        if (X1 - X2 = -1) and (Y1 = Y2) then
            Result := True
        // to right
        else if (X1 - X2 = 1) and (Y1 = Y2) then
            Result := True
        // to down
        else if (X1 = X2) and (Y1 - Y2 = -1) then
            Result := True
        // to up
        else if (X1 = X2) and (Y1 - Y2 = 1) then
            Result := True;
    end;
end;

procedure Backtracking(X1, Y1, X2, Y2 : Integer);
var
    X, Y : Integer;
begin
    Visited[X1][Y1] := True;

    if (X1 = X2) and (Y1 = Y2) then
    begin
        if Sum = N then
        begin
          Inc(Count);
        end;
    end
    else
    for X := Low(Checkboard) to High(Checkboard) do
        for Y := Low(Checkboard[X]) to High(Checkboard[X]) do
            if (Visited[X][Y] = False) and IsNeighbour(X1,Y1,X,Y) then
            begin
                Form1.Memo1.Append('[' + IntToStr(X) + ',' + IntToStr(Y) + ']');
                Inc(Sum, Checkboard[X][Y]);
         //       Sleep(100);

                if Sum <= N then
                  Backtracking(X, Y, X2, Y2);

                Dec(Sum, Checkboard[X][Y]);
            end;

    Visited[X1][Y1] := False;
end;

begin
    Sum := 0;
    Count := 0;

    // Fill arrays
    for X := Low(Checkboard) to High(Checkboard) do
        for Y := Low(Checkboard[X]) to High(Checkboard[X]) do
            Checkboard[X][Y] := Random(N div 2);
    for X := Low(Visited) to High(Visited) do
        for Y := Low(Visited[X]) to High(Visited[X]) do
            Visited[X][Y] := False;

    // Start backtrack
    Backtracking(1, 1, A, B);
end.