TweetFollow Us on Twitter

The Eight Queens Problem

Volume Number: 13 (1997)
Issue Number: 12
Column Tag: Programming Techniques

Solving The Eight Queens Problem

by F.C. Kuechmann

Using the graphics of a Macintosh to explore the recursion and backtracking-based solution to this common puzzle

One of the oldest and most familiar intellectual puzzles whose solution is uniquely suited to the computer is the eight queens problem, in which the goal is to systematically determine each of the 92 different ways eight queens can be placed on a chessboard without conflict. Of the 92 solutions, 12 [numbers 1, 2, 5, 6, 7, 8, 9, 10, 11, 14, 17 and 18] are unique; the remaining 80 are variations on the twelve -- mirror images on the vertical, horizontal or diagonal axes, or 90, 180 or 270 degree rotations.

Since queens can move any number of squares in any direction, each queen must be placed on its own row, column and diagonals. Niklaus Wirth [1976, 1986] describes it as a familiar problem and states that Gauss considered it as early as 1850. No straightforward mathematical formula has ever been devised for its solution. The trial-and-error method, often combined with such problem solving techniques as recursion and backtracking, while tedious and error prone for humans, is well-suited to the computer. (A computer doesn't get bored, make mistakes, or have a cat that jumps onto the chess board.) Each time the active queen is moved to a new position the new location is tested for conflict unless that position is off the board. In that case, we backtrack to the previous column or row, advance that previously secure queen, and proceed. Thus a backtrack involves a move without testing the new position for conflict. 981 queen moves (876 position tests plus 105 backtracks) are required for the first solution alone. 16,704 moves (14,852 tests and 1852 backtracks) are needed to find all 92 solutions. If we continue testing until all possibilities are exhausted, we've made 17,684 moves -- 15,720 tests plus 1964 backtracks. Given those figures, it's easy to see why the solution is best left to computers.

While text-oriented computers can determine the solutions as well as any, a graphically-oriented computer like the Mac is ideally suited for illustrating the underlying algorithm.

The widespread use of the personal computer as a teaching tool has contributed to the appearance of the eight queens problem in several textbooks in the past 20-plus years, including especially Wirth [1976, 1986] and Budd [1987, 1991, 1996]. Niklaus Wirth's solutions are in Pascal and Modula-2. Timothy Budd has discussed object-oriented solutions, in languages ranging from SmallTalk to Object Pascal to Java, in at least three books. Microware furnished a structured BASIC version of Wirth's Pascal solution with their BASIC09 interpreter, which probably received its widest distribution packaged for the Radio Shack Color Computer 2 and 3.

A web search on the phrase "eight queens" will uncover several graphic Java solutions, some interactive, based on a problem posed by Budd [1996]. For some reason with my PowerPC Mac 6500/225 and Quadra 650, Microsoft's Internet Explorer browser works better in displaying the interactive Java versions on the web than does Netscape's Navigator.

WIRTH's Algorithm

The queen conflict tracking mechanism employed by Wirth consists of three Boolean arrays that track queen status for each row and diagonal. TRUE means no queen is on that row or diagonal; FALSE means a queen is already there.

Figure 1 shows the mapping of the arrays to the chess board for Pascal. All array elements are initialized to TRUE. The Row array elements 1-8 correspond to rows 1-8 on the board. A queen in row n sets rows array element n to FALSE.

Column-Row array elements are numbered from -7 to 7 and correspond to the difference between column and row numbers.

A queen at column 1, row 1 sets array element zero to FALSE. A queen at column 1, row 8 sets array element -7 to FALSE.

The Column+Row array elements are numbered 2-16 and correspond to the sum of the column and row. A queen placed in column 1, row 1 sets array element 2 to FALSE. A queen placed in column 3, row 5 sets array element 8 to FALSE.

Figures 2, 3 and 4 show the changes in array element values as 1, 2 and 3 queens are placed on the board.

In Figure 2, Row array element 1, Column-Row array element 0, and Column+Row array element 2 are all set to FALSE.

Figure 2. One conflict queen

Figure 3. Two conflict-free queens.

In Figure 3, Row array element 3, Column-Row array element -1, and Column+Row Array element 5 are set also set FALSE.

Figure 4. Three conflict-free queens.

In Figure 4, Row Array element 5, Column-Row array element -2, and Column+Row array element 8 are added to the FALSE list.

It would require hundreds of pages to show the entire move sequence just for the first solution, which is shown in Figure 5. All 981 moves can be easily visualized by stepping through the program, either in single-step mode or at slow speed, while observing changes in the Boolean array values displayed to the right of the board, as queens are set and removed.

Figure 5. The first solution.

The Trouble With C

In the C language, with its zero-based arrays, the mapping of the arrays to the board is a bit more complicated. Array elements are numbered 0-n and the mapping of board positions to the arrays is compensated accordingly. The Row array elements 0-7 correspond to rows 1-8 on the board. A queen in row n sets Row array element n-1 to FALSE. Column-Row array elements are numbered from 0 to 14 and correspond to the difference between column and row numbers, plus 7. A queen at column 1, row 1 sets array element 7 (1-1+7=7) to FALSE. A queen at column 1, row 8 sets array element 0 (1-8+7=0) to FALSE. The Column+Row array elements are numbered 0-14 and correspond to the sum of the column and row, minus 2. A queen placed in column 1, row 1 sets array element 0 (1+1-2=0) to FALSE. A queen placed in column 3, row 5 sets array element 6 (3+5-2=6) to FALSE.

Many Ways to Tango

Recursive and non-recursive variations of Wirth's method are easy to implement on the Macintosh and other computers in most popular languages, including Pascal, C and structured BASIC. The major code differences between recursive and non-recursive variations are these:

  1. The non-recursive version adds an 8-element integer array to hold the queen row for each column; with recursion this housekeeping is handled by the system.
  2. The recursive program's main procedure uses a single for loop, with backtracking handled by the system, whereas the non-recursive version uses two nested repeat loops and a separate procedure to handle backtracking.

With these exceptions, the code for the two variations is identical.

In Pascal, the main loop of the recursive solution looks like this:

procedure Try(column:integer);
  begin
    for row := 1 to 8 do
      begin
        { code }
        if column < 8 then
          Try(column + 1)  { procedure calls itself }
        else
          PrintSolution;
        { code }
      end;    {for}
  end;

The core of the non-recursive solution:

    repeat
      repeat
        { code }
      until row > 8;
      backtrack;
    until column < 1;

Listing 1. Try Try

This procedure is called with a column value of 1 after initializing the gRowe, gColPlusRow and gColMinusRow Boolean arrays to TRUE. When it finishes, all 92 solutions have been found.

procedure Try (column: integer);
  var
    row: integer;
    rowFlag,plusFlag,minusFlag,: Boolean;
  begin
    for row := 1 to 8 do
      begin
        rowFlag := gRowe[row];
        plusFlag := gColPlusRow[column + row];
        minusFlag := gColMinusRow[column - row];

        if rowFlag and plusFlag and 
                          minusFlag then
          begin
            gSolutionStash[column] := row;
            SetQueen(row, column);
            if column < 8 then
              Try(column + 1)
            else
              PrintSolution;

            RemoveQueen(row, column);
          end;  {if k}
      end;    {for}
  end;    {Try}

Listing 1 shows the complete Try() procedure for a simplified, non-interactive version of the recursive solution. The for loop repeatedly tests the Boolean arrays at indices consisting of the row, sum of row and column, and difference between row and column. The initial row and column values are both 1. If these three Boolean tests are TRUE, a queen is placed in the current column and row positions; if the column value is 8, we have a queen in each column and print the solution. After printing, the queen in column 8 is removed and the row increments at the top of the loop in pursuit of the next solution.

Otherwise when column < 8, the Try() procedure calls itself with an incremented column value and position testing starts anew at row 1. If any of three Boolean array locations are FALSE, the for loop row index increments and the tests repeated. If row exceeds a value of 8 (that is, the active queen drops off the board), execution continues after the Try(column+1) line in the previous iteration of the procedure unless the column value equals 1 when row exceeds 8. (In that case, all solutions have been found and operation passes back to whatever called Try initially.) The queen at the row position for the current column is removed, the row increments at the top of the loop, etc.

Listing 2a. SetQueen

SetQueen

procedure SetQueen (row, column: integer);
  begin
    gRowe[row] := false;
    gColPlusRow[column + row] := false;
    gColMinusRow[column - row] := false;
  end;

Listing 2b. RemoveQueen

RemoveQueen

procedure RemoveQueen (row, column: integer);
  begin
    gRowe[row] := true;
    gColPlusRow[column + row] := true;
    gColMinusRow[column - row] := true;
  end;

Listing 2 shows the SetQueen and RemoveQueen procedures that update the Boolean arrays.

Listing 3a. Try

Try

procedure Try;
  var
    row, column: integer;
    rowFlag,plusFlag,minusFlag: Boolean;
  begin
    row := 1;
    column := 1;
    repeat
      repeat
        rowFlag := gRowe[row];
        plusFlag := gColPlusRow[column + row];
        minusFlag := gColMinusRow[column - row];
        if rowFlag and plusFlag and minusFlag then
          begin
            gSolutionStash[column] := row;
            SetQueen(row, column);
            if column < 8 then
              begin
                gRowForCol[column] := row;
                row := 1;
                Inc(column);
                Leave;
              end
            else
              begin
                PrintSolution;
                RemoveQueen(row, column);
                Inc(row);
              end;
          end
        else
          Inc(row);
      until row > 8;

      if row > 8 then
        BakTrak(row, column);

  until column < 1;
end;    {procedure Try}

Listing 3b. BakTrak

BakTrak

procedure BakTrak (var row, column: integer);
  begin
    repeat
      Dec(column);
      if column > 0 then
        begin
          row := gRowForCol[column];
          RemoveQueen(row, column);
          Inc(row);
        end;
    until (row < 9) or (column < 1);
  end;

Listing 3 gives the Try and BakTrak procedures for a non-recursive solution. The biggest differences from Listing 1 are the two nested repeat loops the global array gRowForCol, which holds the row number of the queen in each column.

These listings generate only the row number for the queen in each column and do not show the event-handling calls or other fancifications needed to implement an interactive program with variable execution speeds, single-step mode, etc. For that, see Listing 4 and the full source code files.

Listing 4. DoColumns

DoColumns

I call this procedure DoColumns instead of Try in order to distinguish it from the corresponding procedure in my "sideways" solution, which is called DoRows.

procedure DoColumns (column: Integer);
  var
    row,n,rotNum,rotSize: integer;
    rowFlag,plusFlag,minusFlag,mirFlag,whiteDiagFlag,
      redDiagFlag,topBotFlipFlag,leftRtFlipFlag,
      rotFlag: boolean;
    elapsedTime,currentTime: longint;
    bn : byte;
  begin
    ggCol   := column;
    for row := 1 to 8 do
      begin
          {update active queen position unless in ultra-fast}
        if not ggUfastFlag then
          begin
            DrawQueen(row, column);
            if not ggVfastFlag then
              UpDateBoolean;
          end;
          
          {test active queen for conflicts}
        rowFlag     := ggRowFlags[row];
        plusFlag   := ggColPlusRow[column + row];
        minusFlag   := ggColMinusRow[Column-Row];
        Inc(ggTests);
        UpdateTestCount;

            { put this here to update boolean display before halting }
            { in step mode -- if no conflict }
        if rowFlag and plusFlag and minusFlag then
          begin
            SetQueen(row, column);
            UpDateBoolean;
          end;

        if not ggUfastFlag then
          gBoardNotClear := true;  
                  {flag used in ultra-fast mode to clear}
                  {board completely 1st solution after}
                  {ultra-fast mode is selected; only   }
                  {those queens that have changed pos-}
                  {ition are erased subsequently  }

        if ggStepModeFlag = true then
          ggStepFlag := true
        else
          ggStepFlag := false;

        if (not ggVfastFlag) and (not ggUfastFlag)
                            and (not ggStepModeFlag) then
              {delay according to speed and mode}
          Stall(ggStallVal);  
          
          {handle events except in very-fast or ultra-fast modes}
        if ((not ggUfastFlag) and (not ggVfastFlag))
                                or ggStepModeFlag then
          begin
            repeat
              HandleEvent;
            until (not ggStepFlag) or ggDoneFlag;
          end;
        if not ggStartClockFlag then
          begin
            ggStartClockFlag := true;
            GetDateTime(ggStartTime);
            if not gRunFlag then
              begin
                GetDateTime(ggStartTotalTime);
                gRunFlag := true;
              end;
          end;

        if rowFlag and plusFlag and minusFlag then
          begin
              {active queen position is ok, so save row}
            ggRowStash[ggSolNum, column] := row;
              {no solution yet; do next column}
            if column < 8 then
              begin
                Inc(column);
                ggCol := column;
                  {procedure calls itself}
                DoColumns(column);

                if not ggUfastFlag then
                  Stall(ggStallVal);
                Dec(column);
                  {ggCol is used in event-triggered board redraws}
                ggCol := column;  

                Inc(ggBakTrak);
                UpDateBakTrax;
                if ggStepModeFlag = true then
                  begin
                    ggStepFlag := true;
                    while ggStepFlag = true do
                      HandleEvent;
                  end
                else if not ggUfastFlag then
                  HandleEvent;

                if column > 0 then
                  begin
                    if not ggUfastFlag then
                      SnuffQueen(row, column);
                    RemoveQueen(row, column);
                  end;
              end
            else
              begin
                {we have a conflict-free queen in each column}
                {In ultra - fast mode we need to update the}
                {board and statistics}

                if ggUfastFlag then
                  begin
                    DoUfastUpdate;
                    UpDateBoolean;
                    UpdateTestCount;
                    UpdateBakTrax;
                    GetDateTime(currentTime);
                    elapsedTime := currentTime - 
                                        ggStartTime;
                    DrawElapsed(elapsedTime);
                  end;
                  
                  {get ready to test for unique solution}
                InitForMirrors(rotFlag, whiteDiagFlag, 
                  redDiagFlag,topBotFlipFlag,leftRtFlipFlag,
                   mirFlag, gMirrorNum);
                    {freeze time counter}
                ggStartClockFlag := false;
                    { no board redraws}     
                ggShowFlag := true;
                TestForMirrors(gMirrorNum,rotNum,rotSize,
                  mirFlag,whiteDiagFlag,redDiagFlag, 
                  topBotFlipFlag, leftRtFlipFlag, rotFlag);
                ggShowFlag := false;
                if (not mirFlag) and (not rotFlag) then
                  begin
                    ggUniqueSols[ggSolNum] := gUniqueSolNum;
                    Inc(gUniqueSolNum);
                  end;

                DrawSolStatus(mirFlag,whiteDiagFlag,
                  redDiagFlag,topBotFlipFlag,leftRtFlipFlag,
                  rotFlag,gMirrorNum,gUniqueSolNum,rotNum,
                  rotSize);

                ggSolFlag := TRUE;    {avoid board redraw}
                if not ggWaitFlag then
                  WaitDelaySecs
                else
                  begin    
                        {wait for run or step button push or quit}
                        {set up and call event handler}
                    ShowControl(ggStepButtonHdl);
                    HiliteControl(ggStepButtonHdl, 0);
                    ShowControl(ggRunButtonHdl);
                    HiliteControl(ggRunButtonHdl, 0);
                    ShowControl(ggStepButtonHdl);
                    HiliteControl(ggStepButtonHdl, 0);
                    SetControlTitle(ggRunButtonHdl, 'Run');
                    ggStepModeFlag := true;
                    ggStepFlag := true;
                    repeat
                      HandleEvent;
                    until (not ggStepModeFlag) or
                          (not ggStepFlag) or ggDoneFlag;

              {STEP button pushed in fast modes plus wait}
              { so drop to medium speed, step mode}
                    if (ggUfastFlag or ggVfastFlag) and
                                  (ggStepModeFlag and
                                  (not ggStepFlag)) then
                      begin
                        ggUfastFlag:= false;
                        ggVfastFlag:= false;
                        ggSpeedMenuHdl:=
                          GetMenuHandle(ggcSPEED_MENU_ID);
                        CheckItem(ggSpeedMenuHdl,
                                  ggOldSpeed,
                                  ggcREMOVE_CHECK_MARK);
                        CheckItem(ggSpeedMenuHdl,
                                  ggcMEDIUM_ITEM,
                                  ggcADD_CHECK_MARK);
                        ggOldSpeed := ggcMEDIUM_ITEM;
                        ggStallVal := gcMedium;
                      end;
                  end;

                    {init the next solution}
                for n := 1 to 8 do
                  begin
                    bn := ggRowStash[ggSolNum, n];
                    ggRowStash[ggSolNum + 1, n] := bn;
                  end;

                if not ggUfastFlag then
                  SnuffQueen(row, column);
                Inc(ggSolNum);
                DrawSolNum;
                GetDateTime(ggStartTime);
                ggStartClockFlag := true;  {start the clock}
                elapsedTime := 0;
                DrawElapsed(elapsedTime);
                RemoveQueen(row, column);
                EraseSolStat;
                gTotalTests:=gTotalTests+ggTests;
                gTotalMoves:=gTotalMoves+ggTests+ggBakTrak;
                gTotalTestsSol:=gTotalTestsSol+ggTests;
                gMovesForSol:=gMovesForSol+ggBakTrak+
                                        ggTests;
                EraseTestCount;
                ggTests := 0;
                UpdateTestCount;
                EraseBakTrax;
                ggBakTrak := 0;
                UpDateBakTrax;
                EraseTime;
                  {allow board redraws}
                ggSolFlag := FALSE;  
              end;
          end
        else
          begin
            if not ggUfastFlag then
              SnuffQueen(row, Column);
          end;

        if ggDoneFlag then
          Leave;
      end; {for}

  end;    {procedure DoColumns}

Listing 4 shows the recursive version of the Eight Queens program's main loop all dressed up for the event-driven Macintosh party with speed and mode variations.

Running the Program

The Macintosh programs EightQueens I and EightQueens II have two operating modes -- run and single-step. At startup, the chessboard is drawn and a startup window is displayed for 30 seconds or until the Go button is pushed. To the right of the chess board is an area giving the following information:

  • The time to achieve each solution.
  • The solution number 1-92.
  • The solution status -- unique or variation on a prior solution.
  • The number of position tests required to achieve each solution.
  • The number of backtracks.
  • The values of the elements of the Row or Column, Column plus Row, and Column minus Row Boolean arrays used to determine the conflict status of the queens.

All but the 2nd and 3rd are updated continuously as each solution progresses.

At bottom right are the Run and Step buttons. In single-step mode, pushing the Step button single-steps the currently-active queen. Pushing the Run button causes. Push the Step button to re-select single-step mode.

The program operates initially in single-step mode in which the active queen steps when the Step button is pressed. If the Run button is pressed, run mode is entered; the Step button disappears, the Run button is re-labeled Step, and the active queen steps continuously until a solution is achieved. It then delays (default delay is 10 seconds) before stepping to the next solution unless Wait is selected from the Delay menu. Both the step rate and the duration of the delay can be varied via the Speed and Delay menu. Speeds vary from about 1 step per second at the slow end to hundreds per second. Default speed is about 4 steps per second on a PowerPC Mac 6500/225. The delay between solutions can be varied from none to 30 seconds in 5-second increments, or Wait can be selected and the program will enter single-step mode after each solution. The Step button changes to Next, and the program waits for a click on the Run or Next button.

To determine whether a solution is unique or a variation on one of the twelve unique solutions, the program creates seven variations of each solution to compare with the previous ones. The variations are -- left-to-right flip (vertical axis mirror), top-to-bottom flip (horizontal axis mirror), upper-left-to-lower-right (red) diagonal mirror, lower-left-to-upper-right(white) diagonal mirror, and 90 degree, 180 degree and 270 degree clockwise rotations. To view these in sequence, click the Next button. The variations will continue to be displayed in sequence as long as the Next button is clicked.

If you click the Run button, the Next button is re-labeled Step, and the solution status line tells whether the solution is unique or variant. When the status line says, for example, at solution #12, Rotate 90 deg CW #10, it means "rotating solution #12 90 degrees clockwise gets solution #10"; at solution #21 "Left-Right Flip #11" means that, if solution #21 is flipped left-to-right, we get solution #11. At #13 , "Red diag mir #8" means that if solution #13 is flipped on the red (upper-left-to-lower-right) diagonal axis, we get solution #8. Solution #16 is a white (lower-left-to-upper-right) diagonal axis mirror of solution #8. Solution #75 is a top-to-bottom flip of #18, etc.

Clicking the Run button again steps the active queen continuously at the previous speed to the next solution, while clicking Step single-steps the active queen and sets the speed to Medium. When the program ceases pursuing solutions either because all possibilities have been exhausted or because Quit has been selected from the File menu (or Command-Q from the keyboard), the area to the right of the board clears and displays statistics on the number of solutions achieved, number of position tests and backtracks, etc. The right button appears, labeled Stop, while the left button is labeled Run. The user can then choose to either resume seeking solutions starting at the beginning by clicking Run, or terminate operation by clicking Stop.

Sourcecode

Sourcecode for two variations of Wirth's algorithm for solving the eight queens problem is supplied for CodeWarrior Professional Pascal. Those readers familiar with Dave Mark's books may notice some resemblances between the eight queens sourcecode and some of that found in Dave's books -- things like some of the names of constants and general structure of the event loop. The resemblance isn't accidental. I used the Timer project from the Macintosh Pascal Programming Primer, Vol. 1, by Dave Mark and Cartwright Reed, as a "skeleton" for EightQueens. While most of the code is mine, underneath there's still a bit of Mark and Reed code holding things together.

Variations

Wirth's recursive algorithm used in EightQueens I indexes rows in the single for loop and columns via recursion, but the method works equally well if the rows and columns are switched. The movement of the queens is then from left-to-right, starting at the top row. We get the same 92 solutions, but in a different order. The first solution with horizontal queen movement is the same as the fourth with vertical movement. Each solution, however, takes the same number of tests and backtracks as with Wirth's algorithm -- 876 tests and 105 backtracks for the first solution, 264 tests and 33 backtracks for the second, 200 tests and 25 backtracks for the third, etc. The reason becomes obvious if you think about it. Take the board set for vertical queen movement, with a single queen upper left. Flip the board on the vertical axis so the queen is in the upper right corner, then rotate it 90 degrees counter-clockwise to put the queen upper left. Start successive queens in column one, incrementing left-to-right. Test queens have exactly the same positions relative to the first queen as in Wirth's original approach. EightQueens II shows this "sideways" approach implemented non-recursively using two nested repeat loops.

Bibliography and References

  • Wirth, Niklaus, Algorithms + Data Structures = Programs, (Englewood Cliffs NJ: Prentice-Hall, 1976).
  • Wirth, Niklaus, Algorithm s and Data Structures, (Englewood Cliffs NJ: Prentice-Hall, 1986)
  • Budd, Timothy, A Little Smalltalk, (Reading, MA: Addison-Wesley, 1987).
  • Budd, Timothy, An Introduction to Object-Oriented Programming, (Reading, MA: Addison-Wesley, 1991).
  • Budd, Timothy, An Introduction to Object-Oriented Programming, 2nd Edition, (Reading, MA: Addison-Wesley, 1996).

F.C. Kuechmann, fk@aone.com, is a hardware designer, programmer and consultant with degrees from the University of Illinois at Chicago and Clark College who is currently building a programmers' clock that gives the time in hexadecimal.

 
AAPL
$99.76
Apple Inc.
+2.09
MSFT
$44.08
Microsoft Corpora
+0.45
GOOG
$520.84
Google Inc.
+9.67

MacTech Search:
Community Search:

Software Updates via MacUpdate

Macgo Blu-ray Player 2.10.9.1750 - Blu-r...
Macgo Mac Blu-ray Player can bring you the most unforgettable Blu-ray experience on your Mac. Overview Macgo Mac Blu-ray Player can satisfy just about every need you could possibly have in a Blu-ray... Read more
Apple iOS 8.1 - The latest version of Ap...
The latest version of iOS can be downloaded through iTunes. Apple iOS 8 comes with big updates to apps you use every day, like Messages and Photos. A whole new way to share content with your family.... Read more
TechTool Pro 7.0.5 - Hard drive and syst...
TechTool Pro is now 7, and this is the most advanced version of the acclaimed Macintosh troubleshooting utility created in its 20-year history. Micromat has redeveloped TechTool Pro 7 to be fully 64... Read more
PDFKey Pro 4.0.2 - Edit and print passwo...
PDFKey Pro can unlock PDF documents protected for printing and copying when you've forgotten your password. It can now also protect your PDF files with a password to prevent unauthorized access and/... Read more
Yasu 2.9.1 - System maintenance app; per...
Yasu was originally created with System Administrators who service large groups of workstations in mind, Yasu (Yet Another System Utility) was made to do a specific group of maintenance tasks... Read more
Hazel 3.3 - Create rules for organizing...
Hazel is your personal housekeeper, organizing and cleaning folders based on rules you define. Hazel can also manage your trash and uninstall your applications. Organize your files using a... Read more
Autopano Giga 3.7 - Stitch multiple imag...
Autopano Giga allows you to stitch 2, 20, or 2,000 images. Version 3.0 integrates impressive new features that will definitely make you adopt Autopano Pro or Autopano Giga: Choose between 9... Read more
MenuMeters 1.8 - CPU, memory, disk, and...
MenuMeters is a set of CPU, memory, disk, and network monitoring tools for Mac OS X. Although there are numerous other programs which do the same thing, none had quite the feature set I was looking... Read more
Coda 2.5 - One-window Web development su...
Coda is a powerful Web editor that puts everything in one place. An editor. Terminal. CSS. Files. With Coda 2, we went beyond expectations. With loads of new, much-requested features, a few... Read more
Arq 4.6.1 - Online backup to Google Driv...
Arq is super-easy online backup for the Mac. Back up to your own Google Drive storage (15GB free storage), your own Amazon Glacier ($.01/GB per month storage) or S3, or any SFTP server. Arq backs up... Read more

Latest Forum Discussions

See All

This Week at 148Apps: October 13-17, 201...
Expert App Reviewers   So little time and so very many apps. What’s a poor iPhone/iPad lover to do? Fortunately, 148Apps is here to give you the rundown on the latest and greatest releases. And we even have a tremendous back catalog of reviews; just... | Read more »
Angry Birds Transformers Review
Angry Birds Transformers Review By Jennifer Allen on October 20th, 2014 Our Rating: :: TRANSFORMED BIRDSUniversal App - Designed for iPhone and iPad Transformed in a way you wouldn’t expect, Angry Birds Transformers is a quite... | Read more »
GAMEVIL Announces the Upcoming Launch of...
GAMEVIL Announces the Upcoming Launch of Mark of the Dragon Posted by Jessica Fisher on October 20th, 2014 [ permalink ] Mark of the Dragon, by GAMEVIL, put | Read more »
Interview With the Angry Birds Transform...
Angry Birds Transformers recently transformed and rolled out worldwide. This run-and-gun title is a hit with young Transformers fans, but the ample references to classic Transformers fandom has also earned it a place in the hearts of long-time... | Read more »
Find Free Food on Campus with Ypay
Find Free Food on Campus with Ypay Posted by Jessica Fisher on October 20th, 2014 [ permalink ] iPhone App - Designed for the iPhone, compatible with the iPad | Read more »
Strung Along Review
Strung Along Review By Jordan Minor on October 20th, 2014 Our Rating: :: GOT NO STRINGSUniversal App - Designed for iPhone and iPad A cool gimmick and a great art style keep Strung Along from completely falling apart.   | Read more »
P2P file transferring app Send Anywhere...
File sharing services like Dropbox have security issues. Email attachments can be problematic when it comes to sharing large files. USB dongles don’t fit into your phone. Send Anywhere, a peer-to-peer file transferring application, solves all of... | Read more »
Zero Age Review
Zero Age Review By Jordan Minor on October 20th, 2014 Our Rating: :: MORE THAN ZEROiPad Only App - Designed for the iPad With its mind-bending puzzles and spellbinding visuals, Zero Age has it all.   | Read more »
Hay Ewe Review
Hay Ewe Review By Campbell Bird on October 20th, 2014 Our Rating: :: SAVE YOUR SHEEPLEUniversal App - Designed for iPhone and iPad Pave the way for your flock in this line drawing puzzle game from the creators of Worms.   | Read more »
My Very Hungry Caterpillar (Education)
My Very Hungry Caterpillar 1.0.0 Device: iOS Universal Category: Education Price: $3.99, Version: 1.0.0 (iTunes) Description: Care for your very own Very Hungry Caterpillar! My Very Hungry Caterpillar will captivate you as he crawls... | Read more »

Price Scanner via MacPrices.net

2013 15-inch 2.0GHz Retina MacBook Pro availa...
B&H Photo has leftover previous-generation 15″ 2.0GHz Retina MacBook Pros now available for $1599 including free shipping plus NY sales tax only. Their price is $400 off original MSRP. B&H... Read more
Updated iPad Prices
We’ve updated our iPad Air Price Tracker and our iPad mini Price Tracker with the latest information on prices and availability from Apple and other resellers, including the new iPad Air 2 and the... Read more
Apple Pay Available to Millions of Visa Cardh...
Visa Inc. brings secure, convenient payments to iPad Air 2 and iPad mini 3as well as iPhone 6 and 6 Plus. Starting October 20th, eligible Visa cardholders in the U.S. will be able to use Apple Pay,... Read more
Textkraft Pocket – the missing TextEdit for i...
infovole GmbH has announced the release and immediate availability of Textkraft Pocket 1.0, a professional text editor and note taking app for Apple’s iPhone. In March 2014 rumors were all about... Read more
C Spire to offer iPad Air 2 and iPad mini 3,...
C Spire on Friday announced that it will offer iPad Air 2 and iPad mini 3, both with Wi-Fi + Cellular, on its 4G+ LTE network in the coming weeks. C Spire will offer the new iPads with a range of... Read more
Belkin Announces Full Line of Keyboards and C...
Belkin International has unveiled a new lineup of keyboard cases and accessories for Apple’s newest iPads, featuring three QODE keyboards and a collection of thin, lightweight folios for both the... Read more
Verizon offers new iPad Air 2 preorders for $...
Verizon Wireless is accepting preorders for the new iPad Air 2, cellular models, for $100 off MSRP with a 2-year service agreement: - 16GB iPad Air 2 WiFi + Cellular: $529.99 - 64GB iPad Air 2 WiFi... Read more
Price drops on refurbished Mac minis, now ava...
The Apple Store has dropped prices on Apple Certified Refurbished previous-generation Mac minis, with models now available starting at $419. Apple’s one-year warranty is included with each mini, and... Read more
Apple refurbished 2014 MacBook Airs available...
The Apple Store has Apple Certified Refurbished 2014 MacBook Airs available for up to $180 off the cost of new models. An Apple one-year warranty is included with each MacBook, and shipping is free.... Read more
Refurbished 2013 MacBook Pros available for u...
The Apple Store has Apple Certified Refurbished 13″ and 15″ MacBook Pros available starting at $929. Apple’s one-year warranty is standard, and shipping is free: - 13″ 2.5GHz MacBook Pros (4GB RAM/... Read more

Jobs Board

*Apple* Retail - Multiple Positions (US) - A...
Job Description: Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, Read more
Position Opening at *Apple* - Apple (United...
…customers purchase our products, you're the one who helps them get more out of their new Apple technology. Your day in the Apple Store is filled with a range of Read more
Position Opening at *Apple* - Apple (United...
**Job Summary** At the Apple Store, you connect business professionals and entrepreneurs with the tools they need in order to put Apple solutions to work in their Read more
Position Opening at *Apple* - Apple (United...
**Job Summary** The Apple Store is a retail environment like no other - uniquely focused on delivering amazing customer experiences. As an Expert, you introduce people Read more
Position Opening at *Apple* - Apple (United...
**Job Summary** As businesses discover the power of Apple computers and mobile devices, it's your job - as a Solutions Engineer - to show them how to introduce these Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.