by Thomas Westbom

Reviewed by William T. Pelletier
Author of The Logic Problems Page
August 1998

X-Sums 98 by Thomas Westbom is a superb computer implementation of the popular CrossSum puzzles which appear in many puzzle magazines. X-Sums 98 has a number of solving aids which make it easier, more fun, and less messy to solve CrossSum puzzles on the computer than on paper, and it can generate an inexhaustible supply of puzzles of many different sizes at 3 difficulty levels. A typical screen-print of the game window for an 8x10 puzzle is at the right.

X-Sums 98 runs on Windows 95 & 98 and on Windows NT 4.0.

A CrossSum puzzle is similar to a Crossword puzzle except that the squares are filled with numbers instead of letters. Each "number-word" is a series of digits that sum to a given number in a black square above or below a diagonal. A number above a diagonal is the sum of digits to the right (Across). A number below a diagonal is the sum of digits directly below (Down). Only the digits 1 through 9 may be used, and each "number-word" cannot contain a digit more than once. The objective is to figure out the correct digits for the Across and Down entries.

CrossSum is a popular type of numerical puzzle which appears by various names in a number of puzzle magazines. Only simple arithmetic and logic are needed to enjoy solving these puzzles.

X-Sums 98 Features

I have enjoyed doing CrossSum puzzles for some time and was delighted recently to learn of a computerized version of the game. Tom Westbom's X-Sums 98 is at least several cuts above the average shareware program tossed onto the Web, and I am very impressed with it. It reflects the mark of one who himself enjoys solving CrossSums, and as a result it has a number of convenient solving-aids:
  1. Numbers can be entered with the keyboard or by clicking the mouse in the appropriate "square-ninth" of a cell.
  2. One can enter small "tentative guesses" in any of the 4 corners and then easily convert them to the main large cell entry.
  3. Entries can be erased and redone.
  4. There are toolbar buttons which can be used for help if one gets stuck.
    Click the Error button "E" to highlight in RED any incorrectly entered digits.
    Click Correction button "C" to correct and highlight in MAGENTA any incorrectly entered digits.
    Click the Hint button "H" to display in BLUE the correct digit for any single cell or click the clue sum to display all the digits of "number-word".
    Click the Solution button "S" to display the entire solution to the puzzle in GREEN.
    These buttons are a big help which are not available with paper puzzles.
  5. The puzzles can be printed in color or black and white for normal solving on a piece of paper.
  6. Of course any puzzle can be saved in any state and reopened to work on later.

One beauty of X-Sums98 is that one can generate practically any desired grid size from 8x10 to 50x50 simply by changing the size of the game window by dragging the border with the mouse. The popular commercial sizes of 14x14, 18x24, and 24x18 are unavailable, but the program will generate puzzles of all other sizes. The grid size of a particular puzzle is conveniently displayed in the status bar at the bottom right. The size of one's monitor is probably the most relevant factor determining the maximum size of puzzle one can generate. The larger the puzzle, however, the longer it takes to generate. My personal favorite sizes are 16x16 and 24x20. The latter is because that is the largest size that conveniently fits on a clipboard for solving when I'm away from the computer.

In addition to varying the grid size from small to large puzzles by dragging the game window, one can also zoom (scale) a specific puzzle to change the individual cell size. It is very nice to be able to scale down a large puzzle to fit on a small monitor. For children it is helpful to scale up a puzzle to make the cells larger. Children sometimes are not too coordinated in the use of a mouse, so larger cells make it easier for them to use the number pad feature for entering digits. Four display options or zoom levels are available on the Options menu: Zoom Small, Zoom Normal, Zoom Large, and Zoom XLarge. Puzzles at all zoom levels print beautifully. For example, with the Zoom Small option, one can print a 28x36 puzzle on a single 8.5 x 11 sheet of paper.

There are 3 different difficulty levels which are identified on the Options menu as Easier, Less Difficult, and Most Difficult in order of increasing difficulty. The difficulty level of a particular puzzle is indicated in the status bar at the bottom right by E, LD, or MD respectively. The maximum number of digits per sum for each difficulty level is in the range 4-5, 5-7, or 6-9 digits respectively. After having worked many of Dell's Cross Sums puzzles and many computer-generated X-Sums 98 puzzles, my opinion is that the computer-generated puzzles are on average significantly harder than the average comparably sized puzzles in magazines. This is true even for the Easier level of X-Sums 98.

In general X-Sums 98 is much superior to working a paper puzzle with a pencil. Except for the following items, X-Sums 98 has everything a paper puzzle has and more.

  1. Most commercial pzls have either a "starter number" printed on the pzl or an across or down number outlined which can be looked up separately from the solution. Experienced solvers never use these, but some people depend on them to get started. X-Sums 98 does not identify a "starter number", but one can use the Hint button to make one's own starter number anywhere on the puzzle.
  2. At the edge of a puzzle, I frequently list numbers which must be used in a sum or numbers which will NOT appear in a sum. There is currently no facility in X-Sums 98 for doing this.


X-Sums 98 is simply an outstanding program; there is no better way to put it. The author has paid careful attention to details so that an easily discernible aura of excellence pervades the program. I strongly recommend X-Sums 98 to CrossSums lovers and to all who enjoy logic or number puzzles. I even recommend this program to those who have not tried CrossSums before, for they will quickly find them addictive. For only $20, X-Sums 98 provides an inexhaustible supply of CrossSum puzzles of varying difficulty levels and of many different sizes. This is less than the cost of a year's worth of CrossSums from commercial magazines. Moreover, these computer puzzles are always correct. I have found errors in the published Dell puzzles, but I have yet to find an error in one of Westbom's computer-generated puzzles. I believe he has used robust algorithms and has carefully implemented them, so that the generated puzzles are error-free.

CrossSums are good puzzles for children. They hone children's arithmetic skills while they are having fun solving puzzles. They help children learn to think logically and to develop persistence. I have found X-Sums 98 to be a good tool for introducing my own children to the joy of solving CrossSums. X-Sums 98 is easy to use with well-written on-line Help. My children have used Help on their own to figure out how to do things in the program.

Go to X-Sums 98 to download a demo version of this program or to order the full program. The demo version does not generate any puzzles, but it has built-in puzzles to illustrate all the features of the program. There are 2 puzzles at each of the 3 difficulty levels in each of 2 sizes (11x13 and 13x15) for a total of 12 puzzles.

Go to Sample Puzzle to see a sample Cross Sums puzzle generated by X-Sums 98. A new one is posted weekly.

Suggested Enhancements

No program is perfect, and all programs can be improved with good user feedback. Based on my use of X-Sums 98, I propose the following enhancements for future versions. These are not intended as criticisms, but simply as ideas to make an already excellent program even better. Other users who also want these enhancements should so inform the program's developer, Thomas Westbom. He is responsive to customer feedback.
  1. Editor
    Add an Edit function which would allow a player to build a puzzle. It would increase the appeal and usability of the program to implement a method by which a user could input a Cross Sum puzzle into the program. Users who get stuck on a magazine Cross Sum could input it into X-Sums 98 in order to use some of the built in solving aids (C, E, H buttons). A player can always look at the solution at the back of the magazine, but it's hard to look at just the piece one wants without seeing extra information. Moreover, the E button could show him what is incorrect without revealing the answer; H would give him a single hint where he needed it. An edit mode would also allow players to construct their own puzzles, which could be an additional selling point. There could be Edit aids analogous to the solving aids which could aid users in building their own puzzles. This could double the already not insignificant enjoyment one gets from X-Sums 98.
  2. Timer
    Add an optional timer to track how long a user takes to solve a given puzzle. This could go on the bottom status bar. The user should be able to turn it off if he does not want to "race the clock" or does not want to feel any time pressure.
  3. Multiple Players
    Add file management functions so that multiple players could use the program on the same computer and keep their work separate. Maybe set up separate player subdirectories in which their puzzles and individual statistics are automatically stored. Display the player's name in the game window.
  4. Records
    Add an optional facility to keep statistics on each player such as filename, grid size, difficulty level, time to complete.
  5. Clear All
    Add a Clear All or Erase All item to the Options menu which would clear the entire grid of all numbers. This would save having to wipe the Eraser over the entire grid.
  6. Print
    Print the filename, grid size, and difficulty level on a single line right below the puzzle.
  7. Automatic Sizing
    List some "standard" grid sizes on the Options menu (maybe 8x10, 12x12, 16x16, 20x20, 24x20), so that when one clicked on them, the program window would immediately go to that size. Currently one has to drag to a guess for the desired size. Even better would be to let the user set his own 5 "standard" grid sizes to jump to.
  8. Children
    I would like to see the Easier difficulty level made even easier for children. My experience has been that except for small grid size puzzles, the Easier level still produces puzzles that are harder than comparably sized commercial puzzles. This can be frustrating for children. I encourage the developer to see if he can adjust his algorithms to generate easier puzzles for the Easier difficulty level. I think this would greatly help sales to families who purchase the program primarily for their children's use.
  9. Cross Sums variations
    Popular published variations for experts are:
    1. CrossSum puzzles for which every number-word has exactly 1 digit which occurs exactly twice.
    2. CrossSum puzzles for which every number-word has exactly 1 zero.
    With a little bit of tweaking, I suspect the X-Sums 98 algorithms could produce these kinds of puzzles also.

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