Option 1 The standard goal is to unscramble a picture. (For Numbers picture, solve as 1,2,3,4 first row, 5,6,7,8 second row, 9,10,11,12 third row, 13,14,15,hole fourth row.)

Click on a tile left, right, up or down from the hole. The tile clicked on plus any toward the hole will move one space toward the hole. Keep moving tiles until you unscramble the picture.

Clicking on a tile diagonally away from the hole will be ignored.

If you unscramble the picture with the hole in the lower right corner, then the last piece of the picture will show in the hole.

Option 2 For the Numbers picture, an alternative way to play is to try to reach one of the patterns shown by clicking:

Main Game Page where you can choose a different game to play.

Go to this page to see several of the 20,922,789,888,000 (16!) possible patterns for the Number puzzle.

Suggestion: When you start the Number puzzle, pick one of the patterns and work to it, then pick another and work to it. (There is no need to go back to 1234,5678,... Standard pattern. Just go from one pattern to the next pattern directly.)

You might want to doodle patterns of your own to add to these.

Option 1 When you finish a game, you can start a new game by clicking . (Can do even in the middle of a game.)

Option 2 If you time how long it takes you to solve a pattern and you want to see if you can solve that particular pattern faster, click to go back to the beginning. (Can do even in the middle of a game.)

Option 3 Enter your own pattern.

You can request an arbitrary, initial pattern.

For example, if you wanted to have several players compete in a contest. You could start them all with the same pattern by showing it and having them enter it in the edit box.

The pattern must have exactly one of each of the digits 0, 1, 2, ..., 9 and the letters A, B, C, D, E, F (upper or lower case ok).

You can use other characters such as a comma or blank to separate the pattern into blocks of 4. For example, enter 83a5,6C04,b7f2,Ed91 The program will discard the commas. They just make it easy for you to enter the characters by row. You are limited to 20 total characters for the line.

The first digit or letter tells which tile to put in the upper left corner. The next three digits or letters tell which tiles to finish out the first row.

The remaining digits and letters fill in the second, then third, then fourth row (from left to right).

Each digit or letter codes for a particular tile. 0 codes for first tile, 1 codes for second tile, 2 codes for third tile, ... 9 codes for tenth tile, A codes for eleventh tile, B codes for twelfth tile, E codes for fifteenth tile, F codes for hole.

(For those familiar with hexadecimal notation, note that the tiles are numbered from 1 to 15 while the codes are 0 to 9, A to E for tiles and F for hole.)

At any time (even in the middle of a game), you can change the picture by clicking a different one of the picture choices. (The old picture will be discarded. The new picture will appear with a new scrambling as if you had pressed the “new” button.)

An n x n magic square has all the numbers from 1 to n² such that each row, each column and each main diagonal adds up to a magic constant.

For the mathematically inclined, the magic constant is easy to determine.

If you add the rows, they will have a combined sum of n * magic constant. They will also have the sum of all the numbers.

Thus, n * magic constant = 1 + 2 + 3 + ... + n²

There is a simple formula for the sum of consecutive numbers: 1 + 2 + ... + k = k * (k+1) /2

Thus, magic constant = n * (n² + 1) / 2

For the 4x4 magic square, the formula gives a magic constant of 34.

It is trivial to convert a 4x4 magic square to a 15 puzzle pattern.

Simply subtract 1 from each number so you have numbers 0,1,2,3, ..., 15.

Call 0 the hole and you have numbers 1,2,3,4, ..., 15 plus the hole which is a 15 puzzle pattern.

Since you have subtracted 1 from each number, then you have subtracted 4 from each row so the magic constant is reduced to 30.

You can see an example on the number patterns page. Each row, column and main diagonal adds up to 30. Also the 2x2 corner squares and 2x2 center square each add up to 30.

You may have a problem with the two animations: Flower and Gravity. The parts of the picture may be out of step. One part may show the beginning of the film; another part may show the end of the film.

You can try to get the parts synchronized by doing the following:

*** When you choose Flower (or Gravity) for the first time, do not play it yet. It is downloading tiles from my website, across the internet, to your computer. This can be slow. The tiles can end up out of order.

*** When the tiles are all showing Flower pictures, choose a different picture, say, Totem. (Do not play it either.)

*** Choose Flower a second time. Now, it loads the picture from the storage area on your computer. This should be fast. All the tiles should march in order. Now, you can play the game.

You may have a problem when you win Flower (It is not a problem for Gravity.) where only the last tile (the one that covers the hole when you win) is out of step. You can try to get it in step by doing the following:

*** The hole is in the lower right corner when you win. Click on the tile immediately to the left. It will move to where the hole was. The position will no longer be a win. (So, a hole will appear where the tile you just moved started from.)

*** Click on the tile you just moved. It will be in the lower right corner. It will move left one space back to where it came from. The position will once again be a win. Special code will reload all of the tiles of the picture from your computer's storage area. Hopefully, this will get the picture back in order.