## The 15-Tile Puzzle

 1 2 3 x x x x 4 x x x x x x x

# ???

#### Slide the #4 tile directly below the #3 tile:

 1 2 3 x x x 4 x x x x x x x x

#### Get the empty space at the very bottom left:

 1 2 3 x x x 4 x x x x x x x x

#### Drop the entire left column down:

 2 3 x 1 x 4 x x x x x x x x x

#### Slide the #2 and #3 tiles to the left, leaving a space above the #4 tile:

 2 3 x 1 x 4 x x x x x x x x x

#### Push the #4 tile up:

 2 3 4 x 1 x x x x x x x x x x

#### Only one tile can go left. Slide that tile to the left:

 2 3 4 x 1 x x x x x x x x x x

#### Only one tile can go down. Drop that tile down:

 2 3 4 1 x x x x x x x x x x x

#### Slide the entire top row to the right:

 2 3 4 1 x x x x x x x x x x x

#### Push the entire left column up:

 1 2 3 4 x x x x x x x x x x x

#### Arrange the next three tiles (#5, #6 & #7):

 1 2 3 4 5 6 7 x x x x x x x x

#### Slide the #8 tile directly below the #7 tile:

 1 2 3 4 5 6 7 x x x 8 x x x x

#### Use the same method as before (without disturbing the top row) to get the #8 tile in place:

 1 2 3 4 5 6 7 8 x x x x x x x

#### Slide the #9 tile in place, with the empty space at the very bottom right:

 1 2 3 4 5 6 7 8 9 x x x x x x

#### If the #10 tile is below the #9 tile, then use these steps to get those tiles side-by-side:

 start right down left up left 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 5 6 7 8 5 6 7 8 5 6 7 8 5 6 7 8 5 6 7 8 5 6 7 8 9 x x x 9 x x x x x x x x x x 10 x x x 10 x x 10 x x 10 x x 9 10 x x 9 10 x x 9 x x 9 x x down right up left down left 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 5 6 7 8 5 6 7 8 5 6 7 8 5 6 7 8 5 6 7 8 5 6 7 8 x 10 x x 10 x 9 x 10 x 9 x 10 x 9 10 x 9 10 x 9 x x x 9 x x x x x x x x x x x x x x x x x

#### If the #10 tile is not below the #9 tile, then merely rotate the 5 bottom-right tiles until the two tiles are next to each other; for example:

 start right down left 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 5 6 7 8 5 6 7 8 5 6 7 8 5 6 7 8 9 x x 10 9 x x 10 9 x 10 9 x 10 x x x x x x x x x x x x x x up right down left 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 5 6 7 8 5 6 7 8 5 6 7 8 5 6 7 8 9 x 10 x 9 x 10 x 9 10 x 9 10 x x x x x x x x x x x x x x x

#### Rotate the two bottom rows counter-clockwise so that the #9 tile is below the #10 tile:

 1 2 3 4 5 6 7 8 10 x x 9 x x x

#### Rotate the 5 bottom-right tiles until the #11 tile is next to the #10 tile:

 1 2 3 4 5 6 7 8 10 11 x x 9 x x

#### Rotate the two bottom rows counter-clockwise until the #10 tile is below the #11 tile:

 1 2 3 4 5 6 7 8 11 x x x 10 9 x

#### If the #12 tile is above the #9 tile, then skip the the rest of this section. Otherwise; rotate the 3 bottom-right tiles until the #12 tile is in its place:

 1 2 3 4 5 6 7 8 11 x x 12 10 9 x

#### Get the empty space next to the #9 tile:

 1 2 3 4 5 6 7 8 11 x x 12 10 9 x

#### Rotate the 5 bottom-left tiles clockwise until the the #9, #10 & #11 tiles are arranged in place:

 1 2 3 4 5 6 7 8 9 10 11 12 x x x

#### The last row is easy. Rotate the bottom two rows counter-clockwise until the #9 tile is below the #12 tile:

 1 2 3 4 5 6 7 8 11 12 x 10 9 x x

#### Rotate the 3 bottom-right tiles until the #15 tile is next to the #12 tile:

 1 2 3 4 5 6 7 8 11 12 15 14 10 9 13

#### Rotate the bottom two rows clockwise until the third row is intact again:

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15