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Chapter 6: Sixteen

Another sliding tile puzzle, visually similar to Fifteen (see chapter 5) but with a different type of move. This time, there is no hole: all 16 squares on the grid contain numbered squares. Your move is to shift an entire row left or right, or shift an entire column up or down; every time you do that, the tile you shift off the grid re-appears at the other end of the same row, in the space you just vacated. To win, arrange the tiles into numerical order (1,2,3,4 on the top row, 13,14,15,16 on the bottom). When you've done that, try playing on different sizes of grid.

I might have invented this game myself, though only by accident if so (and I'm sure other people have independently invented it). I thought I was imitating a screensaver I'd seen, but I have a feeling that the screensaver might actually have been a Fifteen-type puzzle rather than this slightly different kind. So this might be the one thing in my puzzle collection which represents creativity on my part rather than just engineering.

6.1 Sixteen controls

Left-clicking on an arrow will move the appropriate row or column in the direction indicated. Right-clicking will move it in the opposite direction.

Alternatively, use the cursor keys to move the position indicator around the edge of the grid, and use the return key to move the row/column in the direction indicated.

(All the actions described in section 2.1 are also available.)

6.2 Sixteen parameters

The parameters available from the ‘Custom...’ option on the ‘Type’ menu are:

• Width and Height, which are self-explanatory.
• You can ask for a limited shuffling operation to be performed on the grid. By default, Sixteen will shuffle the grid in such a way that any arrangement is about as probable as any other. You can override this by requesting a precise number of shuffling moves to be performed. Typically your aim is then to determine the precise set of shuffling moves and invert them exactly, so that you answer (say) a four-move shuffle with a four-move solution. Note that the more moves you ask for, the more likely it is that solutions shorter than the target length will turn out to be possible.