Number Slide Puzzle — Plain Tiles, No Picture

A number slide puzzle is the original form of the game: tiles labelled 1, 2, 3, … on a square grid, one empty cell, and the goal of putting them in order by sliding. Before app stores existed, before photos were sliced on the fly, the slide puzzle was a wood-and-cardboard toy with painted digits. That toy is what computer scientists, mathematicians, and puzzle-history writers mean when they say "the slide puzzle".

Why numbers, not pictures

Three reasons, going from practical to philosophical:

Numbers are unambiguous. Tile 7 is tile 7. There is no question whether it is "the one with the lighter sky" or "the one near the corner of the roof". The state of the puzzle is fully described by the position of each numbered tile. That makes the puzzle a clean mathematical object — and that is exactly why textbooks and search-algorithm papers use the numeric version.

Numbers reveal the strategy. When you place tile 1 in the top-left, then tile 2 next to it, then tile 3 — you can see the row filling. With a picture, you can see the row filling too, but only if you can recognise the picture. With numbers, the strategy is explicit. Many players prefer learning on numbers and then switching to photos once the strategy is internal.

Numbers are fast. A confident solver does a 15-tile number puzzle in 90 seconds to two minutes. The same person on a photo puzzle at the same size takes three to five — picture-recognition adds time. If you are speed-solving, you are solving numbers.

What the goal looks like

For an N×N number puzzle, the conventional goal is:

 1  2  3 ...  N
 N+1 ...      2N
 ...
            (last tile)  □

With the empty cell in the bottom-right. Some variants put the empty in the top-left and number from 0 to N²-2, but the bottom-right convention is the one Loyd used and the one most apps follow.

When to choose numbers over photos

Three honest cases for numbers:

1. Speed-solving. If you are racing the clock or trying to beat your previous time, numbers are 20–40% faster.
2. Teaching. If you are showing a child the strategy, numbers are clearer.
3. Maths-mode. If you are following along with a textbook proof, demonstrating parity, or testing an algorithm, you need numbers.

And three cases for photos:

1. Relaxation. A photo puzzle is more leisurely. You play it for the visual reveal, not the speed.
2. Variety. 300 photos give you 300 puzzles, even at one size. Numbers give you one puzzle per size.
3. Children under nine. Picture cues land faster than digit cues for younger children. (See slide puzzle for kids.)

The middle ground: numbers over photos

Most modern apps, including ours, let you toggle the numeric overlay on a photo puzzle. You see the picture tile and a small number in the corner. It's a hybrid mode — picture for orientation, number for confirmation. Good for the "I almost recognise this tile" moment, when a tiny number resolves the ambiguity.

It is also the right mode for stepping up to the 24 puzzle and the 35 puzzle, where pictures alone become demanding.

A small historical note

The first commercial slide puzzles, sold around 1880, were almost all wooden boxes with painted numerals on small square tiles. Picture versions appeared within a year — printed paper labels glued onto blank tiles — but the numeric version stayed dominant for decades. It is the version that gives the puzzle its name in many languages: taquin in French (from a numeric tin toy), Schiebefax in German, "fifteen puzzle" in English.

When you choose a number-only slide puzzle today, you are playing the same game that filled drawing rooms in 1881. That is part of the appeal — and part of why it endures.