Why Do Jigsaw Puzzle Pieces Interlock?

A rounded tab on one side, a hollow blank on the other. Say “puzzle piece” and everyone pictures this shape. It is so familiar that it seems it must always have been this way, but at first it was not this shape.

Early puzzles that fell apart at a nudge of the elbow

Early puzzles of the 18th and 19th centuries mostly had pieces that did not lock together. They were cut along the borders of a map, or with straight lines and gentle curves. The pieces simply sat next to one another.

So the slightest bump to the table scattered everything. A section you had worked hard to assemble fell apart at one nudge of the elbow.

What interlocking changed

In the 20th century, as cardboard puzzles began to be stamped out in large numbers, today’s interlocking structure became the standard. On a physical puzzle, the tab is usually mushroom-shaped, with a tip wider than its neck. It doesn’t come out when the neighboring piece pushes or pulls; it separates only when lifted straight up from the board. A piece fitted once comes along when you lift its neighbor, so you can even move several pieces as a cluster.

The bigger advantage is the certainty that it is “right.” A piece that doesn’t lock is just set down, so there is no way to know whether it is really in its place. When the tabs fit snugly, that feel itself becomes the signal that you have it right. This immediate satisfaction in the hand is what keeps people at the puzzle.

The cutting method decides the shape

In the days when puzzles were cut by hand with a fretsaw, the curves differed slightly from one puzzle to the next. Because a person cut each one, they were expensive, and even with the same picture, puzzles came out with different piece shapes.

Cardboard puzzles are stamped all at once with a die, a frame fitted with blades. Once a die is made, it can stamp out the same shape endlessly, so the price comes down. On the other hand, in cheap boxed puzzles it is common for pieces of the same shape to repeat regularly. Some wooden puzzles are laser-cut. Because the laser follows curves drawn on a computer exactly, the piece shapes can be changed freely, and the cut edges sometimes show scorch marks.

How the pieces on screen are shaped

The pieces here were made on the same principle. The picture is divided into a grid of columns × rows, with one piece in each cell, and each piece gets rounded tabs and matching blanks. Unlike a physical puzzle, the necks are not pinched in. Pieces on a screen don’t stay put by catching on each other; instead, they are judged to join when brought close.

The outer edges were left flat. A piece with one flat side is an edge piece, and one with two flat sides is a corner. How many border pieces there are depends on the number of rows and columns. In a 6 × 4 grid of 24 pieces, there are 16 border pieces including the 4 corners, a full two-thirds of the total. In a 19 × 15 grid of 285 pieces, there are 64, a little over one-fifth. This is why starting from the border works so well when there are fewer pieces.

The combination that returns every four rows

There is a rule to where the tabs and blanks go, too. Horizontally, two tabs and two blanks alternate, and this order is exactly the same in every row. The same goes vertically. So pieces in the same column have the same combination of left and right shapes, and pieces in the same row have the same combination of top and bottom shapes. The same combination returns every four rows.

Knowing this, you can greatly narrow down the candidate positions from a single piece. For example, pieces with tabs on all four sides appear only where the 5th, 9th, 13th, and 17th columns meet the 5th, 9th, and 13th rows. On a 19 × 15 board of 285 pieces, there are only twelve such pieces. Put the other way around, there are at most 36 different outlines, so even as the piece count rises to 300, it is hard to pin down a single position from shape alone. Shape narrows the candidates; the picture makes the final decision.

Solve this painting as a puzzle → about 5 minutes on Easy

This rule is especially useful in a picture with few color clues, like Dawn.

There is one more thing. Because many pieces share the same shape, pieces are not joined just because their shapes fit. Only pieces that should actually be next to each other in the picture join. So if a piece snapped on, that is its place. What happens with a physical puzzle, forcing a piece in and only realizing much later that it was wrong, doesn’t happen here.

Shapes checked by eye instead of by hand

On screen, there is no need to flip pieces, and unless you turn on rotation mode, every piece starts upright. You also can’t feel scattered pieces with your hand to check their shapes. Instead, you can zoom in and compare the arrangement of tabs and blanks by eye.

When sorting pieces, checking whether a piece is an edge along with its color makes it easier to find a starting point. This is all the more true in a busy picture like The Natchez.

A shape that arose to keep pieces from scattering on the table is now used on screen as a clue to finding their places. The use has changed, but tabs and blanks still do the same job: telling you that a piece has found its place.