How To Calculate the Edge Pieces in a 1000-Piece Jigsaw Puzzle

Robotime has recently introduced a range of 1000-piece jigsaw puzzles that look like works of art when solved. However, have you ever wondered how many edge pieces are in a 1000-piece puzzle? This article will tell you how to work out the number of side pieces and why you would want to know.

Why Does It Matter How Many Edge Pieces There Are

Most people start solving a jigsaw puzzle by finding the edge and corner pieces and laying them down first so the puzzle looks like a frame. There will always be four corner pieces in a square or rectangular jigsaw puzzle, but the number of edge pieces differs with the size and shape of the puzzle. 

A Brief History of Jigsaws and Edge Pieces

Jigsaw puzzles were invented in 1767 by John Spilsbury,  a cartographer and engraver. He attached maps of the world to pieces of wood and then cut out each country. They were called ‘dissected maps’ and were intended to be used in schools.

In the late 1800s, cardboard jigsaw puzzles were introduced and were die-cut. However, puzzles didn’t take off until the Great Depression of the late 1920s and early 1930s, when people needed something inexpensive to do during times of hardship. Using hydraulic presses, jigsaw puzzles were now mass-produced. 

These days,  jigsaw puzzles are big business and a popular hobby for many people. In 2023, the jigsaw puzzle market was worth USD 897.43 million.

So let’s take a look at edge pieces. Nowadays, unless you buy a circular puzzle, jigsaw puzzles have edge pieces with straight lines, which help you solve the puzzle more quickly.

However, it wasn’t always so easy. Throughout history, puzzle makers have had innovative ideas that made the puzzles more difficult to solve. For example, they cut straight lines in the inner pieces of some puzzles, while in others, the lines of the puzzle followed the image lines. Either way, they were difficult to solve. 

Edge Pieces Vs Corner Pieces

Are corner pieces edge pieces? The jury is out on this one, as some sources say they are, others disagree. You have to decide which you agree with, as it will affect the total number of edge pieces. We will look at the different options later. 

There are four corner pieces in a rectangular or square puzzle, one for each corner. They are easy to find as they have two straight sides, while the edge pieces have just one straight side.  

How Many Edge Pieces in a 1000-Piece Jigsaw Puzzle?

1000-Piece Rectangular Puzzles

We will first look at rectangular puzzles, which are the most commonly produced. However, it is a little complicated as the length and the width don’t have the same number of end pieces. The two lengths have the same number as each other, while the two widths are the same. However, how does this work out when you are trying to find out the number of edge pieces?

When creating a rectangular puzzle, a standard design is often used, though not always. This is called the ‘golden section’. It has been used throughout history in art and architecture, and relates to the width/height ratio and what looks best to the eye. You will find that many paintings follow this rule. 

The golden section goes back as far as the Ancient Greeks in the 1st century BC. It was then decided that the ratio should be 1:1.6, so if there are 10 units on the width, there should be 16 on the length. 

As it so happens, a rectangular 1000-piece puzzle fashioned on the scale of 1:1.6 would have 40 pieces on the long sides and 25 pieces on the shorter sides. This would mean that the puzzle would have the following formula:

(2 x 40) + (2 x 25), equalling 130 end pieces.

Sounds easy, doesn’t it?  

But wait, would the puzzle really have 130 edge pieces? Haven’t we added the corner pieces twice? With this formula, each long side has been counted with 2 corner pieces, and the same goes for the short sides. You will need to take 2 corner pieces off from one of the long sides and 2 from one of the short sides.

The formula would then look like this:

(2 x no of length pieces - 2) + (2 x no of width pieces - 2) = total number of pieces

For a 1000-piece puzzle, this would be:

(2 x 40 pieces - 2) + (2 x 25 pieces - 2) =

(80 - 2) + (50 - 2) =

78 + 48 + 126 end pieces

There is another way of working out how many edge pieces are in a 1000-piece puzzle, and that is by considering that the corner pieces are not edge pieces and just counting the pieces in between them. The formula would look like this:

(40 pieces - 2) + (40 pieces - 2) + (25 pieces - 2) + (25 pieces - 2)=

38 + 38 + 23 + 23 = 122 pieces

However, we believe that the corner pieces should be added to the calculation of the number of edge pieces, as they are on the edge of the puzzle. They should not, however, be added twice. Therefore, the second formula is correct, and there are 126 edge pieces in a 1000-piece puzzle.  

Other Sizes of Jigsaw Puzzles

If we work on this principle, we can determine the number of edge pieces in different-sized puzzles. As with a 1000-piece puzzle,  the width of one side multiplied by the length of one side equals the number of pieces in the puzzle. 

Here are some calculations for different-sized puzzles.

Square Puzzles

Square puzzles aren’t very common, but you can purchase them. Therefore, it is worth looking at them. It is a little easier to work out how many edge pieces there are in a square puzzle than in a rectangular one because all the sides have the same number of pieces. 

The total number of pieces in a square puzzle is two sides multiplied. This would be the same number for a square puzzle and would be around 30 pieces each side for a 1000-piece puzzle. 

30 x 30 = 900

31 x 31 = 961

32 x 32 = 1024

You would probably either get a puzzle with 961 pieces or one with 1024, if the puzzle maker is feeling generous. Math, unfortunately, doesn’t allow you to have exactly 1000 pieces in a square jigsaw puzzle. 

So if the puzzle has 961 pieces, the formula for working out how many edge pieces there are is as follows;

(2 x 31 - 2) + (2 x 31 - 2) = 120 edge pieces

If the puzzle has 1024 pieces, the formula would be as follows:

(2 x 32 - 2) + (2 x 32 - 2) = 124 edge pieces

Summary

To summarize, a rectangular 1000-piece puzzle has 126 edge pieces while a square 1000-piece puzzle has either 120 or 124 edge pieces. Yes, it is strange that it isn’t the same number, but that’s the weird way math works. 

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