The Jigazo puzzle – the latest puzzle out from Japan – is a jigsaw puzzle consisting of a rectangular arrangement of 300 pieces, all identically shaped. The pieces are arranged in a 15 piece wide, and 20 piece high rectangle. All the pieces have the same color, in varying levels of intensity, and shading. The pieces are identified by unique icons. These icons allow the jigsaw puzzle pieces to be individually identified, so that they can be placed in the proper position to form an image. This is done by following an image map for the desired picture. By placing the pieces in the right way, virtually any image can be created.
The word Jigazo in Japanese means “self portrait”. To create a self-portrait (or any other picture you want) with the Jigazo puzzle, you email a copy of your picture to the puzzle manufacturer, and in a few minutes, you will receive an icon map. This map shows where each of the 300 jigsaw puzzle pieces has to be placed, and shows the proper orientation of the pieces needed to form the completed image. There is, naturally, a limit to the amount of detail that the Jigazo puzzle can reproduce – but the fact that it works at all is remarkable!
Okay, so now we’ve identified how a group of pieces with identical shapes but differing color shading can be changed around to make different pictures – but how is it possible that just 300 puzzle pieces could create a picture of anyone on Earth? Let’s face it, there are almost 7,000,000,000 people on the earth – surely one puzzle can’t possibly create that many different pictures…can it?
Yes, Jigazo can – without even breaking a sweat! In fact the number of unique images this jigsaw puzzle can produce staggers the imagination. The total is a number so humongous that it is greater than the numbers that count anything that is real in the known Universe!
Let’s take a look at how that is possible: Start with any random arrangement of the 300 Jigazo pieces in the puzzle. That’s picture number one. Now, since each of the pieces has the identical shape, every one of those 300 pieces can be placed in four different positions, by rotating it 90 degrees each time. By rotating the piece at the top left corner, we will have created four (ever so slightly) different pictures.
Now, for each of those four versions of the picture, we can take the next piece on the top row, and rotate it to four different positions as well. When we do that, each of the four (ever so slightly) different pictures we created by turning the first piece now has four unique versions as well.
Now, you can see a pattern forming. By placing the first piece in its four different positions, we created 4 different pictures. By rotating the second piece for each of those 4 pictures, we created 4 new pictures as well. So, for the first 2 pieces, the number of pictures we created is given by 4 x 4 = 16. This can also be expressed as an exponential formula: 4^2 = 4 x 4 = 16. In this notation, as shown, 4^2 means: “the number 4 multiplied by itself”.
Now, if we repeat this process with the next (piece #3), we will have created 4 x 4 x 4 = 64 different pictures. Following the exponential way of writing this, we have four multiplied by itself three times, or 4^3 = 4 x 4 x 4 = 64.
Now that you understand the pattern, the $64 dollar question is, what number results when you multiply 4 times itself, 300 times? Well, in order to show that, we have to use another form of exponential number – the “powers of 10″. This might be familiar to you, since 10^2 = 10 x 10 = 100 = or, the number 1 followed by 2 zeros (2 is called the “exponent” of the expression). In the same manner, 10^3 = 10 x 10 x 10 = 1000 = 1 followed by three zeros – so you can see that for exponents of 10, the exponent tells us how many zeros to write behind the 1, to write out the actual number. Every time the number that is the exponent goes up by one, the number itself becomes ten times larger than it was before. So, 10^2 = 100, 100 x 10 = 10^3 = 1000, and so on.
So, back to the beginning question: just how large a number is 4^300? Well, it turns out that 4^300 is approximately equal to this number: 10^180 – or, the number 1 followed by 180 zeros! How big is that number? It’s Monstrous! It’s so large, it is larger than the number of protons (one of the elementary particles in the nucleus of every atom) in the entire known universe. If you’re wondering about that number, it’s approximately equal to 1.575 x 10^79. This is known as The Eddington Number. Click on that link to explore more about it, and other large numbers.
But, let’s get back to our Jigazo puzzle. We have now seen that for just one layout of Jigazo puzzle pieces, if we simply rotate each of the pieces to their four possible positions – without ever moving them, we can create 10^180 different pictures…but we’ve just begun! To discover how many pictures the Jigazo puzzle can create once you start moving the pieces around, and to watch a video demonstration of the Mona Lisa being transformed into Beethoven, follow the links in the resource box to other puzzle sites, and to some web-based puzzles as well.
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