The Jigazo puzzle - the new puzzle out of Japan - is a jigsaw puzzle that has a rectangular arrangement of 300 pieces, all identically shaped, in a rectangle 15 pieces wide, and 20 pieces high. All pieces have the same color, in varying degrees of intensity, and gradation. The pieces are marked with unique icons. These icons allow the jigsaw puzzle pieces to be individually identified, so that they can be placed in the correct position to create an image by following the image map for the desired picture. By arranging these pieces in just the right places, virtually any image can be recreated.
In Japanese, the word Jigazo means "self portrait". To make a self-portrait (or any other picture you desire) with the Jigazo puzzle, you simply email a copy of the picture (or any other picture) to the company that makes it, and in just a few minutes, you will receive a map. This map shows you where each of the 300 jigsaw puzzle pieces must be placed, and the proper orientation for each piece, to form the desired image. There is, certainly, a limit to the amount of detail that the Jigazo puzzle can reproduce - but the fact that it works at all is incredible!
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 peek at how that is possible: Begin with an arbitrary arrangement of the 300 Jigazo pieces in the puzzle. That's picture number one. Since all the pieces have identical shapes, each of those 300 pieces can be assembled into the puzzle in four different ways, by rotating it 90 degrees each time. Doing that with the piece at the top left corner, we will have created four (ever so slightly) different pictures.
Now, in each of those four versions of the picture, we can take the piece next to it on the top row, and rotate it 90 degrees three times, into four different positions as well. That means that each of the four (ever so slightly) different pictures we created by turning the first piece now has four new versions as well.
At this point you can begin to see the pattern forming. Rotating the first piece, we have 4 different pictures. Rotating the second piece for each one of those 4 pictures creates 4 pictures as well. So, for the first 2 pieces, the total number of pictures we can create is given by multiplying 4 x 4 = 16. This can also be written as an exponential formula as: 4^2 = 4 x 4 = 16. In this notation, 4^2 means: "the number 4 multiplied by itself".
Now, if we do this same thing with the third piece, we will have made 4 x 4 x 4 = 64 different pictures. Following the exponential way of expressing 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 original question: how large a number is 4^300? Well, when you calculate it, 4^300 is about equal to this number: 10^180 - or, the number 1 followed by 180 zeros! How big is that number? It's Gigantic! It's so large, it is larger than the number of protons (one of the particles in the nucleus of every atom) in the entire known universe. If you want to learn more about that number, it's approximately 1.575 x 10^79. This is known as The Eddington Number. Click on that link to learn 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.
In Japanese, the word Jigazo means "self portrait". To make a self-portrait (or any other picture you desire) with the Jigazo puzzle, you simply email a copy of the picture (or any other picture) to the company that makes it, and in just a few minutes, you will receive a map. This map shows you where each of the 300 jigsaw puzzle pieces must be placed, and the proper orientation for each piece, to form the desired image. There is, certainly, a limit to the amount of detail that the Jigazo puzzle can reproduce - but the fact that it works at all is incredible!
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 peek at how that is possible: Begin with an arbitrary arrangement of the 300 Jigazo pieces in the puzzle. That's picture number one. Since all the pieces have identical shapes, each of those 300 pieces can be assembled into the puzzle in four different ways, by rotating it 90 degrees each time. Doing that with the piece at the top left corner, we will have created four (ever so slightly) different pictures.
Now, in each of those four versions of the picture, we can take the piece next to it on the top row, and rotate it 90 degrees three times, into four different positions as well. That means that each of the four (ever so slightly) different pictures we created by turning the first piece now has four new versions as well.
At this point you can begin to see the pattern forming. Rotating the first piece, we have 4 different pictures. Rotating the second piece for each one of those 4 pictures creates 4 pictures as well. So, for the first 2 pieces, the total number of pictures we can create is given by multiplying 4 x 4 = 16. This can also be written as an exponential formula as: 4^2 = 4 x 4 = 16. In this notation, 4^2 means: "the number 4 multiplied by itself".
Now, if we do this same thing with the third piece, we will have made 4 x 4 x 4 = 64 different pictures. Following the exponential way of expressing 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 original question: how large a number is 4^300? Well, when you calculate it, 4^300 is about equal to this number: 10^180 - or, the number 1 followed by 180 zeros! How big is that number? It's Gigantic! It's so large, it is larger than the number of protons (one of the particles in the nucleus of every atom) in the entire known universe. If you want to learn more about that number, it's approximately 1.575 x 10^79. This is known as The Eddington Number. Click on that link to learn 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.
About the Author:
A Jigazo Puzzle makes a wonderful gift. You can order the Jigazo Puzzle online at: Jigazo-Puzzle.com. Watch the Mona Lisa transformation as she transforms to Beethoven on the site as well. There are links to other puzzle sources. This article, Jigazo Puzzle - 300 Pieces Create Billions Of Faces is available for free reprint.
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