The Jigazo puzzle - the latest new thing out of Japan - is a jigsaw puzzle with a rectangular arrangement of 300 pieces, all having the same shape, in a 15 piece wide, and 20 piece high rectangle. Each piece has the same color on it, in varying levels of intensity, and gradation. The pieces are marked with different icons. These icons make it possible for the jigsaw puzzle pieces to be individually identified, so that they can be placed in the correct position to form a picture by following the image map for the desired picture. By arranging these pieces in exactly the right way, 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 seen how a set of puzzle pieces with identical shapes but different color shading can be changed around to make different pictures - but how can it be possible that just 300 puzzle pieces could generate a picture of every person on Earth? I mean, there are close to 7,000,000,000 people on the earth - surely there's no way one puzzle can reproduce that many different pictures...can it?
Yes, Jigazo can do that - without even trying! In fact the number of unique images this jigsaw puzzle can create staggers the imagination. The total is a number so enormous that it is greater than the numbers that correspond to anything real in the entire 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, with each of those four unique pictures, we can go to the next piece on the top row, and rotate it to four different positions the same way. Once we do that, each of the four (very slightly) different pictures we created by rotating the starting piece now has four different 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".
If we follow the same process with the third piece, we will have created 4 x 4 x 4 = 64 unique pictures. Following the exponential method of showing this, we have four multiplied by itself three times, or 4^3 = 4 x 4 x 4 = 64.
Once you see the pattern, the huge question is, what number will you get when you multiply 4 times 4 times 4...., 300 times? Well, in order to show that, we have to introduce another version of an exponential number - the "powers of 10". This is perhaps familiar to you, since 10^2 = 10 x 10 = 100 = the number 1 followed by 2 zeros (2 is referred to as the "exponent"). Likewise, 10^3 = 10 x 10 x 10 = 1000 = 1 followed by three zeros - so when we are writing numbers as exponents of 10, the exponent simply tells us the number of zeros we have to write following the 1, to write out the number. Every time the exponent goes up by one, the number becomes ten times larger than it was before.
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 return to the puzzle. We now have computed that for just one layout of Jigazo puzzle pieces, by simply rotating all of the pieces to each of their four possible positions - without moving them, gives us the ability to create 10^180 different pictures...but we've only just begun! To find out how many pictures the Jigazo puzzle can produce when you start moving the pieces around, and to see a video demonstration of the Mona Lisa being transformed into Beethoven, click on the links to other puzzle sites, and to some on-line 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 seen how a set of puzzle pieces with identical shapes but different color shading can be changed around to make different pictures - but how can it be possible that just 300 puzzle pieces could generate a picture of every person on Earth? I mean, there are close to 7,000,000,000 people on the earth - surely there's no way one puzzle can reproduce that many different pictures...can it?
Yes, Jigazo can do that - without even trying! In fact the number of unique images this jigsaw puzzle can create staggers the imagination. The total is a number so enormous that it is greater than the numbers that correspond to anything real in the entire 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, with each of those four unique pictures, we can go to the next piece on the top row, and rotate it to four different positions the same way. Once we do that, each of the four (very slightly) different pictures we created by rotating the starting piece now has four different 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".
If we follow the same process with the third piece, we will have created 4 x 4 x 4 = 64 unique pictures. Following the exponential method of showing this, we have four multiplied by itself three times, or 4^3 = 4 x 4 x 4 = 64.
Once you see the pattern, the huge question is, what number will you get when you multiply 4 times 4 times 4...., 300 times? Well, in order to show that, we have to introduce another version of an exponential number - the "powers of 10". This is perhaps familiar to you, since 10^2 = 10 x 10 = 100 = the number 1 followed by 2 zeros (2 is referred to as the "exponent"). Likewise, 10^3 = 10 x 10 x 10 = 1000 = 1 followed by three zeros - so when we are writing numbers as exponents of 10, the exponent simply tells us the number of zeros we have to write following the 1, to write out the number. Every time the exponent goes up by one, the number becomes ten times larger than it was before.
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 return to the puzzle. We now have computed that for just one layout of Jigazo puzzle pieces, by simply rotating all of the pieces to each of their four possible positions - without moving them, gives us the ability to create 10^180 different pictures...but we've only just begun! To find out how many pictures the Jigazo puzzle can produce when you start moving the pieces around, and to see a video demonstration of the Mona Lisa being transformed into Beethoven, click on the links to other puzzle sites, and to some on-line puzzles as well.
About the Author:
The Jigazo Puzzle makes a great gift. You can order the Jigazo Puzzle online at: Jigazo-Puzzle.com. Watch the Mona Lisa transformation as she turns into Beethoven on the site as well. There are links to other puzzle sources. This article, Jigazo Puzzle - 300 Pieces Create Billions Of Faces has free reprint rights.
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