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Jigazo Puzzle - 300 Pieces Make Billions of Faces
Each piece has the same color on it, in varying degrees of intensity, and gradation. The pieces are marked with unique icons. These icons allow the pieces to be individually identified, so that they can be placed in the correct position to form an image by following the image map for the desired picture. By arranging these pieces in just the right way, virtually any image can be recreated.
In Japan, the word Jigazo means "self portrait". To make a self-portrait (or any other picture you wish) with the Jigazo puzzle, just email a copy of your picture (or any other picture) to the puzzle manufacturer, and in a few minutes, you will receive a map. This map shows where each of the 300 pieces must be placed, and the proper orientation of each piece, to form the completed image. There is, of course, 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 set 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 pieces could create a picture of anyone on Earth? After all, there are nearly 7,000,000,000 people on the earth - surely one puzzle can't possibly produce that many different pictures...can it?
Yes, it can - without even trying! In fact the number of different images this puzzle can create staggers the imagination. The total is a number so large that it exceeds the numbers that correspond to anything real in the known Universe!
Let's take a peek at how that is possible: Start with an arbitrary arrangement of the 300 pieces in the puzzle. That's picture number one. Now, since all pieces have identical shapes, each of those 300 pieces can be placed in four different positions, 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 next piece on the top row, and rotate it to four different positions as well. That means that each of the four (very slightly) different pictures we created by turning the first piece now has four different versions as well.
Now, you can see a pattern forming. Rotating the first piece, we have 4 different pictures. Rotating the second piece for each of those 4 pictures creates 4 pictures as well. So, for the first 2 pieces, the total number of pictures is given by 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 showing this, we have four multiplied by itself three times, or 4^3 = 4 x 4 x 4 = 64.
Now that you see the pattern, the big question is, what number do you end up with when you multiply 4 times itself, 300 times? Well, in order to show that, we have to introduce another form of 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 called the "exponent"). Likewise, 10^3 = 10 x 10 x 10 = 1000 = 1 followed by three zeros - so for exponents of 10, the exponent simply tells us how many zeros to write behind the 1, to write out the number. Each time the exponent goes up by one, the number gets ten times larger.
So, back to our original question: how big a number is 4^300? Well, it turns out that 4^300 is about equal to this number: 10^180 - or the number 1 followed by 180 zeros! How big is that number? Really BIG! Its so large, it is larger than the number of protons in the entire known universe. If you're curious about that number, its approximately 1.575 x 10^79. This is known as The Eddington Number. Follow that link to learn more about it, and other large numbers.
But, back to our puzzle. We now see that for one arrangement of pieces, simply rotating all of the pieces to their four different positions - without changing their location, gives us the ability to create 10^180 different pictures...but we've only just begun! To find out how many pictures the puzzle can create when you start moving the pieces around, and to see a video demonstration of the Mona Lisa changing to Beethoven, visit the website link in the Resource Box.
The Jigazo Puzzle is now available. To learn more about it, go to Jigazo Puzzle and browse the website. A video of the transformation of the Mona Lisa into a picture of Beethoven can be found at: Jigazo Puzzle Examples. Other site pages have more detailed information, and the rest of the calculations.
About the Author
A total piece of GARBAGE poem? Comments/snickers?
Trash Day
by Koye Lott
You can toss this one to the curb
cause it reeks
It talks more trash than two birds
with four beaks
It doesn't mind if you misfire
it heat seeks
Its like a cheerleader wearing a skirt
with no pleats
Don't stick this in produce
it likes meat
Don't try to line stripe it like tar
its concrete
But it won't give you goose bumps
just the creeps
It's like a bowlegged centipede
with bad feet
Okay... I won't torture you any more.
Destined... this poem was meant as humor.
Job security
for the sanitation workers
(2/12) Battlefield I The Battle of Berlin Episode 12 (GDH)