| The Jigazo puzzle - the new thing out of Japan - | | | | slightly) different pictures we created by turning |
| is a jigsaw puzzle consisting of a rectangular | | | | the first piece now has four different versions as |
| arrangement of 300 pieces, all identically shaped, in | | | | well. |
| a 15 piece wide, and 20 piece high rectangle. Each | | | | Now, you can see a pattern forming. Rotating the |
| piece has the same color on it, in varying degrees | | | | first piece, we have 4 different pictures. Rotating |
| of intensity, and gradation. The pieces are marked | | | | the second piece for each of those 4 pictures |
| with unique icons. These icons allow the pieces to | | | | creates 4 pictures as well. So, for the first 2 |
| be individually identified, so that they can be | | | | pieces, the total number of pictures is given by 4 |
| placed in the correct position to form an image by | | | | x 4 = 16. This can also be written as an |
| following the image map for the desired picture. | | | | exponential formula as: 4^2 = 4 x 4 = 16. In this |
| By arranging these pieces in just the right way, | | | | notation, 4^2 means: "the number 4 multiplied by |
| virtually any image can be recreated. | | | | itself". |
| In Japan, the word Jigazo means "self portrait". To | | | | Now, if we do this same thing with the third |
| make a self-portrait (or any other picture you | | | | piece, we will have made 4 x 4 x 4 = 64 |
| wish) with the Jigazo puzzle, just email a copy of | | | | different pictures. Following the exponential way |
| your picture (or any other picture) to the puzzle | | | | of showing this, we have four multiplied by itself |
| manufacturer, and in a few minutes, you will | | | | three times, or 4^3 = 4 x 4 x 4 = 64. |
| receive a map. This map shows where each of | | | | Now that you see the pattern, the big question is, |
| the 300 pieces must be placed, and the proper | | | | what number do you end up with when you |
| orientation of each piece, to form the completed | | | | multiply 4 times itself, 300 times? Well, in order to |
| image. There is, of course, a limit to the amount | | | | show that, we have to introduce another form of |
| of detail that the Jigazo puzzle can reproduce - | | | | exponential number - the "powers of 10". This is |
| but the fact that it works at all is incredible! | | | | perhaps familiar to you, since 10^2 = 10 x 10 = |
| Okay, so now we've identified how a set of | | | | 100 = the number 1 followed by 2 zeros (2 is |
| pieces with identical shapes but differing color | | | | called the "exponent"). Likewise, 10^3 = 10 x 10 x |
| shading can be changed around to make different | | | | 10 = 1000 = 1 followed by three zeros - so for |
| pictures - but how is it possible that just 300 | | | | exponents of 10, the exponent simply tells us |
| pieces could create a picture of anyone on Earth? | | | | how many zeros to write behind the 1, to write |
| After all, there are nearly 7,000,000,000 people | | | | out the number. Each time the exponent goes up |
| on the earth - surely one puzzle can't possibly | | | | by one, the number gets ten times larger. |
| produce that many different pictures...can it? | | | | So, back to our original question: how big a |
| Yes, it can - without even trying! In fact the | | | | number is 4^300? Well, it turns out that 4^300 is |
| number of different images this puzzle can create | | | | about equal to this number: 10^180 - or the |
| staggers the imagination. The total is a number so | | | | number 1 followed by 180 zeros! How big is that |
| large that it exceeds the numbers that | | | | number? Really BIG! Its so large, it is larger than |
| correspond to anything real in the known | | | | the number of protons in the entire known |
| Universe! | | | | universe. If you're curious about that number, its |
| Let's take a peek at how that is possible: Start | | | | approximately 1.575 x 10^79. This is known as |
| with an arbitrary arrangement of the 300 pieces | | | | The Eddington Number. Follow that link to learn |
| in the puzzle. That's picture number one. Now, | | | | more about it, and other large numbers. |
| since all pieces have identical shapes, each of | | | | But, back to our puzzle. We now see that for one |
| those 300 pieces can be placed in four different | | | | arrangement of pieces, simply rotating all of the |
| positions, by rotating it 90 degrees each time. | | | | pieces to their four different positions - without |
| Doing that with the piece at the top left corner, | | | | changing their location, gives us the ability to |
| we will have created four (ever so slightly) | | | | create 10^180 different pictures...but we've only |
| different pictures. | | | | just begun! To find out how many pictures the |
| Now, in each of those four versions of the | | | | puzzle can create when you start moving the |
| picture, we can take the next piece on the top | | | | pieces around, and to see a video demonstration |
| row, and rotate it to four different positions as | | | | of the Mona Lisa changing to Beethoven, visit the |
| well. That means that each of the four (very | | | | website link in the Resource Box. |